Abstract

Spectroscopic reflectometry was used within 700–1600 nm wavelength range to investigate dispersion curves for In0.06Al0.94As, In0.06Al0.1Ga0.84As, and In0.06Ga0.94As layers, which constituted the purpose-made metamorphic InAlGaAs/GaAs Bragg reflector (BR). The procedure for determining the refractive index based on analyzing variations in cross-correlation coefficient obtained for reflection coefficient calculated and experimental dependences is presented. The sensitivity of the proposed method for variations in refractive index was investigated depending on the number of BR periods, the extinction coefficient of the layers of BR, and the wavelength range with respect to the main reflection maximum.

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

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References

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  6. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E Sci. Instrum. 16(12), 1214–1222 (1983).
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  7. J. C. Manifacier, J. Gasiot, and P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
    [Crossref]
  8. P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
    [Crossref]
  9. J. Humliček, F. Lukeš, K. Navrátil, M. Garriga, and K. Ploog, “Ellipsometric and reflectance studies of GaAs/AlAs superlattices,” Appl. Phys., A Mater. Sci. Process. 49(4), 407–412 (1989).
    [Crossref]
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    [Crossref]
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    [Crossref]
  13. M. Linnik and A. Christou, “Calculations of optical properties for quaternary III–V semiconductor alloys in the transparent region and above (0.2–4.0 eV),” Physica B 318(2-3), 140–161 (2002).
    [Crossref]
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    [Crossref] [PubMed]
  15. D. V. Rybalchenko, S. A. Mintairov, R. A. Salii, M. Z. Shvarts, N. K. Timoshina, and N. A. Kalyuzhnyy, “Optimization of structural and growth parameters of metamorphic InGaAs photovoltaic converters grown by MOCVD,” Semiconductors 51(1), 93–99 (2017).
    [Crossref]
  16. N. A. Kalyuzhnyy, S. A. Mintairov, A. M. Nadtochiy, V. N. Nevedomskiy, D. V. Rybalchenko, and M. Z. Shvarts, “InGaAs metamorphic laser (1064 nm) power converters with over 40% efficiency,” Electron. Lett. 53(3), 173–175 (2017).
    [Crossref]
  17. D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
    [Crossref]
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    [Crossref]
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  20. A. N. Pikhtin and A. D. Yas’kov, “Dispersion of the refractive index of semiconducting solid solutions with the main reflection maximum sphalerite structure,” Sov. Phys. Semicond. 14(4), 389–392 (1980).
  21. M. Z. Shvarts, A. E. Chalov, E. A. Ionova, V. R. Larionov, D. A. Malevskiy, V. D. Rumyantsev, and S. S. Titkov, “Indoor characterization of the multijunction III-V solar cells and concentrator modules,” in Proceedings of the 20th European Photovoltaic Solar Energy Conference and Exhibition, (Barcelona, 2005), pp. 278–281.

2017 (2)

D. V. Rybalchenko, S. A. Mintairov, R. A. Salii, M. Z. Shvarts, N. K. Timoshina, and N. A. Kalyuzhnyy, “Optimization of structural and growth parameters of metamorphic InGaAs photovoltaic converters grown by MOCVD,” Semiconductors 51(1), 93–99 (2017).
[Crossref]

N. A. Kalyuzhnyy, S. A. Mintairov, A. M. Nadtochiy, V. N. Nevedomskiy, D. V. Rybalchenko, and M. Z. Shvarts, “InGaAs metamorphic laser (1064 nm) power converters with over 40% efficiency,” Electron. Lett. 53(3), 173–175 (2017).
[Crossref]

2002 (1)

M. Linnik and A. Christou, “Calculations of optical properties for quaternary III–V semiconductor alloys in the transparent region and above (0.2–4.0 eV),” Physica B 318(2-3), 140–161 (2002).
[Crossref]

1999 (1)

