Abstract

The thin-film limit is derived by a nonconventional approach and equations for transmittance, reflectance and absorptance are presented in highly versatile and accurate form. In the thin-film limit the optical properties do not depend on the absorption coefficient, thickness and refractive index individually, but only on their product. We show that this formalism is applicable to the problem of ultrathin defective layer e.g. on a top of a layer of amorphous silicon. We develop a new method of direct evaluation of the surface defective layer and the bulk defects. Applying this method to amorphous silicon on glass, we show that the surface defective layer differs from bulk amorphous silicon in terms of light soaking.

© 2014 Optical Society of America

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  1. R. Brendel, “The concept of effective film thickness for the determination of bond concentrations from IR spectra of weakly absorbing thin films on silicon,” J. Appl. Phys. 69(11), 7395 (1991).
    [Crossref]
  2. Y. J. Chabal, “Surface infrared spectroscopy,” Surf. Sci. Rep. 8(5–7), 211–357 (1988).
    [Crossref]
  3. P. Drude, Lehrbuch der Optik. (Leipzig, 1900), p. 266.
  4. J. D. E. McIntyre and D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24(2), 417–434 (1971).
    [Crossref]
  5. I. K. Kim and D. E. Aspnes, “Toward nκd spectroscopy: Analytic solution of the three-phase model of polarimetry in the thin-film limit,” Appl. Phys. Lett. 88(20), 201107 (2006).
    [Crossref]
  6. A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
    [Crossref] [PubMed]
  7. J. W. Weber, A. A. Bol, and M. C. M. van de Sanden, “An improved thin film approximation to accurately determine the optical conductivity of graphene from infrared transmittance,” Appl. Phys. Lett. 105(1), 013105 (2014).
    [Crossref]
  8. J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
    [Crossref]
  9. R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
    [Crossref] [PubMed]
  10. W. Jackson and N. Amer, “Direct measurement of gap-state absorption in hydrogenated amorphous silicon by photothermal deflection spectroscopy,” Phys. Rev. B 25(8), 5559–5562 (1982).
    [Crossref]
  11. H. Curtins and M. Favre, “Surface and bulk states determined by photothermal deflection spectroscopy,” in Amorhpous Silicon and Related Materials, H. Fritzsche, ed. (World Sci. Publ. Comp 1988) pp. 329–363.
  12. M. Vaněček, M. Kočka, J. Stuchlík, and J. Tříska, “Direct measurement of the gap states and band tail absorp-tion by constant photocurrent method in amorphous silicon,” Solid State Commun. 39(11), 1199–1202 (1981).
    [Crossref]
  13. M. Vanecek and A. Poruba, “Fourier-transform photocurrent spectroscopy of microcrystalline silicon for solar cells,” Appl. Phys. Lett. 80(5), 719–721 (2002).
    [Crossref]
  14. R. C. Frye, J. J. Kumler, and C. C. Wong, “Investigation of surface passivation of amorphous silicon using photothermal deflection spectroscopy,” Appl. Phys. Lett. 50(2), 101–103 (1987).
    [Crossref]
  15. A. Asano and M. Stutzmann, “Depth profiling of nonuniform optical absorption in thin films: Application to hydrogenated amorphous silicon,” J. Appl. Phys. 70(9), 5025–5034 (1991).
    [Crossref]
  16. G. Grillo and L. Deangelis, “Surface states and in-depth inhomogeneity in a-Si:H thin films: Effects on the shape of the PDS sub-gap spectra,” J. Non-Cryst. Solids 114(2), 750–752 (1989).
    [Crossref]
  17. F. Becker, R. Carius, J.-T. Zettler, J. Klomfass, C. Walker, and H. Wagner, “Photothermal deflection spectroscopy on amorphous semiconductor heterojunctions and determination of the interface defect densities,” Mater. Sci. Forum 173–174, 177–182 (1995).
    [Crossref]
  18. J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
    [Crossref]
  19. J. Holovsky, Institute of Physics of the Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha, S. Nicolay, S. De Wolf, and C. Ballif are preparing a manuscript to be called “Effect of thin-film limit on measurable properties of graphene.”
  20. D. Ritter and K. Weiser, “Suppression of interference fringes in absorption measurements on thin films,” Opt. Commun. 57(5), 336–338 (1986).
    [Crossref]
  21. M. Vaněček, J. Kočka, A. Poruba, and A. Fejfar, “Direct measurement of the deep defect density in thin amorphous silicon films with the absolute constant photocurrent method,” J. Appl. Phys. 78(10), 6203 (1995).
    [Crossref]
  22. P. Yeh, Optical Waves in Layered Media (Wiley, 1988).
  23. N. Wyrsch, F. Finger, T. Mcmahon, and M. Vanecek, “How to reach more precise interpretation of subgap absorption spectra in terms of deep defect density in a-Si:H,” J. Non-Cryst. Solids 137–138, 347–350 (1991).
    [Crossref]

