Abstract

The reflectances of evaporated films of Li were measured as functions of angle of incidence for photon energies between 3 and 10.7 eV, and were analyzed, by use of Fresnel’s equations, to determine the optical constants n and k for each energy. Above 6 eV, measurements with photons incident on both vacuum and substrate surfaces gave the same values of n and k within experimental limits of about ±5%. Below 6 eV, values of n and k obtained from the analysis were not reproducible; they depend in a complex way on film thickness, light polarization, and surface structure. Failure of the analysis below 6 eV is attributed to surface-roughness effects on the R (θ) curves, which are not accounted for in Fresnel’s equations. These effects are believed to be small above 6 eV. The dielectric function 1 and 2 and the energy-loss function Im(− 1/) were determined from n and k for photon energies above 6 eV. The plasma energy of Li, as determined from the condition 1 (ω) = 0, is 6.7 eV; and the plasma loss peak in Im(−1/) is centered at 7.1 eV. In contrast to results for the heavy alkali metals K, Rb, and Cs, no evidence was found for an optical-absorption peak in 2 in the spectral region above the plasma frequency.

© 1974 Optical Society of America

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References

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  1. J. C. Sutherland and E. T. Arakawa, J. Opt. Soc. Am. 57, 645 (1967); J. Opt. Soc. Am. 53, 1080 (1968); J. C. Sutherland, R. N. Hamm, and E. T. Arakawa, J. Opt. Soc. Am. 59, 1581 (1969).
    [CrossRef]
  2. U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 6, 2109 (1972).
    [CrossRef]
  3. U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 5, 2118 (1972).
    [CrossRef]
  4. U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Lett. 25, 646 (1970); J. Opt. Soc. Am. 61, 740 (1971).
    [CrossRef]
  5. Monique Rasigni and Georges Rasigni, J. Opt. Soc. Am. 62, 1033 (1972); J. Opt. Soc. Am. 63, 775 (1973).
    [CrossRef]
  6. W. Y. Ching and J. Calloway, Phys. Rev. Lett. 30, 441 (1973).
    [CrossRef]
  7. R. N. Hamm, R. A. MacRae, and E. T. Arakawa, J. Opt. Soc. Am. 55, 1460 (1965).
    [CrossRef]
  8. W. R. Hunter, J. Opt. Soc. Am. 54, 15 (1964); J. Opt. Soc. Am. 55, 1197 (1965).
    [CrossRef]
  9. A. Otto, Z. Phys. 216, 398 (1968); Phys. Stat. Sol. 42, K37 (1970); also see E. Kretschmann. Z. Phys. 241, 313 (1971).
    [CrossRef]
  10. U. S. Whang, E. T. Arakawa, R. N. Hamm, and M. W. Williams, J. Opt. Soc. Am. 63, 305 (1973).
    [CrossRef]
  11. J. Crowell and R. H. Ritchie, J. Opt. Soc. Am. 6, 794 (1970); also see J. M. Elson and R. H. Ritchie, Phys. Rev. B 4, 4129 (1971).
    [CrossRef]
  12. C. Macek, A. Otto, and W. Steinmann, Phys. Stat. Sol. 51, K59 (1972).
    [CrossRef]
  13. A. J. Braundmeier and E. T. Arakawa, J. Phys. Chem. Solids 35, 517 (1974).
    [CrossRef]
  14. J. Bösenberg, Phys. Lett. 41A, 185 (1972).
  15. J. N. Hodgson, in Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abelès (North–Holland, Amsterdam, 1966), p. 60.
  16. C. Kunz, Z. Phys. 196, 311 (1966).
    [CrossRef]

1974 (1)

A. J. Braundmeier and E. T. Arakawa, J. Phys. Chem. Solids 35, 517 (1974).
[CrossRef]

1973 (2)

1972 (5)

C. Macek, A. Otto, and W. Steinmann, Phys. Stat. Sol. 51, K59 (1972).
[CrossRef]

Monique Rasigni and Georges Rasigni, J. Opt. Soc. Am. 62, 1033 (1972); J. Opt. Soc. Am. 63, 775 (1973).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 6, 2109 (1972).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 5, 2118 (1972).
[CrossRef]

J. Bösenberg, Phys. Lett. 41A, 185 (1972).

1970 (2)

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Lett. 25, 646 (1970); J. Opt. Soc. Am. 61, 740 (1971).
[CrossRef]

J. Crowell and R. H. Ritchie, J. Opt. Soc. Am. 6, 794 (1970); also see J. M. Elson and R. H. Ritchie, Phys. Rev. B 4, 4129 (1971).
[CrossRef]

1968 (1)

A. Otto, Z. Phys. 216, 398 (1968); Phys. Stat. Sol. 42, K37 (1970); also see E. Kretschmann. Z. Phys. 241, 313 (1971).
[CrossRef]

1967 (1)

1966 (1)

C. Kunz, Z. Phys. 196, 311 (1966).
[CrossRef]

1965 (1)

1964 (1)

Arakawa, E. T.