E. Grassi, S. R. Johnson, M. Beaudoin, and K. S. Tsakalis, “Modeling of optical constants of InGaAs and InAlAs measured by spectroscopic ellipsometry,” J. Cryst. Growth 201–202, 1081–1084 (1999).
[Crossref]

1992 (1)

C. C. Kim, J. W. Garland, H. Abad, and P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation,” Phys. Rev. B Condens. Matter 45(20), 11749–11767 (1992).
[Crossref] [PubMed]

1989 (3)

S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlGaAs, and InGaAsP,” J. Appl. Phys. 66(12), 6030–6040 (1989).
[Crossref]

J. Humliček, F. Lukeš, K. Navrátil, M. Garriga, and K. Ploog, “Ellipsometric and reflectance studies of GaAs/AlAs superlattices,” Appl. Phys., A Mater. Sci. Process. 49(4), 407–412 (1989).
[Crossref]

A. H. M. Holtslag and P. M. Scholte, “Optical measurement of the refractive index, layer thickness, and volume changes of thin films,” Appl. Opt. 28(23), 5095–5104 (1989).
[Crossref] [PubMed]

1988 (1)

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

1986 (1)

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

1985 (1)

U. Das and P. K. Bhattacharya, “Variation of refractive index in strained InxGa1−xAs-GaAs heterostructures,” J. Appl. Phys. 58(1), 341–344 (1985).
[Crossref]

1983 (2)

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs and InSb from 1,5 to 6 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E Sci. Instrum. 16(12), 1214–1222 (1983).
[Crossref]

1980 (1)

A. N. Pikhtin and A. D. Yas’kov, “Dispersion of the refractive index of semiconducting solid solutions with the main reflection maximum sphalerite structure,” Sov. Phys. Semicond. 14(4), 389–392 (1980).

1976 (1)

J. C. Manifacier, J. Gasiot, and P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
[Crossref]

1950 (1)

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 12(5), 596–640 (1950).
[Crossref]

Abad, H.

C. C. Kim, J. W. Garland, H. Abad, and P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation,” Phys. Rev. B Condens. Matter 45(20), 11749–11767 (1992).
[Crossref] [PubMed]

Abelès, F.

F. Abelès, “Recherches sur la propagation des ondes électromagnétiques sinusoïdales dans les milieux stratifiés,” Ann. Phys. (Paris) 12(5), 596–640 (1950).
[Crossref]

Adachi, S.

S. Adachi, “Optical dispersion relations for GaP, GaAs, GaSb, InP, InAs, InSb, AlGaAs, and InGaAsP,” J. Appl. Phys. 66(12), 6030–6040 (1989).
[Crossref]

Aspnes, D. E.

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs and InSb from 1,5 to 6 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

Beaudoin, M.

E. Grassi, S. R. Johnson, M. Beaudoin, and K. S. Tsakalis, “Modeling of optical constants of InGaAs and InAlAs measured by spectroscopic ellipsometry,” J. Cryst. Growth 201–202, 1081–1084 (1999).
[Crossref]

Bhat, R.

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

Bhattacharya, P. K.

U. Das and P. K. Bhattacharya, “Variation of refractive index in strained InxGa1−xAs-GaAs heterostructures,” J. Appl. Phys. 58(1), 341–344 (1985).
[Crossref]

Chalov, A. E.

M. Z. Shvarts, A. E. Chalov, E. A. Ionova, V. R. Larionov, D. A. Malevskiy, V. D. Rumyantsev, and S. S. Titkov, “Indoor characterization of the multijunction III-V solar cells and concentrator modules,” in Proceedings of the 20th European Photovoltaic Solar Energy Conference and Exhibition, (Barcelona, 2005), pp. 278–281.

Christou, A.

M. Linnik and A. Christou, “Calculations of optical properties for quaternary III–V semiconductor alloys in the transparent region and above (0.2–4.0 eV),” Physica B 318(2-3), 140–161 (2002).
[Crossref]

Das, U.

U. Das and P. K. Bhattacharya, “Variation of refractive index in strained InxGa1−xAs-GaAs heterostructures,” J. Appl. Phys. 58(1), 341–344 (1985).
[Crossref]

De, B. N.

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

Evans, K.

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

Fillard, P.

J. C. Manifacier, J. Gasiot, and P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
[Crossref]

Garland, J. W.

C. C. Kim, J. W. Garland, H. Abad, and P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation,” Phys. Rev. B Condens. Matter 45(20), 11749–11767 (1992).
[Crossref] [PubMed]

Garriga, M.

J. Humliček, F. Lukeš, K. Navrátil, M. Garriga, and K. Ploog, “Ellipsometric and reflectance studies of GaAs/AlAs superlattices,” Appl. Phys., A Mater. Sci. Process. 49(4), 407–412 (1989).
[Crossref]

Gasiot, J.

J. C. Manifacier, J. Gasiot, and P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
[Crossref]

Grassi, E.

E. Grassi, S. R. Johnson, M. Beaudoin, and K. S. Tsakalis, “Modeling of optical constants of InGaAs and InAlAs measured by spectroscopic ellipsometry,” J. Cryst. Growth 201–202, 1081–1084 (1999).
[Crossref]

Holtslag, A. H. M.

Humlicek, J.

J. Humliček, F. Lukeš, K. Navrátil, M. Garriga, and K. Ploog, “Ellipsometric and reflectance studies of GaAs/AlAs superlattices,” Appl. Phys., A Mater. Sci. Process. 49(4), 407–412 (1989).
[Crossref]

Ionova, E. A.

M. Z. Shvarts, A. E. Chalov, E. A. Ionova, V. R. Larionov, D. A. Malevskiy, V. D. Rumyantsev, and S. S. Titkov, “Indoor characterization of the multijunction III-V solar cells and concentrator modules,” in Proceedings of the 20th European Photovoltaic Solar Energy Conference and Exhibition, (Barcelona, 2005), pp. 278–281.

Johnson, S. R.

E. Grassi, S. R. Johnson, M. Beaudoin, and K. S. Tsakalis, “Modeling of optical constants of InGaAs and InAlAs measured by spectroscopic ellipsometry,” J. Cryst. Growth 201–202, 1081–1084 (1999).
[Crossref]

Jones, R.

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

Kalyuzhnyy, N. A.

D. V. Rybalchenko, S. A. Mintairov, R. A. Salii, M. Z. Shvarts, N. K. Timoshina, and N. A. Kalyuzhnyy, “Optimization of structural and growth parameters of metamorphic InGaAs photovoltaic converters grown by MOCVD,” Semiconductors 51(1), 93–99 (2017).
[Crossref]

N. A. Kalyuzhnyy, S. A. Mintairov, A. M. Nadtochiy, V. N. Nevedomskiy, D. V. Rybalchenko, and M. Z. Shvarts, “InGaAs metamorphic laser (1064 nm) power converters with over 40% efficiency,” Electron. Lett. 53(3), 173–175 (2017).
[Crossref]

Kelso, S. M.

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

Kim, C. C.

C. C. Kim, J. W. Garland, H. Abad, and P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation,” Phys. Rev. B Condens. Matter 45(20), 11749–11767 (1992).
[Crossref] [PubMed]

Langer, D. W.

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

Larionov, V. R.

M. Z. Shvarts, A. E. Chalov, E. A. Ionova, V. R. Larionov, D. A. Malevskiy, V. D. Rumyantsev, and S. S. Titkov, “Indoor characterization of the multijunction III-V solar cells and concentrator modules,” in Proceedings of the 20th European Photovoltaic Solar Energy Conference and Exhibition, (Barcelona, 2005), pp. 278–281.

Linnik, M.

M. Linnik and A. Christou, “Calculations of optical properties for quaternary III–V semiconductor alloys in the transparent region and above (0.2–4.0 eV),” Physica B 318(2-3), 140–161 (2002).
[Crossref]

Logan, R. A.

D. E. Aspnes, S. M. Kelso, R. A. Logan, and R. Bhat, “Optical properties of AlxGa1−xAs,” J. Appl. Phys. 60(2), 754–767 (1986).
[Crossref]

Lukeš, F.

J. Humliček, F. Lukeš, K. Navrátil, M. Garriga, and K. Ploog, “Ellipsometric and reflectance studies of GaAs/AlAs superlattices,” Appl. Phys., A Mater. Sci. Process. 49(4), 407–412 (1989).
[Crossref]

Malevskiy, D. A.

M. Z. Shvarts, A. E. Chalov, E. A. Ionova, V. R. Larionov, D. A. Malevskiy, V. D. Rumyantsev, and S. S. Titkov, “Indoor characterization of the multijunction III-V solar cells and concentrator modules,” in Proceedings of the 20th European Photovoltaic Solar Energy Conference and Exhibition, (Barcelona, 2005), pp. 278–281.

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, and P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
[Crossref]

Merkel, K. G.

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

Mintairov, S. A.

D. V. Rybalchenko, S. A. Mintairov, R. A. Salii, M. Z. Shvarts, N. K. Timoshina, and N. A. Kalyuzhnyy, “Optimization of structural and growth parameters of metamorphic InGaAs photovoltaic converters grown by MOCVD,” Semiconductors 51(1), 93–99 (2017).
[Crossref]

N. A. Kalyuzhnyy, S. A. Mintairov, A. M. Nadtochiy, V. N. Nevedomskiy, D. V. Rybalchenko, and M. Z. Shvarts, “InGaAs metamorphic laser (1064 nm) power converters with over 40% efficiency,” Electron. Lett. 53(3), 173–175 (2017).
[Crossref]

Nadtochiy, A. M.

N. A. Kalyuzhnyy, S. A. Mintairov, A. M. Nadtochiy, V. N. Nevedomskiy, D. V. Rybalchenko, and M. Z. Shvarts, “InGaAs metamorphic laser (1064 nm) power converters with over 40% efficiency,” Electron. Lett. 53(3), 173–175 (2017).
[Crossref]

Navrátil, K.

J. Humliček, F. Lukeš, K. Navrátil, M. Garriga, and K. Ploog, “Ellipsometric and reflectance studies of GaAs/AlAs superlattices,” Appl. Phys., A Mater. Sci. Process. 49(4), 407–412 (1989).
[Crossref]

Nevedomskiy, V. N.

N. A. Kalyuzhnyy, S. A. Mintairov, A. M. Nadtochiy, V. N. Nevedomskiy, D. V. Rybalchenko, and M. Z. Shvarts, “InGaAs metamorphic laser (1064 nm) power converters with over 40% efficiency,” Electron. Lett. 53(3), 173–175 (2017).
[Crossref]

Pikhtin, A. N.

A. N. Pikhtin and A. D. Yas’kov, “Dispersion of the refractive index of semiconducting solid solutions with the main reflection maximum sphalerite structure,” Sov. Phys. Semicond. 14(4), 389–392 (1980).

Ploog, K.

J. Humliček, F. Lukeš, K. Navrátil, M. Garriga, and K. Ploog, “Ellipsometric and reflectance studies of GaAs/AlAs superlattices,” Appl. Phys., A Mater. Sci. Process. 49(4), 407–412 (1989).
[Crossref]

Raccah, P. M.

C. C. Kim, J. W. Garland, H. Abad, and P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of the critical-point parabolic-band approximation,” Phys. Rev. B Condens. Matter 45(20), 11749–11767 (1992).
[Crossref] [PubMed]

Rai, A. K.

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

Rumyantsev, V. D.

