Abstract

Values of the transmittance T s and the phase retardation Δ were recorded in situ at two angles during the growth of thin films of tantalum oxide, titanium oxide, and zirconium oxide for deposition angles θν in the range 40°–70°. Column angles for the same films were determined ex situ from scanning electron microscopy photographs of deposition-plane fractures. We show that the experimental column angles are smaller than the corresponding values predicted by the tangent-rule equation ψ = tan-1(0.5 tan θν) and that the experimental values fit a modified form of the equation ψ = tan-1 (E 1 tan θν) where E 1 is less than 0.5. We also show that the principal refractive indices are represented well by quadratic functions of the deposition angle, for example, n 1ν) = A 0 + A 2 θν 2.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. Q. H. Wu, I. J. Hodgkinson, “Transmission-mode perpendicular incidence ellipsometry of anisotropic thin films,” J. Opt. 25, 43–49 (1994).
    [CrossRef]
  4. Q. H. Wu, I. J. Hodgkinson, “Materials for birefringent coatings,” Opt. Photon. News 5(5), S9–S10 (1994).
  5. A. Zuber, H. Jänchen, N. Kaiser, “Perpendicular-incidence photometric ellipsometry of biaxial anisotropic thin films,” Appl. Opt. 35, 5553–5556 (1996).
    [CrossRef] [PubMed]
  6. H. Wang, “Determination of optical constants of absorbing crystalline thin films from reflectance and transmittance measurements with oblique incidence,” J. Opt. Soc. Am. A 11, 2331–2337 (1994).
    [CrossRef]
  7. I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
    [CrossRef]
  8. F. Horowitz, H. A. Macleod, “Determination of principal refractive indices of birefringent films,” in Optical Interference Coatings, Vol. 6 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 203–206.
  9. E. Pelletier, F. Flory, Y. Hu, “Optical characterization of thin films by guided waves,” Appl. Opt. 28, 2918–2924 (1989).
    [CrossRef] [PubMed]
  10. F. Flory, D. Endelema, E. Pelletier, I. J. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO2 films,” Appl. Opt. 32, 5649–5659 (1993).
    [CrossRef] [PubMed]
  11. F. Horowitz, S. B. Mendes, “Envelope and waveguide methods: a comparative study of PbF2 and CeO2 birefringent films,” Appl. Opt. 33, 2659–2663 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
  13. I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313-314, 368–372 (1998).
    [CrossRef]
  14. I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “Real-time monitoring of principal refractive indices during the growth of biaxial films,” paper WR2 presented at 1997 OSA Annual Meeting (Optical Society of America, Washington, D.C., 1997).
  15. M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959).
  16. For a recent review article, see Chap. 27, “Ellipsometry,” by R. M. A. Azzam in Handbook of OpticsM. Bass , ed. (McGraw-Hill, New York, 1995), Vol. 2.
  17. W. C. Herrmann, “E-beam deposition characteristics of reactively evaporated Ta2O5 for optical interference coatings,” J. Vac. Sci. Technol. 18, 1303–1305 (1981).
    [CrossRef]
  18. H. K. Pulker, G. Paesold, E. Ritter, “Refractive indices of TiO2 films produced by reactive evaporation of various titanium-oxygen phases,” Appl. Opt. 15, 2986–2991 (1976).
    [CrossRef] [PubMed]
  19. Technical information from Patinal Newsletter, No. 3, June1994, E. Merc, Patinal-Centre, 64578 Gernsheim, Germany.
  20. R. E. Klinger, C. K. Carniglia, “Optical and crystalline inhomogeneity in evaporated zirconia films,” Appl. Opt. 24, 3184–3187 (1985).
    [CrossRef] [PubMed]
  21. T. Müller, H. K. Pulker, “Thin film morphology in TEM as revealed by heat-shock fracturing and replication of film cross sections,” in Optical Interference Coatings, F. Abèles, ed., Proc. SPIE2253, 584–595 (1994).
    [CrossRef]
  22. J. M. Nieuwenhuizen, H. B. Haanstra, “Microfractography of thin films,” Philips Tech. Rev. 27, 87–91 (1966).
  23. I. J. Hodgkinson, Q. H. Wu, A. J. McPhun, C. B. Rawle, “PS sampler–design, deposition and monitoring of anisotropic coatings,” in Annual Meeting, Vol. ILS-XIII (Optical Society of America, Washington, D.C., 1997), paper WR3.