2014 (1)

J. W. Weber, A. A. Bol, and M. C. M. van de Sanden, “An improved thin film approximation to accurately determine the optical conductivity of graphene from infrared transmittance,” Appl. Phys. Lett. 105(1), 013105 (2014).
[Crossref]

2012 (1)

J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
[Crossref]

2008 (3)

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

2006 (1)

I. K. Kim and D. E. Aspnes, “Toward nκd spectroscopy: Analytic solution of the three-phase model of polarimetry in the thin-film limit,” Appl. Phys. Lett. 88(20), 201107 (2006).
[Crossref]

2002 (1)

M. Vanecek and A. Poruba, “Fourier-transform photocurrent spectroscopy of microcrystalline silicon for solar cells,” Appl. Phys. Lett. 80(5), 719–721 (2002).
[Crossref]

1995 (2)

M. Vaněček, J. Kočka, A. Poruba, and A. Fejfar, “Direct measurement of the deep defect density in thin amorphous silicon films with the absolute constant photocurrent method,” J. Appl. Phys. 78(10), 6203 (1995).
[Crossref]

F. Becker, R. Carius, J.-T. Zettler, J. Klomfass, C. Walker, and H. Wagner, “Photothermal deflection spectroscopy on amorphous semiconductor heterojunctions and determination of the interface defect densities,” Mater. Sci. Forum 173–174, 177–182 (1995).
[Crossref]

1991 (3)

N. Wyrsch, F. Finger, T. Mcmahon, and M. Vanecek, “How to reach more precise interpretation of subgap absorption spectra in terms of deep defect density in a-Si:H,” J. Non-Cryst. Solids 137–138, 347–350 (1991).
[Crossref]

A. Asano and M. Stutzmann, “Depth profiling of nonuniform optical absorption in thin films: Application to hydrogenated amorphous silicon,” J. Appl. Phys. 70(9), 5025–5034 (1991).
[Crossref]

R. Brendel, “The concept of effective film thickness for the determination of bond concentrations from IR spectra of weakly absorbing thin films on silicon,” J. Appl. Phys. 69(11), 7395 (1991).
[Crossref]

1989 (1)

G. Grillo and L. Deangelis, “Surface states and in-depth inhomogeneity in a-Si:H thin films: Effects on the shape of the PDS sub-gap spectra,” J. Non-Cryst. Solids 114(2), 750–752 (1989).
[Crossref]

1988 (1)

Y. J. Chabal, “Surface infrared spectroscopy,” Surf. Sci. Rep. 8(5–7), 211–357 (1988).
[Crossref]

1987 (1)

R. C. Frye, J. J. Kumler, and C. C. Wong, “Investigation of surface passivation of amorphous silicon using photothermal deflection spectroscopy,” Appl. Phys. Lett. 50(2), 101–103 (1987).
[Crossref]

1986 (1)

D. Ritter and K. Weiser, “Suppression of interference fringes in absorption measurements on thin films,” Opt. Commun. 57(5), 336–338 (1986).
[Crossref]

1982 (1)

W. Jackson and N. Amer, “Direct measurement of gap-state absorption in hydrogenated amorphous silicon by photothermal deflection spectroscopy,” Phys. Rev. B 25(8), 5559–5562 (1982).
[Crossref]

1981 (1)

M. Vaněček, M. Kočka, J. Stuchlík, and J. Tříska, “Direct measurement of the gap states and band tail absorp-tion by constant photocurrent method in amorphous silicon,” Solid State Commun. 39(11), 1199–1202 (1981).
[Crossref]

1971 (1)

J. D. E. McIntyre and D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24(2), 417–434 (1971).
[Crossref]

Amer, N.