M. Z. Shvarts, A. E. Chalov, E. A. Ionova, V. R. Larionov, D. A. Malevskiy, V. D. Rumyantsev, and S. S. Titkov, “Indoor characterization of the multijunction III-V solar cells and concentrator modules,” in Proceedings of the 20th European Photovoltaic Solar Energy Conference and Exhibition, (Barcelona, 2005), pp. 278–281.

Rybalchenko, D. V.

D. V. Rybalchenko, S. A. Mintairov, R. A. Salii, M. Z. Shvarts, N. K. Timoshina, and N. A. Kalyuzhnyy, “Optimization of structural and growth parameters of metamorphic InGaAs photovoltaic converters grown by MOCVD,” Semiconductors 51(1), 93–99 (2017).
[Crossref]

N. A. Kalyuzhnyy, S. A. Mintairov, A. M. Nadtochiy, V. N. Nevedomskiy, D. V. Rybalchenko, and M. Z. Shvarts, “InGaAs metamorphic laser (1064 nm) power converters with over 40% efficiency,” Electron. Lett. 53(3), 173–175 (2017).
[Crossref]

Salii, R. A.

D. V. Rybalchenko, S. A. Mintairov, R. A. Salii, M. Z. Shvarts, N. K. Timoshina, and N. A. Kalyuzhnyy, “Optimization of structural and growth parameters of metamorphic InGaAs photovoltaic converters grown by MOCVD,” Semiconductors 51(1), 93–99 (2017).
[Crossref]

Scholte, P. M.

Shvarts, M. Z.

D. V. Rybalchenko, S. A. Mintairov, R. A. Salii, M. Z. Shvarts, N. K. Timoshina, and N. A. Kalyuzhnyy, “Optimization of structural and growth parameters of metamorphic InGaAs photovoltaic converters grown by MOCVD,” Semiconductors 51(1), 93–99 (2017).
[Crossref]

N. A. Kalyuzhnyy, S. A. Mintairov, A. M. Nadtochiy, V. N. Nevedomskiy, D. V. Rybalchenko, and M. Z. Shvarts, “InGaAs metamorphic laser (1064 nm) power converters with over 40% efficiency,” Electron. Lett. 53(3), 173–175 (2017).
[Crossref]

M. Z. Shvarts, A. E. Chalov, E. A. Ionova, V. R. Larionov, D. A. Malevskiy, V. D. Rumyantsev, and S. S. Titkov, “Indoor characterization of the multijunction III-V solar cells and concentrator modules,” in Proceedings of the 20th European Photovoltaic Solar Energy Conference and Exhibition, (Barcelona, 2005), pp. 278–281.

Snyder, P. G.

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

Studna, A. A.

D. E. Aspnes and A. A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs and InSb from 1,5 to 6 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

Stutz, C. E.

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

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R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E Sci. Instrum. 16(12), 1214–1222 (1983).
[Crossref]

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D. V. Rybalchenko, S. A. Mintairov, R. A. Salii, M. Z. Shvarts, N. K. Timoshina, and N. A. Kalyuzhnyy, “Optimization of structural and growth parameters of metamorphic InGaAs photovoltaic converters grown by MOCVD,” Semiconductors 51(1), 93–99 (2017).
[Crossref]

Titkov, S. S.

M. Z. Shvarts, A. E. Chalov, E. A. Ionova, V. R. Larionov, D. A. Malevskiy, V. D. Rumyantsev, and S. S. Titkov, “Indoor characterization of the multijunction III-V solar cells and concentrator modules,” in Proceedings of the 20th European Photovoltaic Solar Energy Conference and Exhibition, (Barcelona, 2005), pp. 278–281.

Tsakalis, K. S.

E. Grassi, S. R. Johnson, M. Beaudoin, and K. S. Tsakalis, “Modeling of optical constants of InGaAs and InAlAs measured by spectroscopic ellipsometry,” J. Cryst. Growth 201–202, 1081–1084 (1999).
[Crossref]

Woollam, J. A.

