Abstract

A method, believed to be new, to simulate Drude parameters for collective oscillation of the free carriers in metallic films is proposed. Plasma resonance frequency and relaxation were simulated simultaneously from both the real and the imaginary parts of the dielectric function of a metallic film after consideration of their correlation in the Drude model. As examples, the contributions of the electrons in Ag films and of the free carriers in metallic silicide, NbSi2 and TaSi2, films have been studied.

© 2001 Optical Society of America

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References

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  1. G. Harbeke, “Optical properties of metals,” in Optical Properties of Solids, F. Abelès, ed. (North-Holland, Amsterdam, 1972), Chap. 3, p. 103.
  2. S. R. Nagel, S. E. Schnatterly, “Frequency dependence of the Drude relaxation time in metal films,” Phys. Rev. B 9, 1299–1303 (1974).
    [CrossRef]
  3. H. Gugger, M. Jurich, J. D. Swalen, “Observation of an index-of-refraction-induced change in the Drude parameters of Ag films,” Phys. Rev. B 30, 4189–4195 (1984).
    [CrossRef]
  4. M. L. Thèye, “Investigation of the optical properties of Au by means of thin semitransparent films,” Phys. Rev. B 2, 3060–3078 (1970).
    [CrossRef]
  5. R. N. Gruzhi, “Mutual electron correlations in metal optics,” Sov. Phys. JETP 8, 673–675 (1974).
  6. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  7. P. E. Sulewski, A. J. Sievers, M. M. Maple, M. S. Torikachili, J. L. Smith, Z. Fisk, “Far-infrared absorptivity of UPt3,” Phys. Rev. 38, 5338–5352 (1988).
    [CrossRef]
  8. J. W. Allen, J. J. C. Mikkelsen, “Optical properties of CrSb, MnSb, BiSb and NiAs,” Phys. Rev. B 15, 2952–2960 (1977).
    [CrossRef]
  9. G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
    [CrossRef]
  10. L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, Y. H. Qian, “Improved rotating analyzer–polarizer type of scanning ellipsometer,” Thin Solid Films 234, 385–389 (1993).
    [CrossRef]
  11. D. W. Lynch, W. R. Hunter, “Comments on the optical constants of metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 350–357.
  12. G. Guizetti, F. Marabelli, “Optical properties,” in Properties of Metal Silicides, K. Maex, M. van Rossum, eds. (INSEC, London, 1995), Chap. 6, p. 238.

2000 (1)

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

1993 (1)

L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, Y. H. Qian, “Improved rotating analyzer–polarizer type of scanning ellipsometer,” Thin Solid Films 234, 385–389 (1993).
[CrossRef]

1988 (1)

P. E. Sulewski, A. J. Sievers, M. M. Maple, M. S. Torikachili, J. L. Smith, Z. Fisk, “Far-infrared absorptivity of UPt3,” Phys. Rev. 38, 5338–5352 (1988).
[CrossRef]

1984 (1)

H. Gugger, M. Jurich, J. D. Swalen, “Observation of an index-of-refraction-induced change in the Drude parameters of Ag films,” Phys. Rev. B 30, 4189–4195 (1984).
[CrossRef]

1977 (1)

J. W. Allen, J. J. C. Mikkelsen, “Optical properties of CrSb, MnSb, BiSb and NiAs,” Phys. Rev. B 15, 2952–2960 (1977).
[CrossRef]

1974 (2)

R. N. Gruzhi, “Mutual electron correlations in metal optics,” Sov. Phys. JETP 8, 673–675 (1974).

S. R. Nagel, S. E. Schnatterly, “Frequency dependence of the Drude relaxation time in metal films,” Phys. Rev. B 9, 1299–1303 (1974).
[CrossRef]

1972 (1)

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1970 (1)

M. L. Thèye, “Investigation of the optical properties of Au by means of thin semitransparent films,” Phys. Rev. B 2, 3060–3078 (1970).
[CrossRef]

Allen, J. W.

J. W. Allen, J. J. C. Mikkelsen, “Optical properties of CrSb, MnSb, BiSb and NiAs,” Phys. Rev. B 15, 2952–2960 (1977).
[CrossRef]

Chen, L. Y.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, Y. H. Qian, “Improved rotating analyzer–polarizer type of scanning ellipsometer,” Thin Solid Films 234, 385–389 (1993).
[CrossRef]

Chen, Y. L.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Chu, J. H.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Feng, X. W.