1998 (1)

I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313-314, 368–372 (1998).
[CrossRef]

1996 (2)

H. Jänchen, D. Endelema, N. Kaiser, F. Flory, “Determination of the refractive indices of highly biaxial anisotropic coatings using guided modes,” Pure Appl. Opt. 5, 405–415 (1996).
[CrossRef]

A. Zuber, H. Jänchen, N. Kaiser, “Perpendicular-incidence photometric ellipsometry of biaxial anisotropic thin films,” Appl. Opt. 35, 5553–5556 (1996).
[CrossRef] [PubMed]

1994 (4)

1993 (1)

1989 (2)

1985 (2)

1981 (1)

W. C. Herrmann, “E-beam deposition characteristics of reactively evaporated Ta2O5 for optical interference coatings,” J. Vac. Sci. Technol. 18, 1303–1305 (1981).
[CrossRef]

1976 (2)

H. K. Pulker, G. Paesold, E. Ritter, “Refractive indices of TiO2 films produced by reactive evaporation of various titanium-oxygen phases,” Appl. Opt. 15, 2986–2991 (1976).
[CrossRef] [PubMed]

R. M. A. Azzam, “PIE: perpendicular-incidence ellipsometry–application to the determination of the optical properties of uniaxial and biaxial absorbing crystals,” Opt. Commun. 19, 122–124 (1976).
[CrossRef]

1966 (1)

J. M. Nieuwenhuizen, H. B. Haanstra, “Microfractography of thin films,” Philips Tech. Rev. 27, 87–91 (1966).

Azzam, R. M. A.

R. M. A. Azzam, “PIE: perpendicular-incidence ellipsometry–application to the determination of the optical properties of uniaxial and biaxial absorbing crystals,” Opt. Commun. 19, 122–124 (1976).
[CrossRef]

For a recent review article, see Chap. 27, “Ellipsometry,” by R. M. A. Azzam in Handbook of OpticsM. Bass , ed. (McGraw-Hill, New York, 1995), Vol. 2.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959).

Carniglia, C. K.

Endelema, D.

H. Jänchen, D. Endelema, N. Kaiser, F. Flory, “Determination of the refractive indices of highly biaxial anisotropic coatings using guided modes,” Pure Appl. Opt. 5, 405–415 (1996).
[CrossRef]

F. Flory, D. Endelema, E. Pelletier, I. J. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO2 films,” Appl. Opt. 32, 5649–5659 (1993).
[CrossRef] [PubMed]

Flory, F.

Haanstra, H. B.

J. M. Nieuwenhuizen, H. B. Haanstra, “Microfractography of thin films,” Philips Tech. Rev. 27, 87–91 (1966).

Hazel, J. C.

I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313-314, 368–372 (1998).
[CrossRef]

I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “Real-time monitoring of principal refractive indices during the growth of biaxial films,” paper WR2 presented at 1997 OSA Annual Meeting (Optical Society of America, Washington, D.C., 1997).

Herrmann, W. C.

W. C. Herrmann, “E-beam deposition characteristics of reactively evaporated Ta2O5 for optical interference coatings,” J. Vac. Sci. Technol. 18, 1303–1305 (1981).
[CrossRef]

Hodgkinson, I. J.

I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313-314, 368–372 (1998).
[CrossRef]

Q. H. Wu, I. J. Hodgkinson, “Transmission-mode perpendicular incidence ellipsometry of anisotropic thin films,” J. Opt. 25, 43–49 (1994).
[CrossRef]

Q. H. Wu, I. J. Hodgkinson, “Materials for birefringent coatings,” Opt. Photon. News 5(5), S9–S10 (1994).

F. Flory, D. Endelema, E. Pelletier, I. J. Hodgkinson, “Anisotropy in thin films: modeling and measurement of guided and nonguided optical properties: application to TiO2 films,” Appl. Opt. 32, 5649–5659 (1993).
[CrossRef] [PubMed]

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
[CrossRef]

I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “Real-time monitoring of principal refractive indices during the growth of biaxial films,” paper WR2 presented at 1997 OSA Annual Meeting (Optical Society of America, Washington, D.C., 1997).

