Abstract

TiO2 films with thicknesses (d) above 15 nm were grown on optically polished surfaces of MgO (001) substrates held at 400 °C by sputtering a Ti target with an argon-ion beam when the partial pressure of O2 was kept at 1.1 × 10-2 Pa. X-ray diffraction patterns show that TiO2 films with d < 56 nm are composed of an a-axis anatase-type structure, whereas those with d > 56 nm are composed of a mixture of phases with the c-axis parallel to the film surface. The thickness dependence of the infrared reflection–absorption spectra shows that TiO2 films with d < 56 nm are composed of both anatase and amorphous phases, whereas those with d > 56 nm are composed of anatase, rutile, and amorphous phases. The crystallinity in TiO2 films is also evaluated from the infrared reflection–absorption spectra by comparison of the observed and the calculated results determined from the dielectric function of anisotropic TiO2 bulk single crystal.

© 2002 Optical Society of America

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References

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  1. T. Aoki, K. Maki, Q. Tang, Y. Kumagai, S. Matsumoto, “Structural control of TiO2 film grown on MgO (001) substrate by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 15, 2485–2488 (1997).
    [CrossRef]
  2. P. A. Morris-Hotsenpiller, G. A. Wilson, A. Roshko, J. B. Rothman, G. S. Rohrer, “Heteroepitaxial growth of TiO2 films by ion-beam sputter deposition,” J. Cryst. Growth 166, 779–785 (1996).
    [CrossRef]
  3. R. G. Greenler, “Infrared study of adsorbed molecules on metal surfaces by reflection techniques,” J. Chem. Phys. 44, 310–315 (1966).
    [CrossRef]
  4. J. D. E. McIntyre, D. E. Aspnes, “Differential reflection spectroscopy of very thin surface films,” Surf. Sci. 24, 417–434 (1971).
    [CrossRef]
  5. W. G. Spitzer, R. C. Miller, D. A. Kleinman, L. E. Howarth, “Far infrared dielectric dispersion in BaTiO3, SrTiO3, and TiO2,” Phys. Rev. 126, 1710–1721 (1962).
    [CrossRef]
  6. R. Summitt, “Infrared absorption in single-crystal stannic oxide: optical lattice-vibration modes,” J. Appl. Phys. 39, 3762–3767 (1968).
    [CrossRef]
  7. F. Gervais, B. Piriou, “Anharmonicity in several-polar-mode crystals: adjusting phonon self-energy of LO and TO modes in Al2O3 and TiO2 to fit infrared reflectivity,” J. Phys. C 7, 2374–2385 (1974).
    [CrossRef]
  8. F. Gervais, B. Piriou, “Temperature dependence of transverse- and longitudinal-optic modes in TiO2 (rutile),” Phys. Rev. B 10, 1642–1654 (1974).
    [CrossRef]
  9. R. J. Gonzalez, R. Zallen, H. Berger, “Infrared reflectivity and lattice fundamentals in anatase TiO2,” Phys. Rev. B 55, 7014–7017 (1997).
    [CrossRef]
  10. 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]
  11. F. Matossi, “The vibration spectrum of rutile,” J. Chem. Phys. 19, 1543–1546 (1951).
    [CrossRef]
  12. D. M. Eagles, “Polar modes of lattice vibration and polaron coupling constants in rutile (TiO2),” J. Phys. Chem. Solids 25, 1243–1251 (1964).
    [CrossRef]
  13. J. Hiraishi, “Effective ionic charges of several uniaxial crystals,” Bull. Chem. Soc. Jpn. 46, 1334–1338 (1973).
    [CrossRef]
  14. E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic, London, 1991).
  15. See, for example, H. Ibach, H. Luth, Solid-State Physics (Springer-Verlag, Berlin, 1990).
  16. J. D. DeLoach, C. R. Aita, “Thickness-dependent crystallinity of sputter-deposited titania,” J. Vac. Sci. Technol. A 16, 1963–1968 (1998).
    [CrossRef]
  17. T. Kurosawa, “Polarization waves in solids,” J. Phys. Soc. Jpn. 16, 1298–1308 (1961).
    [CrossRef]
  18. T. Uchitani, K. Maki, “Change in surface roughness with the thickness of TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 18, 2706–2708 (2000).
    [CrossRef]
  19. A. Kobayashi, D. Osabe, K. Maki, “X-ray diffraction study on thickness-dependence of crystallinity in anatase-type TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” presented at the Thirteenth International Conference on Crystal Growth in conjunction with the Eleventh International Conference on Vapor Growth and Epitaxy, 30 July–4 August 2001, Doshisha University, Kyoto, Japan.