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

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[Crossref]

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[Crossref]

J. Cryst. Growth (1)

E. Grassi, S. R. Johnson, M. Beaudoin, and K. S. Tsakalis, “Modeling of optical constants of InGaAs and InAlAs measured by spectroscopic ellipsometry,” J. Cryst. Growth 201–202, 1081–1084 (1999).
[Crossref]

J. Phys. E Sci. Instrum. (2)

R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E Sci. Instrum. 16(12), 1214–1222 (1983).
[Crossref]

J. C. Manifacier, J. Gasiot, and P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing thin film,” J. Phys. E Sci. Instrum. 9(11), 1002–1004 (1976).
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M. Linnik and A. Christou, “Calculations of optical properties for quaternary III–V semiconductor alloys in the transparent region and above (0.2–4.0 eV),” Physica B 318(2-3), 140–161 (2002).
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Semiconductors (1)

D. V. Rybalchenko, S. A. Mintairov, R. A. Salii, M. Z. Shvarts, N. K. Timoshina, and N. A. Kalyuzhnyy, “Optimization of structural and growth parameters of metamorphic InGaAs photovoltaic converters grown by MOCVD,” Semiconductors 51(1), 93–99 (2017).
[Crossref]

Sov. Phys. Semicond. (1)

A. N. Pikhtin and A. D. Yas’kov, “Dispersion of the refractive index of semiconducting solid solutions with the main reflection maximum sphalerite structure,” Sov. Phys. Semicond. 14(4), 389–392 (1980).

Superlattices Microstruct. (1)

P. G. Snyder, B. N. De, K. G. Merkel, J. A. Woollam, D. W. Langer, C. E. Stutz, R. Jones, A. K. Rai, and K. Evans, “Measurement of superlattice optical properties by variable angle spectroscopic ellipsometry,” Superlattices Microstruct. 4(1), 97–99 (1988).
[Crossref]

Other (5)

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. 7th Edition (Cambridge University Press, 1999).

H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide (John Wiley & Sons, 1999).

M. Schubert, Infrared Ellipsometry on Semiconductor Layer Structures: Phonons, Plasmons, and Polaritons (Springer Verlag, 2005).

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, 2007).

M. Z. Shvarts, A. E. Chalov, E. A. Ionova, V. R. Larionov, D. A. Malevskiy, V. D. Rumyantsev, and S. S. Titkov, “Indoor characterization of the multijunction III-V solar cells and concentrator modules,” in Proceedings of the 20th European Photovoltaic Solar Energy Conference and Exhibition, (Barcelona, 2005), pp. 278–281.

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Figures (6)

Fig. 1
Fig. 1 (a) Structure with a BR for measuring the refractive indices n1 and n2 in the metamorphic layer materials of thicknesses d1 and d2, respectively; (b) SEM image of specimen 2 (see Table 1).
Fig. 2
Fig. 2 Simulated reflection spectrum (а) of a BR centered to 865 nm (n1 = 3.6, n2 = 3.6), and also values of autocorrelation Ψ and of cross-correlation Κ coefficients (b) for it from the analysis window half width λW at different value of deviation of the refractive index n1.
Fig. 3
Fig. 3 Dependence of the normalized contrast function βσR × 100% in the analysis window with λС = 865 nm, λW = 100 nm for a BR (n1 = 3.6, n2 = 3.0, d1 = 62 nm, d2 = 70 nm) on the value of deviation of the refractive index for materials of odd Δn1 (13) and even Δn2 (1’3′) structure layers, and also variation of in the reflection coefficient ΔR × 100% at ordinary reflectometric measurements of a single layer on the surface 4 and inside the structure 5. The number of BR periods N: 1,1' – 20; 2,2' – 12; 3,3′ – 8.
Fig. 4
Fig. 4 Dependence of the normalized contrast function βσR × 100% on the absorption coefficient of the reflector layer material k1,2 for the BR (n1 = 3.6, n2 = 3.0, d1 = 62 nm, d2 = 70 nm) with the number of periods N = 12 (1, 2, 3) and N = 20 (1', 2’, 3′). Halfwidth of the optical window at calculation λW = 100 nm, the window center position λС, nm: 1,1' – 865; 2,2' – 600; 3,3′ – 1200.
Fig. 5
Fig. 5 Calculated (14) and experimental (1’4’) dependencies of the reflection coefficient in experimental BR heterostructures. Numbers of the lines correspond to the specimens from the Table 1.
Fig. 6
Fig. 6 Dispersion curves for nano-dimensional layers in metamorphic heterostructures (1–3) and bulk materials (4–6): 1 – In0.06Ga0.94As, 2 – In0.06Al0.1Ga0.84As, 3 – In0.06Al0.94As, 4 – In0.53Ga0.47As, 5 – GaAs, 6 – AlAs. The data on the bulk materials correspond to the data of [11,17,20].