I. J. Hodgkinson, Q. H. Wu, A. J. McPhun, C. B. Rawle, “PS sampler–design, deposition and monitoring of anisotropic coatings,” in Annual Meeting, Vol. ILS-XIII (Optical Society of America, Washington, D.C., 1997), paper WR3.

Horowitz, F.

Hu, Y.

Jänchen, H.

H. Jänchen, D. Endelema, N. Kaiser, F. Flory, “Determination of the refractive indices of highly biaxial anisotropic coatings using guided modes,” Pure Appl. Opt. 5, 405–415 (1996).
[CrossRef]

A. Zuber, H. Jänchen, N. Kaiser, “Perpendicular-incidence photometric ellipsometry of biaxial anisotropic thin films,” Appl. Opt. 35, 5553–5556 (1996).
[CrossRef] [PubMed]

Kaiser, N.

A. Zuber, H. Jänchen, N. Kaiser, “Perpendicular-incidence photometric ellipsometry of biaxial anisotropic thin films,” Appl. Opt. 35, 5553–5556 (1996).
[CrossRef] [PubMed]

H. Jänchen, D. Endelema, N. Kaiser, F. Flory, “Determination of the refractive indices of highly biaxial anisotropic coatings using guided modes,” Pure Appl. Opt. 5, 405–415 (1996).
[CrossRef]

Klinger, R. E.

Macleod, H. A.

I. J. Hodgkinson, F. Horowitz, H. A. Macleod, M. Sikkens, J. J. Wharton, “Measurement of the principal refractive indices of thin films deposited at oblique incidence,” J. Opt. Soc. Am. A 2, 1693–1697 (1985).
[CrossRef]

F. Horowitz, H. A. Macleod, “Determination of principal refractive indices of birefringent films,” in Optical Interference Coatings, Vol. 6 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 203–206.

McPhun, A. J.

I. J. Hodgkinson, Q. H. Wu, A. J. McPhun, C. B. Rawle, “PS sampler–design, deposition and monitoring of anisotropic coatings,” in Annual Meeting, Vol. ILS-XIII (Optical Society of America, Washington, D.C., 1997), paper WR3.

Mendes, S. B.

Motohiro, T.

Müller, T.

T. Müller, H. K. Pulker, “Thin film morphology in TEM as revealed by heat-shock fracturing and replication of film cross sections,” in Optical Interference Coatings, F. Abèles, ed., Proc. SPIE2253, 584–595 (1994).
[CrossRef]

Nieuwenhuizen, J. M.

J. M. Nieuwenhuizen, H. B. Haanstra, “Microfractography of thin films,” Philips Tech. Rev. 27, 87–91 (1966).

Paesold, G.

Pelletier, E.

Pulker, H. K.

H. K. Pulker, G. Paesold, E. Ritter, “Refractive indices of TiO2 films produced by reactive evaporation of various titanium-oxygen phases,” Appl. Opt. 15, 2986–2991 (1976).
[CrossRef] [PubMed]

T. Müller, H. K. Pulker, “Thin film morphology in TEM as revealed by heat-shock fracturing and replication of film cross sections,” in Optical Interference Coatings, F. Abèles, ed., Proc. SPIE2253, 584–595 (1994).
[CrossRef]

Rawle, C. B.

I. J. Hodgkinson, Q. H. Wu, A. J. McPhun, C. B. Rawle, “PS sampler–design, deposition and monitoring of anisotropic coatings,” in Annual Meeting, Vol. ILS-XIII (Optical Society of America, Washington, D.C., 1997), paper WR3.

Ritter, E.

Sikkens, M.

Taga, Y.

Wang, H.

Wharton, J. J.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959).

Wu, Q. H.