2000 (1)

T. Uchitani, K. Maki, “Change in surface roughness with the thickness of TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 18, 2706–2708 (2000).
[CrossRef]

1998 (1)

J. D. DeLoach, C. R. Aita, “Thickness-dependent crystallinity of sputter-deposited titania,” J. Vac. Sci. Technol. A 16, 1963–1968 (1998).
[CrossRef]

1997 (2)

T. Aoki, K. Maki, Q. Tang, Y. Kumagai, S. Matsumoto, “Structural control of TiO2 film grown on MgO (001) substrate by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 15, 2485–2488 (1997).
[CrossRef]

R. J. Gonzalez, R. Zallen, H. Berger, “Infrared reflectivity and lattice fundamentals in anatase TiO2,” Phys. Rev. B 55, 7014–7017 (1997).
[CrossRef]

1996 (1)

P. A. Morris-Hotsenpiller, G. A. Wilson, A. Roshko, J. B. Rothman, G. S. Rohrer, “Heteroepitaxial growth of TiO2 films by ion-beam sputter deposition,” J. Cryst. Growth 166, 779–785 (1996).
[CrossRef]

1994 (1)

1974 (2)

F. Gervais, B. Piriou, “Anharmonicity in several-polar-mode crystals: adjusting phonon self-energy of LO and TO modes in Al2O3 and TiO2 to fit infrared reflectivity,” J. Phys. C 7, 2374–2385 (1974).
[CrossRef]

F. Gervais, B. Piriou, “Temperature dependence of transverse- and longitudinal-optic modes in TiO2 (rutile),” Phys. Rev. B 10, 1642–1654 (1974).
[CrossRef]

1973 (1)

J. Hiraishi, “Effective ionic charges of several uniaxial crystals,” Bull. Chem. Soc. Jpn. 46, 1334–1338 (1973).
[CrossRef]

1971 (1)

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

1968 (1)

R. Summitt, “Infrared absorption in single-crystal stannic oxide: optical lattice-vibration modes,” J. Appl. Phys. 39, 3762–3767 (1968).
[CrossRef]

1966 (1)

R. G. Greenler, “Infrared study of adsorbed molecules on metal surfaces by reflection techniques,” J. Chem. Phys. 44, 310–315 (1966).
[CrossRef]

1964 (1)

D. M. Eagles, “Polar modes of lattice vibration and polaron coupling constants in rutile (TiO2),” J. Phys. Chem. Solids 25, 1243–1251 (1964).
[CrossRef]

1962 (1)

W. G. Spitzer, R. C. Miller, D. A. Kleinman, L. E. Howarth, “Far infrared dielectric dispersion in BaTiO3, SrTiO3, and TiO2,” Phys. Rev. 126, 1710–1721 (1962).
[CrossRef]

1961 (1)

T. Kurosawa, “Polarization waves in solids,” J. Phys. Soc. Jpn. 16, 1298–1308 (1961).
[CrossRef]

1951 (1)

F. Matossi, “The vibration spectrum of rutile,” J. Chem. Phys. 19, 1543–1546 (1951).
[CrossRef]

Aita, C. R.

J. D. DeLoach, C. R. Aita, “Thickness-dependent crystallinity of sputter-deposited titania,” J. Vac. Sci. Technol. A 16, 1963–1968 (1998).
[CrossRef]

Aoki, T.

T. Aoki, K. Maki, Q. Tang, Y. Kumagai, S. Matsumoto, “Structural control of TiO2 film grown on MgO (001) substrate by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 15, 2485–2488 (1997).
[CrossRef]

Aspnes, D. E.

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

Berger, H.

R. J. Gonzalez, R. Zallen, H. Berger, “Infrared reflectivity and lattice fundamentals in anatase TiO2,” Phys. Rev. B 55, 7014–7017 (1997).
[CrossRef]

DeLoach, J. D.

J. D. DeLoach, C. R. Aita, “Thickness-dependent crystallinity of sputter-deposited titania,” J. Vac. Sci. Technol. A 16, 1963–1968 (1998).
[CrossRef]

Eagles, D. M.

D. M. Eagles, “Polar modes of lattice vibration and polaron coupling constants in rutile (TiO2),” J. Phys. Chem. Solids 25, 1243–1251 (1964).
[CrossRef]

Gervais, F.

F. Gervais, B. Piriou, “Anharmonicity in several-polar-mode crystals: adjusting phonon self-energy of LO and TO modes in Al2O3 and TiO2 to fit infrared reflectivity,” J. Phys. C 7, 2374–2385 (1974).
[CrossRef]

F. Gervais, B. Piriou, “Temperature dependence of transverse- and longitudinal-optic modes in TiO2 (rutile),” Phys. Rev. B 10, 1642–1654 (1974).
[CrossRef]

Gonzalez, R. J.

R. J. Gonzalez, R. Zallen, H. Berger, “Infrared reflectivity and lattice fundamentals in anatase TiO2,” Phys. Rev. B 55, 7014–7017 (1997).
[CrossRef]

Greenler, R. G.

R. G. Greenler, “Infrared study of adsorbed molecules on metal surfaces by reflection techniques,” J. Chem. Phys. 44, 310–315 (1966).
[CrossRef]

Hiraishi, J.

J. Hiraishi, “Effective ionic charges of several uniaxial crystals,” Bull. Chem. Soc. Jpn. 46, 1334–1338 (1973).
[CrossRef]

Howarth, L. E.

W. G. Spitzer, R. C. Miller, D. A. Kleinman, L. E. Howarth, “Far infrared dielectric dispersion in BaTiO3, SrTiO3, and TiO2,” Phys. Rev. 126, 1710–1721 (1962).
[CrossRef]

Ibach, H.

See, for example, H. Ibach, H. Luth, Solid-State Physics (Springer-Verlag, Berlin, 1990).

Kleinman, D. A.

W. G. Spitzer, R. C. Miller, D. A. Kleinman, L. E. Howarth, “Far infrared dielectric dispersion in BaTiO3, SrTiO3, and TiO2,” Phys. Rev. 126, 1710–1721 (1962).
[CrossRef]

Kobayashi, A.

A. Kobayashi, D. Osabe, K. Maki, “X-ray diffraction study on thickness-dependence of crystallinity in anatase-type TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” presented at the Thirteenth International Conference on Crystal Growth in conjunction with the Eleventh International Conference on Vapor Growth and Epitaxy, 30 July–4 August 2001, Doshisha University, Kyoto, Japan.

Kumagai, Y.

T. Aoki, K. Maki, Q. Tang, Y. Kumagai, S. Matsumoto, “Structural control of TiO2 film grown on MgO (001) substrate by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 15, 2485–2488 (1997).
[CrossRef]

Kurosawa, T.

T. Kurosawa, “Polarization waves in solids,” J. Phys. Soc. Jpn. 16, 1298–1308 (1961).
[CrossRef]

Luth, H.

See, for example, H. Ibach, H. Luth, Solid-State Physics (Springer-Verlag, Berlin, 1990).

Maki, K.

T. Uchitani, K. Maki, “Change in surface roughness with the thickness of TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 18, 2706–2708 (2000).
[CrossRef]

T. Aoki, K. Maki, Q. Tang, Y. Kumagai, S. Matsumoto, “Structural control of TiO2 film grown on MgO (001) substrate by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 15, 2485–2488 (1997).
[CrossRef]

A. Kobayashi, D. Osabe, K. Maki, “X-ray diffraction study on thickness-dependence of crystallinity in anatase-type TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” presented at the Thirteenth International Conference on Crystal Growth in conjunction with the Eleventh International Conference on Vapor Growth and Epitaxy, 30 July–4 August 2001, Doshisha University, Kyoto, Japan.

Matossi, F.

F. Matossi, “The vibration spectrum of rutile,” J. Chem. Phys. 19, 1543–1546 (1951).
[CrossRef]

Matsumoto, S.

T. Aoki, K. Maki, Q. Tang, Y. Kumagai, S. Matsumoto, “Structural control of TiO2 film grown on MgO (001) substrate by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 15, 2485–2488 (1997).
[CrossRef]

McIntyre, J. D. E.

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

Miller, R. C.

W. G. Spitzer, R. C. Miller, D. A. Kleinman, L. E. Howarth, “Far infrared dielectric dispersion in BaTiO3, SrTiO3, and TiO2,” Phys. Rev. 126, 1710–1721 (1962).
[CrossRef]

Morris-Hotsenpiller, P. A.

P. A. Morris-Hotsenpiller, G. A. Wilson, A. Roshko, J. B. Rothman, G. S. Rohrer, “Heteroepitaxial growth of TiO2 films by ion-beam sputter deposition,” J. Cryst. Growth 166, 779–785 (1996).
[CrossRef]

Osabe, D.

A. Kobayashi, D. Osabe, K. Maki, “X-ray diffraction study on thickness-dependence of crystallinity in anatase-type TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” presented at the Thirteenth International Conference on Crystal Growth in conjunction with the Eleventh International Conference on Vapor Growth and Epitaxy, 30 July–4 August 2001, Doshisha University, Kyoto, Japan.

Piriou, B.

F. Gervais, B. Piriou, “Temperature dependence of transverse- and longitudinal-optic modes in TiO2 (rutile),” Phys. Rev. B 10, 1642–1654 (1974).
[CrossRef]

F. Gervais, B. Piriou, “Anharmonicity in several-polar-mode crystals: adjusting phonon self-energy of LO and TO modes in Al2O3 and TiO2 to fit infrared reflectivity,” J. Phys. C 7, 2374–2385 (1974).
[CrossRef]

Rohrer, G. S.

P. A. Morris-Hotsenpiller, G. A. Wilson, A. Roshko, J. B. Rothman, G. S. Rohrer, “Heteroepitaxial growth of TiO2 films by ion-beam sputter deposition,” J. Cryst. Growth 166, 779–785 (1996).
[CrossRef]

Roshko, A.

P. A. Morris-Hotsenpiller, G. A. Wilson, A. Roshko, J. B. Rothman, G. S. Rohrer, “Heteroepitaxial growth of TiO2 films by ion-beam sputter deposition,” J. Cryst. Growth 166, 779–785 (1996).
[CrossRef]

Rothman, J. B.

P. A. Morris-Hotsenpiller, G. A. Wilson, A. Roshko, J. B. Rothman, G. S. Rohrer, “Heteroepitaxial growth of TiO2 films by ion-beam sputter deposition,” J. Cryst. Growth 166, 779–785 (1996).
[CrossRef]

Spitzer, W. G.

W. G. Spitzer, R. C. Miller, D. A. Kleinman, L. E. Howarth, “Far infrared dielectric dispersion in BaTiO3, SrTiO3, and TiO2,” Phys. Rev. 126, 1710–1721 (1962).
[CrossRef]

Summitt, R.

R. Summitt, “Infrared absorption in single-crystal stannic oxide: optical lattice-vibration modes,” J. Appl. Phys. 39, 3762–3767 (1968).
[CrossRef]

Tang, Q.

T. Aoki, K. Maki, Q. Tang, Y. Kumagai, S. Matsumoto, “Structural control of TiO2 film grown on MgO (001) substrate by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 15, 2485–2488 (1997).
[CrossRef]

Uchitani, T.

T. Uchitani, K. Maki, “Change in surface roughness with the thickness of TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 18, 2706–2708 (2000).
[CrossRef]

Wang, H.

Wilson, G. A.

P. A. Morris-Hotsenpiller, G. A. Wilson, A. Roshko, J. B. Rothman, G. S. Rohrer, “Heteroepitaxial growth of TiO2 films by ion-beam sputter deposition,” J. Cryst. Growth 166, 779–785 (1996).
[CrossRef]

Zallen, R.

R. J. Gonzalez, R. Zallen, H. Berger, “Infrared reflectivity and lattice fundamentals in anatase TiO2,” Phys. Rev. B 55, 7014–7017 (1997).
[CrossRef]

Bull. Chem. Soc. Jpn. (1)

J. Hiraishi, “Effective ionic charges of several uniaxial crystals,” Bull. Chem. Soc. Jpn. 46, 1334–1338 (1973).
[CrossRef]

J. Appl. Phys. (1)

R. Summitt, “Infrared absorption in single-crystal stannic oxide: optical lattice-vibration modes,” J. Appl. Phys. 39, 3762–3767 (1968).
[CrossRef]

J. Chem. Phys. (2)

R. G. Greenler, “Infrared study of adsorbed molecules on metal surfaces by reflection techniques,” J. Chem. Phys. 44, 310–315 (1966).
[CrossRef]

F. Matossi, “The vibration spectrum of rutile,” J. Chem. Phys. 19, 1543–1546 (1951).
[CrossRef]

J. Cryst. Growth (1)

P. A. Morris-Hotsenpiller, G. A. Wilson, A. Roshko, J. B. Rothman, G. S. Rohrer, “Heteroepitaxial growth of TiO2 films by ion-beam sputter deposition,” J. Cryst. Growth 166, 779–785 (1996).
[CrossRef]

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

J. Phys. C (1)

F. Gervais, B. Piriou, “Anharmonicity in several-polar-mode crystals: adjusting phonon self-energy of LO and TO modes in Al2O3 and TiO2 to fit infrared reflectivity,” J. Phys. C 7, 2374–2385 (1974).
[CrossRef]

J. Phys. Chem. Solids (1)

D. M. Eagles, “Polar modes of lattice vibration and polaron coupling constants in rutile (TiO2),” J. Phys. Chem. Solids 25, 1243–1251 (1964).
[CrossRef]

J. Phys. Soc. Jpn. (1)

T. Kurosawa, “Polarization waves in solids,” J. Phys. Soc. Jpn. 16, 1298–1308 (1961).
[CrossRef]

J. Vac. Sci. Technol. A (3)

T. Uchitani, K. Maki, “Change in surface roughness with the thickness of TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 18, 2706–2708 (2000).
[CrossRef]

T. Aoki, K. Maki, Q. Tang, Y. Kumagai, S. Matsumoto, “Structural control of TiO2 film grown on MgO (001) substrate by Ar-ion beam sputtering,” J. Vac. Sci. Technol. A 15, 2485–2488 (1997).
[CrossRef]

J. D. DeLoach, C. R. Aita, “Thickness-dependent crystallinity of sputter-deposited titania,” J. Vac. Sci. Technol. A 16, 1963–1968 (1998).
[CrossRef]

Phys. Rev. (1)

W. G. Spitzer, R. C. Miller, D. A. Kleinman, L. E. Howarth, “Far infrared dielectric dispersion in BaTiO3, SrTiO3, and TiO2,” Phys. Rev. 126, 1710–1721 (1962).
[CrossRef]

Phys. Rev. B (2)

F. Gervais, B. Piriou, “Temperature dependence of transverse- and longitudinal-optic modes in TiO2 (rutile),” Phys. Rev. B 10, 1642–1654 (1974).
[CrossRef]

R. J. Gonzalez, R. Zallen, H. Berger, “Infrared reflectivity and lattice fundamentals in anatase TiO2,” Phys. Rev. B 55, 7014–7017 (1997).
[CrossRef]

Surf. Sci. (1)

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

Other (3)

A. Kobayashi, D. Osabe, K. Maki, “X-ray diffraction study on thickness-dependence of crystallinity in anatase-type TiO2 film grown on MgO (001) by Ar-ion beam sputtering,” presented at the Thirteenth International Conference on Crystal Growth in conjunction with the Eleventh International Conference on Vapor Growth and Epitaxy, 30 July–4 August 2001, Doshisha University, Kyoto, Japan.

E. D. Palik, ed., Handbook of Optical Constants of Solids II (Academic, London, 1991).

See, for example, H. Ibach, H. Luth, Solid-State Physics (Springer-Verlag, Berlin, 1990).

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Figures (16)

Fig. 1
Fig. 1

Relationship between the thickness of TiO2 film grown on MgO (001), dMgO, and the thickness estimated from the frequency shift of the quartz thickness monitor dquartz.

Fig. 2
Fig. 2

Multilayer model with the z axis normal to the surface (xy plane). The thickness, refractive index, and complex refractive angle in layer m are represented by dm, ñm, and θm, respectively. The incidence angle is θ1 and the refractive index of the first layer is n1.

Fig. 3
Fig. 3

Index ellipsoid with the c axis on the surface with ϕ from the y axis.

Fig. 4
Fig. 4

a2u and eu modes for the optical phonon in TiO2 bulk single crystal.12-14

Fig. 5
Fig. 5

Observed IR RAS from a rutile-type bulk single crystal of TiO2 (100) as a function of ϕ between 400 and 820 cm-1 (dashed curve), calculated IR RAS between 100 and 400 cm-1 from the data listed in Ref. 14 (dashed-dotted curve), and IR RAS calculated by use of the respective parameters in the dielectric function [Eq. (14); factorized model] as listed in Table 1 (solid curve).

Fig. 6
Fig. 6

Observed IR RAS from a MgO (001) (dotted curve) and calculated IR RAS by use of the respective parameters for the dielectric function (Lorentz model) as listed in Table 2 (solid curve). The dash-dot curve represents the calculations made by use of the optical constants in Ref. 14.

Fig. 7
Fig. 7

Calculated IR RAS with ϕ as the parameter in Eqs. (5) for (a) the rutile-type TiO2 and (b) the anatase-type TiO2; see text for details.

Fig. 8
Fig. 8

Intensity and corresponding wave number of absorption in the vicinity of 400–450 cm-1 for anatase-type TiO2 [see also Fig. 7(b)] as a function of d2; see text for details.

Fig. 9
Fig. 9

Intensity and corresponding wave number of absorption in the vicinity of 440–510 cm-1 for rutile-type TiO2 [see also Fig. 7(a)] as a function of d; see text for details.

Fig. 10
Fig. 10

(a) XRD patterns from TiO2 films at Ts = 630 °C as a function of d and (b) A (200) and R (110) intensities normalized to MgO (004) peak intensity as a function of the square of d.

Fig. 11
Fig. 11

(a) XRD patterns from TiO2 films at Ts = 500 °C as a function of d and (b) A (200) and R (110) intensities normalized to MgO (004) peak intensity as a function of the square of d.

Fig. 12
Fig. 12

(a) XRD patterns from TiO2 films at Ts = 400 °C as a function of d and (b) A (200) and R (110) intensities normalized to MgO (004) peak intensity as a function of the square of d.

Fig. 13
Fig. 13

IR RAS for TiO2 films as a function of d corresponding to the XRD patterns in Fig. 12.

Fig. 14
Fig. 14

IR RAS as a function of ϕ in Eqs. (5) for anatase-type TiO2 film at d = 56 nm grown at Ts = 400 °C.

Fig. 15
Fig. 15

(a) IR RAS for anatase-type TiO2 film at d = 56 nm grown at Ts = 400 °C (solid curve) and anatase-rich TiO2 film at d = 50 nm grown at Ts = 630 °C (dotted curve); (b) calculated IR RAS for the anatase-type TiO2 (solid curve) and for the rutile-type TiO2 (dotted curve), which are all averaged Rcal versus ϕ curves in Fig. 7; (c) IR RAS for amorphous TiO2 film at d = 50 nm grown at Ts = 230 °C.

Fig. 16
Fig. 16

Relationship between the absorption intensity in IR RAS and d for (a) the rutile-type TiO2 film and (b) the anatase-type TiO2 film. Each solid curve was drawn by averaging the IR RAS in Fig. 7 over ϕ; see text for details.

Tables (2)

Tables Icon

Table 1 Parameters of the Dielectric Function in Eq. (12) for Rutile-Type and Anatase-Type TiO2 Bulk Crystala

Tables Icon

Table 2 Parameters of the Dielectric Function from the Lorentz Model for MgO

Equations (17)

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

r˜m,m+1p=Ãm,m+1-B˜m,m+1Ãm,m+1+B˜m,m+1,
Ãm,m+1=ñm,y2ñm+1,yñm+1,zñm+1,z2-n12 sin2 θ11/2,
B˜m,m+1=ñm+1,y2ñm,yñm,zñm,z2-n12 sin2 θ1.
ñ3,x=ñ3,y=ñ3,z=ñ3=ñMgO.
ñ2,x=ñoñeño2 sin2 ϕ+ñe2 cos2 ϕ1/2 , ñ2,y=ñoñeño2 cos2 ϕ+ñe2 sin2 ϕ1/2, ñ2,z=ño.
r˜1,2p=r˜air,TiO2p=r˜1,2p+r˜2,3pexp-iΔ21+r˜1,2pr˜2,3pexp-iΔ2=r˜air,TiO2p+r˜TiO2,MgOpexp-iΔTiO21+r˜air,TiO2pr˜TiO2,MgOpexp-iΔTiO2,
r˜2,3p=r˜TiO2,MgOp=r˜TiO2,MgOp+r˜MgO,airp exp-iΔMgO1+r˜TiO2,MgOpr˜MgO,airp exp-iΔMgO,
Δ2=ΔTiO2=4πλ d2ñ2,yñ2,zñ2,z2-n12 sin2 θ11/2=4πλ dTiO2ñTiO2,yñTiO2,zñTiO2,z2-n12 sin2 θ11/2,
Δ3=ΔMgO=4πλ dMgOñMgO2-n12 sin2 θ11/2.
RTiO2/MgO=r˜1,2p*r˜1,2p,
RTiO2/MgO=1π0πr˜1,2p*r˜1,2pdδ.
R=RTiO2/MgO/RMgO,
r˜1,2p=r˜air,MgOp=r˜air,MgOp+r˜MgO,airp exp-iΔMgO1+r˜air,MgOpr˜MgO,airp exp-iΔMgO.
˜ω=ñ2=Πj=1NωLOj2-ω2iγLOjωωTOj2-ω2iγTOjω,
ñe=ña2u, ño=ñeu,
r=n2-κ2, i=2nκ.
σ=1Nj=1NRjobs-Rjcal21/2.

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