W. Jackson and N. Amer, “Direct measurement of gap-state absorption in hydrogenated amorphous silicon by photothermal deflection spectroscopy,” Phys. Rev. B 25(8), 5559–5562 (1982).
[Crossref]

Asano, A.

A. Asano and M. Stutzmann, “Depth profiling of nonuniform optical absorption in thin films: Application to hydrogenated amorphous silicon,” J. Appl. Phys. 70(9), 5025–5034 (1991).
[Crossref]

Aspnes, D. E.

I. K. Kim and D. E. Aspnes, “Toward nκd spectroscopy: Analytic solution of the three-phase model of polarimetry in the thin-film limit,” Appl. Phys. Lett. 88(20), 201107 (2006).
[Crossref]

J. D. E. McIntyre and D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24(2), 417–434 (1971).
[Crossref]

Ballif, C.

J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
[Crossref]

Becker, F.

F. Becker, R. Carius, J.-T. Zettler, J. Klomfass, C. Walker, and H. Wagner, “Photothermal deflection spectroscopy on amorphous semiconductor heterojunctions and determination of the interface defect densities,” Mater. Sci. Forum 173–174, 177–182 (1995).
[Crossref]

Blake, P.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Bol, A. A.

J. W. Weber, A. A. Bol, and M. C. M. van de Sanden, “An improved thin film approximation to accurately determine the optical conductivity of graphene from infrared transmittance,” Appl. Phys. Lett. 105(1), 013105 (2014).
[Crossref]

Booth, T. J.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Brendel, R.

R. Brendel, “The concept of effective film thickness for the determination of bond concentrations from IR spectra of weakly absorbing thin films on silicon,” J. Appl. Phys. 69(11), 7395 (1991).
[Crossref]

Carbone, F.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

Carius, R.

F. Becker, R. Carius, J.-T. Zettler, J. Klomfass, C. Walker, and H. Wagner, “Photothermal deflection spectroscopy on amorphous semiconductor heterojunctions and determination of the interface defect densities,” Mater. Sci. Forum 173–174, 177–182 (1995).
[Crossref]

Chabal, Y. J.

Y. J. Chabal, “Surface infrared spectroscopy,” Surf. Sci. Rep. 8(5–7), 211–357 (1988).
[Crossref]

Chandrashekhar, M.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

Chen, Y.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

Dawlaty, J. M.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

Deangelis, L.

G. Grillo and L. Deangelis, “Surface states and in-depth inhomogeneity in a-Si:H thin films: Effects on the shape of the PDS sub-gap spectra,” J. Non-Cryst. Solids 114(2), 750–752 (1989).
[Crossref]

Despeisse, M.

J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
[Crossref]

Fejfar, A.

M. Vaněček, J. Kočka, A. Poruba, and A. Fejfar, “Direct measurement of the deep defect density in thin amorphous silicon films with the absolute constant photocurrent method,” J. Appl. Phys. 78(10), 6203 (1995).
[Crossref]

Finger, F.

N. Wyrsch, F. Finger, T. Mcmahon, and M. Vanecek, “How to reach more precise interpretation of subgap absorption spectra in terms of deep defect density in a-Si:H,” J. Non-Cryst. Solids 137–138, 347–350 (1991).
[Crossref]

Frye, R. C.

R. C. Frye, J. J. Kumler, and C. C. Wong, “Investigation of surface passivation of amorphous silicon using photothermal deflection spectroscopy,” Appl. Phys. Lett. 50(2), 101–103 (1987).
[Crossref]

Geim, A. K.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

George, P.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

Grigorenko, A. N.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Grillo, G.

G. Grillo and L. Deangelis, “Surface states and in-depth inhomogeneity in a-Si:H thin films: Effects on the shape of the PDS sub-gap spectra,” J. Non-Cryst. Solids 114(2), 750–752 (1989).
[Crossref]

Holovský, J.

J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
[Crossref]

Jackson, W.

W. Jackson and N. Amer, “Direct measurement of gap-state absorption in hydrogenated amorphous silicon by photothermal deflection spectroscopy,” Phys. Rev. B 25(8), 5559–5562 (1982).
[Crossref]

Kim, I. K.

I. K. Kim and D. E. Aspnes, “Toward nκd spectroscopy: Analytic solution of the three-phase model of polarimetry in the thin-film limit,” Appl. Phys. Lett. 88(20), 201107 (2006).
[Crossref]

Klomfass, J.

F. Becker, R. Carius, J.-T. Zettler, J. Klomfass, C. Walker, and H. Wagner, “Photothermal deflection spectroscopy on amorphous semiconductor heterojunctions and determination of the interface defect densities,” Mater. Sci. Forum 173–174, 177–182 (1995).
[Crossref]

Kocka, J.

M. Vaněček, J. Kočka, A. Poruba, and A. Fejfar, “Direct measurement of the deep defect density in thin amorphous silicon films with the absolute constant photocurrent method,” J. Appl. Phys. 78(10), 6203 (1995).
[Crossref]

Kocka, M.

M. Vaněček, M. Kočka, J. Stuchlík, and J. Tříska, “Direct measurement of the gap states and band tail absorp-tion by constant photocurrent method in amorphous silicon,” Solid State Commun. 39(11), 1199–1202 (1981).
[Crossref]

Kumler, J. J.

R. C. Frye, J. J. Kumler, and C. C. Wong, “Investigation of surface passivation of amorphous silicon using photothermal deflection spectroscopy,” Appl. Phys. Lett. 50(2), 101–103 (1987).
[Crossref]

Kuzmenko, A. B.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

McIntyre, J. D. E.

J. D. E. McIntyre and D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24(2), 417–434 (1971).
[Crossref]

Mcmahon, T.

N. Wyrsch, F. Finger, T. Mcmahon, and M. Vanecek, “How to reach more precise interpretation of subgap absorption spectra in terms of deep defect density in a-Si:H,” J. Non-Cryst. Solids 137–138, 347–350 (1991).
[Crossref]

Nair, R. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Novoselov, K. S.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Peres, N. M. R.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Poruba, A.

J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
[Crossref]

M. Vanecek and A. Poruba, “Fourier-transform photocurrent spectroscopy of microcrystalline silicon for solar cells,” Appl. Phys. Lett. 80(5), 719–721 (2002).
[Crossref]

M. Vaněček, J. Kočka, A. Poruba, and A. Fejfar, “Direct measurement of the deep defect density in thin amorphous silicon films with the absolute constant photocurrent method,” J. Appl. Phys. 78(10), 6203 (1995).
[Crossref]

Rana, F.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

Ritter, D.

D. Ritter and K. Weiser, “Suppression of interference fringes in absorption measurements on thin films,” Opt. Commun. 57(5), 336–338 (1986).
[Crossref]

Schmid, M.

J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
[Crossref]

Shivaraman, S.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

Spencer, M. G.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

Stauber, T.

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Strait, J.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

Stuchlík, J.

M. Vaněček, M. Kočka, J. Stuchlík, and J. Tříska, “Direct measurement of the gap states and band tail absorp-tion by constant photocurrent method in amorphous silicon,” Solid State Commun. 39(11), 1199–1202 (1981).
[Crossref]

Stuckelberger, M.

J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
[Crossref]

Stutzmann, M.

A. Asano and M. Stutzmann, “Depth profiling of nonuniform optical absorption in thin films: Application to hydrogenated amorphous silicon,” J. Appl. Phys. 70(9), 5025–5034 (1991).
[Crossref]

Tríska, J.

M. Vaněček, M. Kočka, J. Stuchlík, and J. Tříska, “Direct measurement of the gap states and band tail absorp-tion by constant photocurrent method in amorphous silicon,” Solid State Commun. 39(11), 1199–1202 (1981).
[Crossref]

van de Sanden, M. C. M.

J. W. Weber, A. A. Bol, and M. C. M. van de Sanden, “An improved thin film approximation to accurately determine the optical conductivity of graphene from infrared transmittance,” Appl. Phys. Lett. 105(1), 013105 (2014).
[Crossref]

van der Marel, D.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

van Heumen, E.

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

Vanecek, M.

J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
[Crossref]

M. Vanecek and A. Poruba, “Fourier-transform photocurrent spectroscopy of microcrystalline silicon for solar cells,” Appl. Phys. Lett. 80(5), 719–721 (2002).
[Crossref]

M. Vaněček, J. Kočka, A. Poruba, and A. Fejfar, “Direct measurement of the deep defect density in thin amorphous silicon films with the absolute constant photocurrent method,” J. Appl. Phys. 78(10), 6203 (1995).
[Crossref]

N. Wyrsch, F. Finger, T. Mcmahon, and M. Vanecek, “How to reach more precise interpretation of subgap absorption spectra in terms of deep defect density in a-Si:H,” J. Non-Cryst. Solids 137–138, 347–350 (1991).
[Crossref]

M. Vaněček, M. Kočka, J. Stuchlík, and J. Tříska, “Direct measurement of the gap states and band tail absorp-tion by constant photocurrent method in amorphous silicon,” Solid State Commun. 39(11), 1199–1202 (1981).
[Crossref]

Veksler, D.

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

Wagner, H.

F. Becker, R. Carius, J.-T. Zettler, J. Klomfass, C. Walker, and H. Wagner, “Photothermal deflection spectroscopy on amorphous semiconductor heterojunctions and determination of the interface defect densities,” Mater. Sci. Forum 173–174, 177–182 (1995).
[Crossref]

Walker, C.

F. Becker, R. Carius, J.-T. Zettler, J. Klomfass, C. Walker, and H. Wagner, “Photothermal deflection spectroscopy on amorphous semiconductor heterojunctions and determination of the interface defect densities,” Mater. Sci. Forum 173–174, 177–182 (1995).
[Crossref]

Weber, J. W.

J. W. Weber, A. A. Bol, and M. C. M. van de Sanden, “An improved thin film approximation to accurately determine the optical conductivity of graphene from infrared transmittance,” Appl. Phys. Lett. 105(1), 013105 (2014).
[Crossref]

Weiser, K.

D. Ritter and K. Weiser, “Suppression of interference fringes in absorption measurements on thin films,” Opt. Commun. 57(5), 336–338 (1986).
[Crossref]

Wong, C. C.

R. C. Frye, J. J. Kumler, and C. C. Wong, “Investigation of surface passivation of amorphous silicon using photothermal deflection spectroscopy,” Appl. Phys. Lett. 50(2), 101–103 (1987).
[Crossref]

Wyrsch, N.

N. Wyrsch, F. Finger, T. Mcmahon, and M. Vanecek, “How to reach more precise interpretation of subgap absorption spectra in terms of deep defect density in a-Si:H,” J. Non-Cryst. Solids 137–138, 347–350 (1991).
[Crossref]

Zettler, J.-T.

F. Becker, R. Carius, J.-T. Zettler, J. Klomfass, C. Walker, and H. Wagner, “Photothermal deflection spectroscopy on amorphous semiconductor heterojunctions and determination of the interface defect densities,” Mater. Sci. Forum 173–174, 177–182 (1995).
[Crossref]

Appl. Phys. Lett. (5)

I. K. Kim and D. E. Aspnes, “Toward nκd spectroscopy: Analytic solution of the three-phase model of polarimetry in the thin-film limit,” Appl. Phys. Lett. 88(20), 201107 (2006).
[Crossref]

J. W. Weber, A. A. Bol, and M. C. M. van de Sanden, “An improved thin film approximation to accurately determine the optical conductivity of graphene from infrared transmittance,” Appl. Phys. Lett. 105(1), 013105 (2014).
[Crossref]

J. M. Dawlaty, S. Shivaraman, J. Strait, P. George, M. Chandrashekhar, F. Rana, M. G. Spencer, D. Veksler, and Y. Chen, “Measurement of the optical absorption spectra of epitaxial graphene from terahertz to visible,” Appl. Phys. Lett. 93(13), 131905 (2008).
[Crossref]

M. Vanecek and A. Poruba, “Fourier-transform photocurrent spectroscopy of microcrystalline silicon for solar cells,” Appl. Phys. Lett. 80(5), 719–721 (2002).
[Crossref]

R. C. Frye, J. J. Kumler, and C. C. Wong, “Investigation of surface passivation of amorphous silicon using photothermal deflection spectroscopy,” Appl. Phys. Lett. 50(2), 101–103 (1987).
[Crossref]

J. Appl. Phys. (3)

A. Asano and M. Stutzmann, “Depth profiling of nonuniform optical absorption in thin films: Application to hydrogenated amorphous silicon,” J. Appl. Phys. 70(9), 5025–5034 (1991).
[Crossref]

R. Brendel, “The concept of effective film thickness for the determination of bond concentrations from IR spectra of weakly absorbing thin films on silicon,” J. Appl. Phys. 69(11), 7395 (1991).
[Crossref]

M. Vaněček, J. Kočka, A. Poruba, and A. Fejfar, “Direct measurement of the deep defect density in thin amorphous silicon films with the absolute constant photocurrent method,” J. Appl. Phys. 78(10), 6203 (1995).
[Crossref]

J. Non-Cryst. Solids (3)

N. Wyrsch, F. Finger, T. Mcmahon, and M. Vanecek, “How to reach more precise interpretation of subgap absorption spectra in terms of deep defect density in a-Si:H,” J. Non-Cryst. Solids 137–138, 347–350 (1991).
[Crossref]

G. Grillo and L. Deangelis, “Surface states and in-depth inhomogeneity in a-Si:H thin films: Effects on the shape of the PDS sub-gap spectra,” J. Non-Cryst. Solids 114(2), 750–752 (1989).
[Crossref]

J. Holovský, M. Schmid, M. Stuckelberger, M. Despeisse, C. Ballif, A. Poruba, and M. Vaněček, “Time evolution of surface defect states in hydrogenated amorphous silicon studied by photothermal and photocurrent spectroscopy and optical simulation,” J. Non-Cryst. Solids 358(17), 2035–2038 (2012).
[Crossref]

Mater. Sci. Forum (1)

F. Becker, R. Carius, J.-T. Zettler, J. Klomfass, C. Walker, and H. Wagner, “Photothermal deflection spectroscopy on amorphous semiconductor heterojunctions and determination of the interface defect densities,” Mater. Sci. Forum 173–174, 177–182 (1995).
[Crossref]

Opt. Commun. (1)

D. Ritter and K. Weiser, “Suppression of interference fringes in absorption measurements on thin films,” Opt. Commun. 57(5), 336–338 (1986).
[Crossref]

Phys. Rev. B (1)

W. Jackson and N. Amer, “Direct measurement of gap-state absorption in hydrogenated amorphous silicon by photothermal deflection spectroscopy,” Phys. Rev. B 25(8), 5559–5562 (1982).
[Crossref]

Phys. Rev. Lett. (1)

A. B. Kuzmenko, E. van Heumen, F. Carbone, and D. van der Marel, “Universal optical conductance of graphite,” Phys. Rev. Lett. 100(11), 117401 (2008).
[Crossref] [PubMed]

Science (1)

R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, “Fine structure constant defines visual transparency of graphene,” Science 320(5881), 1308 (2008).
[Crossref] [PubMed]

Solid State Commun. (1)

M. Vaněček, M. Kočka, J. Stuchlík, and J. Tříska, “Direct measurement of the gap states and band tail absorp-tion by constant photocurrent method in amorphous silicon,” Solid State Commun. 39(11), 1199–1202 (1981).
[Crossref]

Surf. Sci. (1)

J. D. E. McIntyre and D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24(2), 417–434 (1971).
[Crossref]

Surf. Sci. Rep. (1)

Y. J. Chabal, “Surface infrared spectroscopy,” Surf. Sci. Rep. 8(5–7), 211–357 (1988).
[Crossref]

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P. Drude, Lehrbuch der Optik. (Leipzig, 1900), p. 266.

H. Curtins and M. Favre, “Surface and bulk states determined by photothermal deflection spectroscopy,” in Amorhpous Silicon and Related Materials, H. Fritzsche, ed. (World Sci. Publ. Comp 1988) pp. 329–363.

J. Holovsky, Institute of Physics of the Academy of Sciences of the Czech Republic, Cukrovarnická 10, 162 00 Praha, S. Nicolay, S. De Wolf, and C. Ballif are preparing a manuscript to be called “Effect of thin-film limit on measurable properties of graphene.”

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

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Figures (3)

Fig. 1
Fig. 1 Sample of layer with surface defective layer at the top surface or at the interface with substrate.
Fig. 2
Fig. 2 Absorption in bulk material – represented by A1/T ratio, and in 3nm thick defective layer – represented by (αdn)ij, either or on surface or on glass-layer interface. Lines are directly simulated, symbols are extracted by the correction method presented here from rigorously simulated data of Atot+/T, Atot–/T (thin black lines).
Fig. 3
Fig. 3 Left part – FTPS spectra, measured from layer side and glass side, divided by transmittance, multiplied by c. Lower curves are consecutively shifted by a factor 1/10 form the one on top. Right part – surface defects in part per thousand of surface atoms and bulk defects in part per million of bulk atoms, extracted by our method.

Equations (21)

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I A I eff αd ,
I= S time = 1 2 ε 0 μ 0 | E | 2 n
A I A I 0 = | E eff | 2 αdn | E 0 | 2 n 0
1= | E eff | 2 | E 0 | 2 αdn n 0 + | E R | 2 | E 0 | 2 + | E T | 2 | E 0 | 2 n 2 n 0
E 0 + E R E eff E T
T TFL = 4 n 0 n 2 ( n 0 + n 2 +αdn ) 2
A TFL = 4αdn n 0 ( n 0 + n 2 +αdn ) 2
R TFL = ( n 0 n 2 αdn ) 2 ( n 0 + n 2 +αdn ) 2
E 01+ E 0+ ( 1+ r 012 )
E 01 E 2 t 210 ,
A 01+ | 1+ r 012 | 2 (αdn) 01 n 0
A 01 | t 210 | 2 (αdn) 01 n 2 = | t 012 | 2 n 2 n 0 2 (αdn) 01 = T 012 (αdn) 01 n 0 ,        where       T 012 = | t 012 | 2 n 2 n 0
A tot+ A 1+ + A 01+ + T 012 R 02 1 R 02 | r 210 | 2 ( A 1 + A 01 )
A tot 1 R 02 1 R 02 | r 210 | 2 ( A 1 + A 01 )
A 1+ / A 1 ( n 0 n 1 2 + n 0 n 2 2 ) / ( n 1 2 n 2 + n 0 2 n 2 ) b
b( 1 R 02 | r 210 | 2 )+ T 012 R 02 c( 1 R 02 )=0,
A tot+ c A tot A 01+ b A 01
A tot+ c A tot (αdn) 01 ( 1 n 0 | 1+ r 012 | 2 b n 2 n 0 2 | t 012 | 2 ),
A 1 A tot 1 R 02 | r 210 | 2 1 R 02 T 012 (αdn) 01 n 0
A tot + c A tot (αdn) 12 ( 1 n 0 | t 012 | 2 b n 2 | 1+ r 210 | 2 ) ,where r 210 = r 21 + r 10 e 2iβ 1 r 10 r 12 e 2iβ
A 1 A tot 1 R 02 | r 210 | 2 1 R 02 | 1+ r 210 | 2 (αdn) 12 n 2

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