I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313-314, 368–372 (1998).
[CrossRef]

Q. H. Wu, I. J. Hodgkinson, “Transmission-mode perpendicular incidence ellipsometry of anisotropic thin films,” J. Opt. 25, 43–49 (1994).
[CrossRef]

Q. H. Wu, I. J. Hodgkinson, “Materials for birefringent coatings,” Opt. Photon. News 5(5), S9–S10 (1994).

I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “Real-time monitoring of principal refractive indices during the growth of biaxial films,” paper WR2 presented at 1997 OSA Annual Meeting (Optical Society of America, Washington, D.C., 1997).

I. J. Hodgkinson, Q. H. Wu, A. J. McPhun, C. B. Rawle, “PS sampler–design, deposition and monitoring of anisotropic coatings,” in Annual Meeting, Vol. ILS-XIII (Optical Society of America, Washington, D.C., 1997), paper WR3.

Zuber, A.

Appl. Opt. (7)

J. Opt. (1)

Q. H. Wu, I. J. Hodgkinson, “Transmission-mode perpendicular incidence ellipsometry of anisotropic thin films,” J. Opt. 25, 43–49 (1994).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. (1)

W. C. Herrmann, “E-beam deposition characteristics of reactively evaporated Ta2O5 for optical interference coatings,” J. Vac. Sci. Technol. 18, 1303–1305 (1981).
[CrossRef]

Opt. Commun. (1)

R. M. A. Azzam, “PIE: perpendicular-incidence ellipsometry–application to the determination of the optical properties of uniaxial and biaxial absorbing crystals,” Opt. Commun. 19, 122–124 (1976).
[CrossRef]

Opt. Photon. News (1)

Q. H. Wu, I. J. Hodgkinson, “Materials for birefringent coatings,” Opt. Photon. News 5(5), S9–S10 (1994).

Philips Tech. Rev. (1)

J. M. Nieuwenhuizen, H. B. Haanstra, “Microfractography of thin films,” Philips Tech. Rev. 27, 87–91 (1966).

Pure Appl. Opt. (1)

H. Jänchen, D. Endelema, N. Kaiser, F. Flory, “Determination of the refractive indices of highly biaxial anisotropic coatings using guided modes,” Pure Appl. Opt. 5, 405–415 (1996).
[CrossRef]

Thin Solid Films (1)

I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “In situ measurement of principal refractive indices of thin films by two-angle ellipsometry,” Thin Solid Films 313-314, 368–372 (1998).
[CrossRef]

Other (7)

I. J. Hodgkinson, J. C. Hazel, Q. H. Wu, “Real-time monitoring of principal refractive indices during the growth of biaxial films,” paper WR2 presented at 1997 OSA Annual Meeting (Optical Society of America, Washington, D.C., 1997).

M. Born, E. Wolf, Principles of Optics (Pergamon, London, 1959).

For a recent review article, see Chap. 27, “Ellipsometry,” by R. M. A. Azzam in Handbook of OpticsM. Bass , ed. (McGraw-Hill, New York, 1995), Vol. 2.

F. Horowitz, H. A. Macleod, “Determination of principal refractive indices of birefringent films,” in Optical Interference Coatings, Vol. 6 of 1988 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1988), pp. 203–206.

I. J. Hodgkinson, Q. H. Wu, A. J. McPhun, C. B. Rawle, “PS sampler–design, deposition and monitoring of anisotropic coatings,” in Annual Meeting, Vol. ILS-XIII (Optical Society of America, Washington, D.C., 1997), paper WR3.

T. Müller, H. K. Pulker, “Thin film morphology in TEM as revealed by heat-shock fracturing and replication of film cross sections,” in Optical Interference Coatings, F. Abèles, ed., Proc. SPIE2253, 584–595 (1994).
[CrossRef]

Technical information from Patinal Newsletter, No. 3, June1994, E. Merc, Patinal-Centre, 64578 Gernsheim, Germany.

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Figures (8)

Fig. 1
Fig. 1

Material axes 1, 2, and 3 and propagation axes x, y, and z for vacuum-deposited biaxial films. The p and the s polarizations for the two ellipsometers are parallel and perpendicular to the deposition plane, respectively, and hence are not coupled by the film.

Fig. 2
Fig. 2

Double ellipsometer used to record transmittance T s and phase retardation Δ during the growth of tilted columnar films.

Fig. 3
Fig. 3

Visualization of the process of choosing an empirical equation to relate column angle to deposition angle for titanium oxide films. The experimental values are plotted in the top right quadrant of the figure (filled triangles), and the values in the bottom left quadrant (open triangles) follow from symmetry. By inspection, a modified version of the tangent rule is found to be an appropriate empirical equation.

Fig. 4
Fig. 4

Plots of the column angle function for tilted columnar tantalum oxide, titanium oxide, and zirconium oxide. The solid curves cover the range of the experimental measurements, and the dashed curves indicate the region of extrapolation. For each of the three materials, the column angles are significantly smaller than the values predicted by the tangent rule.

Fig. 5
Fig. 5

Visualization of the process of choosing empirical equations to relate principal refractive indices to deposition angle for titanium oxide films. The experimental values are plotted in the right side of the figure, and the values in the left side follow from symmetry. The refractive-index profiles of n 2 and n 3 need to touch at θ ν = 0. In the empirical equations, each index is represented by a quadratic function of θ ν .

Fig. 6
Fig. 6

Plots of the principal refractive-index functions for tantalum oxide. The solid curves cover the range of the experimental measurements, and the dashed curves cover the range of extrapolation.

Fig. 7
Fig. 7

Plots of the principal refractive-index functions for titanium oxide. The solid curves cover the range of the experimental measurements, and the dashed curves cover the range of extrapolation.

Fig. 8
Fig. 8

Plots of the principal refractive-index functions for zirconium oxide. The solid curves cover the range of the experimental measurements, and the dashed curves cover the range of extrapolation.

Tables (2)

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Table 1 Experimental Values Recorded for Titanium Oxide Films

Tables Icon

Table 2 Constants for Refractive Index and Column Angle Functions

Equations (15)

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[ n 1 2 cos 2   ψ + n 2 2 sin 2   ψ α 2 + 2 β   cos   ψ   sin   ψ × n 1 2 - n 2 2 α + β 2 n 1 2 sin 2   ψ + n 2 2 cos 2   ψ - n 1 2 n 2 2 ] × α 2 + β 2 - n 3 2 = 0 .
Δ ¯ = 2 π α p - α s d / λ .
α s = n 3 2 - β 2 1 / 2 ,
α p = n 3 2 - β 2 1 / 2 + Δ ¯ λ / 2 π d .
α p = n 3 2 - β 2 1 / 2 + n 3 2 - β 2 1 / 2 Δ ¯ / 2 π .
β 1 = sin   θ 1 ,
β 2 = sin   θ 2 ,
α p 1 = n 3 2 - β 1 2 1 / 2 + n 3 2 - β 1 2 1 / 2 Δ ¯ λ 1 / 2 π ,
α p 2 = n 3 2 - β 2 2 1 / 2 + n 3 2 - β 1 2 1 / 2 Δ ¯ λ 2 / 2 π ,
a = - α p 1 2 - α p 2 2 cos 2   ψ   +   2 α p 1 β 1   -   α p 2 β 2 cos   ψ   sin   ψ + β 1 2 - β 2 2 sin 2   ψ α p 1 2 - α p 2 2 sin 2   ψ - 2 α p 1 β 1 - α p 2 β 2 cos   ψ   sin   ψ + β 1 2 - β 2 2 cos 2   ψ ,
n 2 = α p 1 2 cos 2 , exx   ψ + a   sin 2 ψ + 2 α P 1 β 1 1 - a cos   ψ   sin   ψ + β 1 2 a   cos 2   ψ + sin 2   ψ 1 / 2 ,
n 1 = n 2 / a 1 / 2 .
n 1 = A 0 + A 2 θ ν 2 ,
n 2 = B 0 + B 2 θ ν 2 ,
n 3 = C 0 + C 2 θ ν 2 ,

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