L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, Y. H. Qian, “Improved rotating analyzer–polarizer type of scanning ellipsometer,” Thin Solid Films 234, 385–389 (1993).
[CrossRef]

Fisk, Z.

P. E. Sulewski, A. J. Sievers, M. M. Maple, M. S. Torikachili, J. L. Smith, Z. Fisk, “Far-infrared absorptivity of UPt3,” Phys. Rev. 38, 5338–5352 (1988).
[CrossRef]

Gruzhi, R. N.

R. N. Gruzhi, “Mutual electron correlations in metal optics,” Sov. Phys. JETP 8, 673–675 (1974).

Gugger, H.

H. Gugger, M. Jurich, J. D. Swalen, “Observation of an index-of-refraction-induced change in the Drude parameters of Ag films,” Phys. Rev. B 30, 4189–4195 (1984).
[CrossRef]

Guizetti, G.

G. Guizetti, F. Marabelli, “Optical properties,” in Properties of Metal Silicides, K. Maex, M. van Rossum, eds. (INSEC, London, 1995), Chap. 6, p. 238.

Harbeke, G.

G. Harbeke, “Optical properties of metals,” in Optical Properties of Solids, F. Abelès, ed. (North-Holland, Amsterdam, 1972), Chap. 3, p. 103.

Hunter, W. R.

D. W. Lynch, W. R. Hunter, “Comments on the optical constants of metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 350–357.

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Jurich, M.

H. Gugger, M. Jurich, J. D. Swalen, “Observation of an index-of-refraction-induced change in the Drude parameters of Ag films,” Phys. Rev. B 30, 4189–4195 (1984).
[CrossRef]

Lynch, D. W.

D. W. Lynch, W. R. Hunter, “Comments on the optical constants of metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 350–357.

Ma, H. Z.

L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, Y. H. Qian, “Improved rotating analyzer–polarizer type of scanning ellipsometer,” Thin Solid Films 234, 385–389 (1993).
[CrossRef]

Maple, M. M.

P. E. Sulewski, A. J. Sievers, M. M. Maple, M. S. Torikachili, J. L. Smith, Z. Fisk, “Far-infrared absorptivity of UPt3,” Phys. Rev. 38, 5338–5352 (1988).
[CrossRef]

Marabelli, F.

G. Guizetti, F. Marabelli, “Optical properties,” in Properties of Metal Silicides, K. Maex, M. van Rossum, eds. (INSEC, London, 1995), Chap. 6, p. 238.

Mikkelsen, J. J. C.

J. W. Allen, J. J. C. Mikkelsen, “Optical properties of CrSb, MnSb, BiSb and NiAs,” Phys. Rev. B 15, 2952–2960 (1977).
[CrossRef]

Nagel, S. R.

S. R. Nagel, S. E. Schnatterly, “Frequency dependence of the Drude relaxation time in metal films,” Phys. Rev. B 9, 1299–1303 (1974).
[CrossRef]

Qian, Y. H.

L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, Y. H. Qian, “Improved rotating analyzer–polarizer type of scanning ellipsometer,” Thin Solid Films 234, 385–389 (1993).
[CrossRef]

Schnatterly, S. E.

S. R. Nagel, S. E. Schnatterly, “Frequency dependence of the Drude relaxation time in metal films,” Phys. Rev. B 9, 1299–1303 (1974).
[CrossRef]

Sievers, A. J.

P. E. Sulewski, A. J. Sievers, M. M. Maple, M. S. Torikachili, J. L. Smith, Z. Fisk, “Far-infrared absorptivity of UPt3,” Phys. Rev. 38, 5338–5352 (1988).
[CrossRef]

Smith, J. L.

P. E. Sulewski, A. J. Sievers, M. M. Maple, M. S. Torikachili, J. L. Smith, Z. Fisk, “Far-infrared absorptivity of UPt3,” Phys. Rev. 38, 5338–5352 (1988).
[CrossRef]

Su, Y.

L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, Y. H. Qian, “Improved rotating analyzer–polarizer type of scanning ellipsometer,” Thin Solid Films 234, 385–389 (1993).
[CrossRef]

Sulewski, P. E.

P. E. Sulewski, A. J. Sievers, M. M. Maple, M. S. Torikachili, J. L. Smith, Z. Fisk, “Far-infrared absorptivity of UPt3,” Phys. Rev. 38, 5338–5352 (1988).
[CrossRef]

Swalen, J. D.