A. J. Braundmeier and E. T. Arakawa, J. Phys. Chem. Solids 35, 517 (1974).
[CrossRef]

U. S. Whang, E. T. Arakawa, R. N. Hamm, and M. W. Williams, J. Opt. Soc. Am. 63, 305 (1973).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 5, 2118 (1972).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 6, 2109 (1972).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Lett. 25, 646 (1970); J. Opt. Soc. Am. 61, 740 (1971).
[CrossRef]

J. C. Sutherland and E. T. Arakawa, J. Opt. Soc. Am. 57, 645 (1967); J. Opt. Soc. Am. 53, 1080 (1968); J. C. Sutherland, R. N. Hamm, and E. T. Arakawa, J. Opt. Soc. Am. 59, 1581 (1969).
[CrossRef]

R. N. Hamm, R. A. MacRae, and E. T. Arakawa, J. Opt. Soc. Am. 55, 1460 (1965).
[CrossRef]

Bösenberg, J.

J. Bösenberg, Phys. Lett. 41A, 185 (1972).

Braundmeier, A. J.

A. J. Braundmeier and E. T. Arakawa, J. Phys. Chem. Solids 35, 517 (1974).
[CrossRef]

Callcott, T. A.

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 5, 2118 (1972).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 6, 2109 (1972).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Lett. 25, 646 (1970); J. Opt. Soc. Am. 61, 740 (1971).
[CrossRef]

Calloway, J.

W. Y. Ching and J. Calloway, Phys. Rev. Lett. 30, 441 (1973).
[CrossRef]

Ching, W. Y.

W. Y. Ching and J. Calloway, Phys. Rev. Lett. 30, 441 (1973).
[CrossRef]

Crowell, J.

J. Crowell and R. H. Ritchie, J. Opt. Soc. Am. 6, 794 (1970); also see J. M. Elson and R. H. Ritchie, Phys. Rev. B 4, 4129 (1971).
[CrossRef]

Hamm, R. N.

Hodgson, J. N.

J. N. Hodgson, in Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abelès (North–Holland, Amsterdam, 1966), p. 60.

Hunter, W. R.

Kunz, C.

C. Kunz, Z. Phys. 196, 311 (1966).
[CrossRef]

Macek, C.

C. Macek, A. Otto, and W. Steinmann, Phys. Stat. Sol. 51, K59 (1972).
[CrossRef]

MacRae, R. A.

Otto, A.

C. Macek, A. Otto, and W. Steinmann, Phys. Stat. Sol. 51, K59 (1972).
[CrossRef]

A. Otto, Z. Phys. 216, 398 (1968); Phys. Stat. Sol. 42, K37 (1970); also see E. Kretschmann. Z. Phys. 241, 313 (1971).
[CrossRef]

Rasigni, Georges

Rasigni, Monique

Ritchie, R. H.

J. Crowell and R. H. Ritchie, J. Opt. Soc. Am. 6, 794 (1970); also see J. M. Elson and R. H. Ritchie, Phys. Rev. B 4, 4129 (1971).
[CrossRef]

Steinmann, W.

C. Macek, A. Otto, and W. Steinmann, Phys. Stat. Sol. 51, K59 (1972).
[CrossRef]

Sutherland, J. C.

Whang, U. S.

U. S. Whang, E. T. Arakawa, R. N. Hamm, and M. W. Williams, J. Opt. Soc. Am. 63, 305 (1973).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 5, 2118 (1972).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 6, 2109 (1972).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Lett. 25, 646 (1970); J. Opt. Soc. Am. 61, 740 (1971).
[CrossRef]

Williams, M. W.

J. Opt. Soc. Am. (6)

J. Phys. Chem. Solids (1)

A. J. Braundmeier and E. T. Arakawa, J. Phys. Chem. Solids 35, 517 (1974).
[CrossRef]

Phys. Lett. (1)

J. