Abstract

Ellipsometric studies are generally carried out in the reflection mode rather than in the transmission mode, requiring invariably opaque substrates or substrates in which the backreflection is minimized or suppressed by different methods. In the present research we used a transmission and reflection photoellipsometry method to study electrochromic materials and their multilayer systems deposited on thick substrates. The role of the substrate is examined carefully, and the contributions from multiple reflections in the substrate are taken into account in the theoretical treatment. This procedure not only allows the study of thin films deposited on quasi-transparent substrates, but when carried out in conjunction with reflection measurements it greatly improves the accuracy in the determination of the optical constants. Optical measurements are carried out on an automatic reflection transmission spectroscopic ellipsometer. Solid-state ionic materials used in electrochromic systems such as indium tin oxide, tungsten oxide, and their multilayer structures deposited on glass substrates are used as examples. A software based on the above theory, optikan, was developed to model and analyze such systems. It is demonstrated that the photoellipsometry method proposed is especially suited to analyzing electrochromic materials and transmitting devices in a nondestructive way.

© 1998 Optical Society of America

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References

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  1. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).
  2. C. M. Lampert, C. G. Granqvist, eds., Large Area Chromogenics: Materials and Device for Transmittance Control, Vol. IS4 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1990).
  3. P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 47–57 (1993).
    [CrossRef]
  4. G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection transmission photoellipsometry: theory and experiments,” Appl. Opt. 34, 1684–1691 (1995).
    [CrossRef] [PubMed]
  5. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1992), p. 683.
  6. P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong, “Electrochromic materials for smart window applications,” in Optical Data Storage Technologies, S. Chua, J. C. McCallum, eds., Proc. SPIE1401, 119–129 (1990).
    [CrossRef]
  7. H. Demiryont, H. Schulz, “Stoichiometry considerations on optical and electrochromic properties of sputtered tungsten oxide films,” in Optical Materials Technologies for Energy Efficiency and Solar Energy Conversion VIII, C. G. Granqvist, C. M. Lampert, eds., Proc. SPIE1149, 28–39 (1989).
    [CrossRef]
  8. S. Badilescu, N. Minh-Ha, G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Structure and infrared spectra of sol-gel derived tungsten oxide thin films,” J. Mol. Struct. 297, 393–400 (1993).
    [CrossRef]
  9. B. W. Faughnan, R. S. Crandall, P. M. Heyman, “Electrochromism in WO3 amorphous films,” RCA Rev. 36, 177–197 (1975).
  10. H. Demiryont, “Quasi symmetric electrochromic device for light modulation,” Appl. Opt. 31, 250–254 (1992).
    [CrossRef] [PubMed]
  11. S. Badilescu, P. V. Ashrit, N. Minh-Ha, G. Bader, F. E. Girouard, Vo-Van Truong, “Study of lithium intercalation into tungsten oxide films prepared by different methods,” Thin Solid Films 250, 47–52 (1994).
    [CrossRef]
  12. F. Kanai, S. Kurita, S. Sugioka, H. Li, Y. Mita, “Optical characteristics of WO3 electrochromic cells under heavy Li ion injection,” J. Electrochem. Soc. 129, 2633–2635 (1982).
    [CrossRef]
  13. Vu Hong Fong, S. Badilescu, P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong , “Optical and electrical properties of doped indium tin oxide films prepared by a sol-gel method,” Proceedings of the Canadian Association of Physicist (CAP) Congress “CAM-95”, 11–16 June (Université Laval, Québec, Canada, 1995).
  14. T. Furusaki, J. Takahashi, K. Kodaira, “Preparation of ITO thin films by sol-gel method,” J. Ceramic Soc. Jpn. (Int. Edition) 102, 202–205 (1992).

1995 (1)

1994 (1)

S. Badilescu, P. V. Ashrit, N. Minh-Ha, G. Bader, F. E. Girouard, Vo-Van Truong, “Study of lithium intercalation into tungsten oxide films prepared by different methods,” Thin Solid Films 250, 47–52 (1994).
[CrossRef]

1993 (2)

S. Badilescu, N. Minh-Ha, G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Structure and infrared spectra of sol-gel derived tungsten oxide thin films,” J. Mol. Struct. 297, 393–400 (1993).
[CrossRef]

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 47–57 (1993).
[CrossRef]

1992 (2)

H. Demiryont, “Quasi symmetric electrochromic device for light modulation,” Appl. Opt. 31, 250–254 (1992).
[CrossRef] [PubMed]

T. Furusaki, J. Takahashi, K. Kodaira, “Preparation of ITO thin films by sol-gel method,” J. Ceramic Soc. Jpn. (Int. Edition) 102, 202–205 (1992).

1982 (1)

F. Kanai, S. Kurita, S. Sugioka, H. Li, Y. Mita, “Optical characteristics of WO3 electrochromic cells under heavy Li ion injection,” J. Electrochem. Soc. 129, 2633–2635 (1982).
[CrossRef]

1975 (1)

B. W. Faughnan, R. S. Crandall, P. M. Heyman, “Electrochromism in WO3 amorphous films,” RCA Rev. 36, 177–197 (1975).

Ashrit, P. V.

G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection transmission photoellipsometry: theory and experiments,” Appl. Opt. 34, 1684–1691 (1995).
[CrossRef] [PubMed]

S. Badilescu, P. V. Ashrit, N. Minh-Ha, G. Bader, F. E. Girouard, Vo-Van Truong, “Study of lithium intercalation into tungsten oxide films prepared by different methods,” Thin Solid Films 250, 47–52 (1994).
[CrossRef]

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 47–57 (1993).
[CrossRef]

S. Badilescu, N. Minh-Ha, G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Structure and infrared spectra of sol-gel derived tungsten oxide thin films,” J. Mol. Struct. 297, 393–400 (1993).
[CrossRef]

Vu Hong Fong, S. Badilescu, P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong , “Optical and electrical properties of doped indium tin oxide films prepared by a sol-gel method,” Proceedings of the Canadian Association of Physicist (CAP) Congress “CAM-95”, 11–16 June (Université Laval, Québec, Canada, 1995).

P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong, “Electrochromic materials for smart window applications,” in Optical Data Storage Technologies, S. Chua, J. C. McCallum, eds., Proc. SPIE1401, 119–129 (1990).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

Bader, G.

G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection transmission photoellipsometry: theory and experiments,” Appl. Opt. 34, 1684–1691 (1995).
[CrossRef] [PubMed]

S. Badilescu, P. V. Ashrit, N. Minh-Ha, G. Bader, F. E. Girouard, Vo-Van Truong, “Study of lithium intercalation into tungsten oxide films prepared by different methods,” Thin Solid Films 250, 47–52 (1994).
[CrossRef]

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 47–57 (1993).
[CrossRef]

S. Badilescu, N. Minh-Ha, G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Structure and infrared spectra of sol-gel derived tungsten oxide thin films,” J. Mol. Struct. 297, 393–400 (1993).
[CrossRef]

P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong, “Electrochromic materials for smart window applications,” in Optical Data Storage Technologies, S. Chua, J. C. McCallum, eds., Proc. SPIE1401, 119–129 (1990).
[CrossRef]

Vu Hong Fong, S. Badilescu, P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong , “Optical and electrical properties of doped indium tin oxide films prepared by a sol-gel method,” Proceedings of the Canadian Association of Physicist (CAP) Congress “CAM-95”, 11–16 June (Université Laval, Québec, Canada, 1995).

Badilescu, S.

S. Badilescu, P. V. Ashrit, N. Minh-Ha, G. Bader, F. E. Girouard, Vo-Van Truong, “Study of lithium intercalation into tungsten oxide films prepared by different methods,” Thin Solid Films 250, 47–52 (1994).
[CrossRef]

S. Badilescu, N. Minh-Ha, G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Structure and infrared spectra of sol-gel derived tungsten oxide thin films,” J. Mol. Struct. 297, 393–400 (1993).
[CrossRef]

Vu Hong Fong, S. Badilescu, P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong , “Optical and electrical properties of doped indium tin oxide films prepared by a sol-gel method,” Proceedings of the Canadian Association of Physicist (CAP) Congress “CAM-95”, 11–16 June (Université Laval, Québec, Canada, 1995).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

Benaissa, K.

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 47–57 (1993).
[CrossRef]

Crandall, R. S.

B. W. Faughnan, R. S. Crandall, P. M. Heyman, “Electrochromism in WO3 amorphous films,” RCA Rev. 36, 177–197 (1975).

Demiryont, H.

H. Demiryont, “Quasi symmetric electrochromic device for light modulation,” Appl. Opt. 31, 250–254 (1992).
[CrossRef] [PubMed]

H. Demiryont, H. Schulz, “Stoichiometry considerations on optical and electrochromic properties of sputtered tungsten oxide films,” in Optical Materials Technologies for Energy Efficiency and Solar Energy Conversion VIII, C. G. Granqvist, C. M. Lampert, eds., Proc. SPIE1149, 28–39 (1989).
[CrossRef]

Faughnan, B. W.

B. W. Faughnan, R. S. Crandall, P. M. Heyman, “Electrochromism in WO3 amorphous films,” RCA Rev. 36, 177–197 (1975).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1992), p. 683.

Fong, Vu Hong

Vu Hong Fong, S. Badilescu, P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong , “Optical and electrical properties of doped indium tin oxide films prepared by a sol-gel method,” Proceedings of the Canadian Association of Physicist (CAP) Congress “CAM-95”, 11–16 June (Université Laval, Québec, Canada, 1995).

Furusaki, T.

T. Furusaki, J. Takahashi, K. Kodaira, “Preparation of ITO thin films by sol-gel method,” J. Ceramic Soc. Jpn. (Int. Edition) 102, 202–205 (1992).

Girouard, F. E.

G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection transmission photoellipsometry: theory and experiments,” Appl. Opt. 34, 1684–1691 (1995).
[CrossRef] [PubMed]

S. Badilescu, P. V. Ashrit, N. Minh-Ha, G. Bader, F. E. Girouard, Vo-Van Truong, “Study of lithium intercalation into tungsten oxide films prepared by different methods,” Thin Solid Films 250, 47–52 (1994).
[CrossRef]

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 47–57 (1993).
[CrossRef]

S. Badilescu, N. Minh-Ha, G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Structure and infrared spectra of sol-gel derived tungsten oxide thin films,” J. Mol. Struct. 297, 393–400 (1993).
[CrossRef]

Vu Hong Fong, S. Badilescu, P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong , “Optical and electrical properties of doped indium tin oxide films prepared by a sol-gel method,” Proceedings of the Canadian Association of Physicist (CAP) Congress “CAM-95”, 11–16 June (Université Laval, Québec, Canada, 1995).

P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong, “Electrochromic materials for smart window applications,” in Optical Data Storage Technologies, S. Chua, J. C. McCallum, eds., Proc. SPIE1401, 119–129 (1990).
[CrossRef]

Heyman, P. M.

B. W. Faughnan, R. S. Crandall, P. M. Heyman, “Electrochromism in WO3 amorphous films,” RCA Rev. 36, 177–197 (1975).

Kanai, F.

F. Kanai, S. Kurita, S. Sugioka, H. Li, Y. Mita, “Optical characteristics of WO3 electrochromic cells under heavy Li ion injection,” J. Electrochem. Soc. 129, 2633–2635 (1982).
[CrossRef]

Kodaira, K.

T. Furusaki, J. Takahashi, K. Kodaira, “Preparation of ITO thin films by sol-gel method,” J. Ceramic Soc. Jpn. (Int. Edition) 102, 202–205 (1992).

Kurita, S.

F. Kanai, S. Kurita, S. Sugioka, H. Li, Y. Mita, “Optical characteristics of WO3 electrochromic cells under heavy Li ion injection,” J. Electrochem. Soc. 129, 2633–2635 (1982).
[CrossRef]

Li, H.

F. Kanai, S. Kurita, S. Sugioka, H. Li, Y. Mita, “Optical characteristics of WO3 electrochromic cells under heavy Li ion injection,” J. Electrochem. Soc. 129, 2633–2635 (1982).
[CrossRef]

Minh-Ha, N.

S. Badilescu, P. V. Ashrit, N. Minh-Ha, G. Bader, F. E. Girouard, Vo-Van Truong, “Study of lithium intercalation into tungsten oxide films prepared by different methods,” Thin Solid Films 250, 47–52 (1994).
[CrossRef]

S. Badilescu, N. Minh-Ha, G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Structure and infrared spectra of sol-gel derived tungsten oxide thin films,” J. Mol. Struct. 297, 393–400 (1993).
[CrossRef]

Mita, Y.

F. Kanai, S. Kurita, S. Sugioka, H. Li, Y. Mita, “Optical characteristics of WO3 electrochromic cells under heavy Li ion injection,” J. Electrochem. Soc. 129, 2633–2635 (1982).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1992), p. 683.

Schulz, H.

H. Demiryont, H. Schulz, “Stoichiometry considerations on optical and electrochromic properties of sputtered tungsten oxide films,” in Optical Materials Technologies for Energy Efficiency and Solar Energy Conversion VIII, C. G. Granqvist, C. M. Lampert, eds., Proc. SPIE1149, 28–39 (1989).
[CrossRef]

Sugioka, S.

F. Kanai, S. Kurita, S. Sugioka, H. Li, Y. Mita, “Optical characteristics of WO3 electrochromic cells under heavy Li ion injection,” J. Electrochem. Soc. 129, 2633–2635 (1982).
[CrossRef]

Takahashi, J.

T. Furusaki, J. Takahashi, K. Kodaira, “Preparation of ITO thin films by sol-gel method,” J. Ceramic Soc. Jpn. (Int. Edition) 102, 202–205 (1992).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1992), p. 683.

Truong, Vo-Van

G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Reflection transmission photoellipsometry: theory and experiments,” Appl. Opt. 34, 1684–1691 (1995).
[CrossRef] [PubMed]

S. Badilescu, P. V. Ashrit, N. Minh-Ha, G. Bader, F. E. Girouard, Vo-Van Truong, “Study of lithium intercalation into tungsten oxide films prepared by different methods,” Thin Solid Films 250, 47–52 (1994).
[CrossRef]

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 47–57 (1993).
[CrossRef]

S. Badilescu, N. Minh-Ha, G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Structure and infrared spectra of sol-gel derived tungsten oxide thin films,” J. Mol. Struct. 297, 393–400 (1993).
[CrossRef]

P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong, “Electrochromic materials for smart window applications,” in Optical Data Storage Technologies, S. Chua, J. C. McCallum, eds., Proc. SPIE1401, 119–129 (1990).
[CrossRef]

Vu Hong Fong, S. Badilescu, P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong , “Optical and electrical properties of doped indium tin oxide films prepared by a sol-gel method,” Proceedings of the Canadian Association of Physicist (CAP) Congress “CAM-95”, 11–16 June (Université Laval, Québec, Canada, 1995).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1992), p. 683.

Appl. Opt. (2)

J. Ceramic Soc. Jpn. (Int. Edition) (1)

T. Furusaki, J. Takahashi, K. Kodaira, “Preparation of ITO thin films by sol-gel method,” J. Ceramic Soc. Jpn. (Int. Edition) 102, 202–205 (1992).

J. Electrochem. Soc. (1)

F. Kanai, S. Kurita, S. Sugioka, H. Li, Y. Mita, “Optical characteristics of WO3 electrochromic cells under heavy Li ion injection,” J. Electrochem. Soc. 129, 2633–2635 (1982).
[CrossRef]

J. Mol. Struct. (1)

S. Badilescu, N. Minh-Ha, G. Bader, P. V. Ashrit, F. E. Girouard, Vo-Van Truong, “Structure and infrared spectra of sol-gel derived tungsten oxide thin films,” J. Mol. Struct. 297, 393–400 (1993).
[CrossRef]

RCA Rev. (1)

B. W. Faughnan, R. S. Crandall, P. M. Heyman, “Electrochromism in WO3 amorphous films,” RCA Rev. 36, 177–197 (1975).

Solid State Ion. (1)

P. V. Ashrit, K. Benaissa, G. Bader, F. E. Girouard, Vo-Van Truong, “Lithiation studies on some transition metal oxides for an all-solid thin film electrochromic system,” Solid State Ion. 59, 47–57 (1993).
[CrossRef]

Thin Solid Films (1)

S. Badilescu, P. V. Ashrit, N. Minh-Ha, G. Bader, F. E. Girouard, Vo-Van Truong, “Study of lithium intercalation into tungsten oxide films prepared by different methods,” Thin Solid Films 250, 47–52 (1994).
[CrossRef]

Other (6)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light, 2nd ed. (North-Holland, Amsterdam, 1987).

C. M. Lampert, C. G. Granqvist, eds., Large Area Chromogenics: Materials and Device for Transmittance Control, Vol. IS4 of SPIE Institute Series (SPIE Press, Bellingham, Wash., 1990).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, England, 1992), p. 683.

P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong, “Electrochromic materials for smart window applications,” in Optical Data Storage Technologies, S. Chua, J. C. McCallum, eds., Proc. SPIE1401, 119–129 (1990).
[CrossRef]

H. Demiryont, H. Schulz, “Stoichiometry considerations on optical and electrochromic properties of sputtered tungsten oxide films,” in Optical Materials Technologies for Energy Efficiency and Solar Energy Conversion VIII, C. G. Granqvist, C. M. Lampert, eds., Proc. SPIE1149, 28–39 (1989).
[CrossRef]

Vu Hong Fong, S. Badilescu, P. V. Ashrit, G. Bader, F. E. Girouard, Vo-Van Truong , “Optical and electrical properties of doped indium tin oxide films prepared by a sol-gel method,” Proceedings of the Canadian Association of Physicist (CAP) Congress “CAM-95”, 11–16 June (Université Laval, Québec, Canada, 1995).

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Figures (10)

Fig. 1
Fig. 1

Layout of the spectroscopic multiple-angle reflection transmission ellipsometer: a, filter; b, rotating polarizer; c, goniometric sample and two detector rotators; d, rotating analyzer; e, CCD spectrometric detector; f, optional compensator; and g and h, automatic translators.

Fig. 2
Fig. 2

Transmission and reflection parameters as a function of wavelength for the as-deposited WO3 film (no lithium) for an incident angle of 40°. Theoretical curves in all the cases pertaining to the single-film model are represented by filled circles and experimental points by pluses. Curves a, b, and c correspond, respectively, to Re R ps , R p , and R s . Curves d, e, and f correspond, respectively, to T s , ReT ps , and T p .

Fig. 3
Fig. 3

Optical constants n and k as functions of wavelength for the as-deposited WO3 film (no lithium) on a glass substrate.

Fig. 4
Fig. 4

Transmission and reflection parameters as functions of wavelength at 40° incidence for the WO3 film intercalated with 3.5 nm of lithium. Theoretical curves pertaining to the single-film model are represented by filled circles and experimental data by pluses. Curves a, b, and c correspond, respectively, to Re R ps , R p , and R s . Curves d, e, and f correspond, respectively, to T s , ReT ps , and T p .

Fig. 5
Fig. 5

Optical constants n and k for the WO3 film intercalated with 3.5 nm of lithium.

Fig. 6
Fig. 6

Transmission and reflection parameters as functions of wavelength for the WO3 film intercalated with 6 nm of lithium for an incident angle of 40°. Theoretical curves pertaining to the double-layer model are represented by filled circles and experimental data by pluses. Curves a, b, and c correspond, respectively, to Re R ps , R p , and R s . Curves d, e, and f correspond, respectively, to T s , ReT ps , and T p .

Fig. 7
Fig. 7

Optical constants n and k for the inner layer in the 6-nm lithium intercalated WO3 film.

Fig. 8
Fig. 8

Optical constants n and k for the outer layer in the 6-nm lithium intercalated WO3 film.

Fig. 9
Fig. 9

Transmission and reflection parameters as functions of wavelength for the ITO/SiO2/glass/SiO2/ITO film system for an incident angle of 30°. Theoretical curves pertaining to the five-layer model are represented by filled circles and experimental data by pluses. Curves a, b, and c correspond, respectively, to Re R ps , R p , and R s . Curves d, e, and f correspond, respectively, to T s , ReT ps , and T p .

Fig. 10
Fig. 10

Optical constants n and k of the ITO film.

Equations (13)

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

I R = k c R p   cos 2   θ a   cos 2   θ p + R s   sin 2   θ a   sin 2   θ p + 2   Re R ps   sin   θ a   cos   θ a   sin   θ p   cos   θ p ,
I T = k c T p   cos 2   θ a   cos 2   θ p + T s   sin 2   θ a   sin 2   θ p + 2   Re T ps   sin   θ a   cos   θ a   sin   θ p   cos   θ p ,
tan   ψ R = R p R s ,   cos   DR = Re R ps R p R s ,
tan   ψ T = T p T s ,   cos   DT = Re T ps T p T s ,
cos   Δ R = Re R ps | R ps | ,
cos   Δ T = Re T ps | T ps | .
sin   DR = Im R ps R p R s ,   sin   Δ R = Im R ps | R ps | ,
sin   DT = Im T ps T p T s ,   sin   Δ T = Im T ps | T ps | .
R s = r s r s * ,   R p = r p r p * ,   R ps = r p r s * ,
T s = t s t s * ,   T p = t p t p * ,   T ps = t p t s * ,
R p ,   R s ,   Re   R ps ,   R unpolarized ,   cos   DR ,   tan   Ψ R ,   T p ,   T s , Re   T ps ,   T unpolarized ,   cos   DT ,   tan   Ψ T .
N = 99   wavelengths × 7   angles × 12   results = 8316 .
σ 2 = 1 N photoellipsometric   quantities wavelength angles experiment - theory 2 σ experiment 2 ,

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