H. Gugger, M. Jurich, J. D. Swalen, “Observation of an index-of-refraction-induced change in the Drude parameters of Ag films,” Phys. Rev. B 30, 4189–4195 (1984).
[CrossRef]

Thèye, M. L.

M. L. Thèye, “Investigation of the optical properties of Au by means of thin semitransparent films,” Phys. Rev. B 2, 3060–3078 (1970).
[CrossRef]

Torikachili, M. S.

P. E. Sulewski, A. J. Sievers, M. M. Maple, M. S. Torikachili, J. L. Smith, Z. Fisk, “Far-infrared absorptivity of UPt3,” Phys. Rev. 38, 5338–5352 (1988).
[CrossRef]

Wang, S. Y.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Wang, Z. M.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Xia, G. Q.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Yang, Y. M.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Zhang, R. J.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Zhao, H. B.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Zheng, Y. X.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Zhou, S. M.

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Phys. Rev. (1)

P. E. Sulewski, A. J. Sievers, M. M. Maple, M. S. Torikachili, J. L. Smith, Z. Fisk, “Far-infrared absorptivity of UPt3,” Phys. Rev. 38, 5338–5352 (1988).
[CrossRef]

Phys. Rev. B (5)

J. W. Allen, J. J. C. Mikkelsen, “Optical properties of CrSb, MnSb, BiSb and NiAs,” Phys. Rev. B 15, 2952–2960 (1977).
[CrossRef]

S. R. Nagel, S. E. Schnatterly, “Frequency dependence of the Drude relaxation time in metal films,” Phys. Rev. B 9, 1299–1303 (1974).
[CrossRef]

H. Gugger, M. Jurich, J. D. Swalen, “Observation of an index-of-refraction-induced change in the Drude parameters of Ag films,” Phys. Rev. B 30, 4189–4195 (1984).
[CrossRef]

M. L. Thèye, “Investigation of the optical properties of Au by means of thin semitransparent films,” Phys. Rev. B 2, 3060–3078 (1970).
[CrossRef]

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Rev. Sci. Instrum. (1)

G. Q. Xia, R. J. Zhang, Y. L. Chen, H. B. Zhao, S. Y. Wang, S. M. Zhou, Y. X. Zheng, Y. M. Yang, L. Y. Chen, J. H. Chu, Z. M. Wang, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000).
[CrossRef]

Sov. Phys. JETP (1)

R. N. Gruzhi, “Mutual electron correlations in metal optics,” Sov. Phys. JETP 8, 673–675 (1974).

Thin Solid Films (1)

L. Y. Chen, X. W. Feng, Y. Su, H. Z. Ma, Y. H. Qian, “Improved rotating analyzer–polarizer type of scanning ellipsometer,” Thin Solid Films 234, 385–389 (1993).
[CrossRef]

Other (3)

D. W. Lynch, W. R. Hunter, “Comments on the optical constants of metals,” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 350–357.

G. Guizetti, F. Marabelli, “Optical properties,” in Properties of Metal Silicides, K. Maex, M. van Rossum, eds. (INSEC, London, 1995), Chap. 6, p. 238.

G. Harbeke, “Optical properties of metals,” in Optical Properties of Solids, F. Abelès, ed. (North-Holland, Amsterdam, 1972), Chap. 3, p. 103.

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Figures (4)

Fig. 1
Fig. 1

Spectra of the dielectric function of evaporated Ag and the data taken from Ref. 11. Inset, the absorption coefficient of Ag in the infrared region.

Fig. 2
Fig. 2

Real and imaginary parts of the (a), (b) dielectric function of evaporated Ag film and of (c), (d) the data taken from Ref. 11 versus 1/(ω2 + Γ2) and (Γ/(ω3 + ωΓ2), respectively. Inset, the real part ε1 of the dielectric function of evaporated Ag film versus ω-2 in the visible region.

Fig. 3
Fig. 3

Real and imaginary parts of the dielectric functions of (a), (b) NbSi2 and (c), (d) TaSi2 films versus 1/(ω2 + Γ2) and Γ/(ω3 + ωΓ2), respectively; the data were taken from Ref. 12. Insets, ε1 versus ω-2 in the visible region.

Fig. 4
Fig. 4

Reciprocal relaxation versus ω2 for (a) the Ag films and (b) the NbSi2 and TaSi2 films.

Equations (4)

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

ε1=εb-ωP2ω2+Γ2,
ε2=ωP2ω3+ωΓ2,
Γ=ωε2εb-ε1.
ε1=εb-ωP2ω2,  ε2=ωP2Γω3.

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