Tables (1)

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Table 1 Thicknesses of the layers in the BR structures

Equations (14)

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R max = { r +(1 r ) r j=0 N1 [ (1 r ) 2j+1 (1 r ) 2j expi φ 1 ] } 2 ,
φ 1 = 4π n 1 d 1 λ max , λ max =2( n 1 d 1 + n 2 d 2 ),
( R ^ λ )| λ= λ j = R( λ j+1 )R( λ j1 ) λ j+1 λ j1 ,j=1,2...M,
Κ( R 1 λ , R 0 λ )= λ 1 λ M R 1 λ R 0 λ g(λ)dλ j=1 M ( R ^ 1 λ R ^ 0 λ )| λ= λ j g( λ j ) λ S ,
Ψ( R 0 λ )= λ 1 λ M ( R 0 λ ) 2 g(λ)dλ j=1 N ( R ^ 0 λ ) 2 | λ= λ j g( λ j ) λ S ,
g(λ)=exp( (λ λ C ) 2 2 λ W 2 ).
| β( R 1 , R 0 ) |min:β( R 1 , R 0 )= Ψ( R 0 λ )Κ( R 1 λ , R 0 λ ) σ Κ ,
Δ ( R ^ 1 λ )| λ= λ j = R 1 ( λ j+1 ) R 1 ( λ j1 )+2Δ R 1 λ j+1 λ j1 R 1 ( λ j+1 ) R 1 ( λ j1 ) λ j+1 λ j1 = Δ R 1 λ S .
ΔΚ( R 1 λ , R 0 λ )= j=1 M [ Δ( R ^ 1 λ ) R 0 λ ]| λ= λ j g( λ j ) λ S = j=1 M ( R 0 λ )| λ= λ j g( λ j ) Δ R 1 .
σ Κ 2 = ΔK( R 1 λ , R 0 λ ) = j=1 M [ R ^ 0 λ | λ= λ j g( λ j ) ] 2 Δ R 1 + + j=1 M k=j kj M R ^ 0 λ | λ= λ j R ^ 0 λ | λ= λ k g( λ j )g( λ k ) Δ R 1j Δ R 1k .
σ Κ 2 = j=1 N [ R ^ 0 λ | λ= λ j g( λ j ) ] 2 σ R 2 .
[ n 1 (0) ( λ C j ), n 2 (0) ( λ C j ) ]: Λ 0j = Λ 1j , Λ 0j = Λ 1j , Λ 0j :max[ R 0 λ ]= R 0 λ | λ= Λ 0j , Λ 1j :max[ R 1 λ ]= R 1 λ | λ= Λ 1j , Λ 0j :min[ R 0 λ ]= R 0 λ | λ= Λ 0j , Λ 1j :min[ R 1 λ ]= R 1 λ | λ= Λ 1j , j=1,2...S,
n 1 (λ)= n 10 + γ 1 λ 2 , n 2 (λ)= n 20 + γ 2 λ 2 ,
j=1 P k=1 6 β j x k =0,x=( n 10 , n 20 , γ 1 , γ 2 , d 1 , d 2 ),

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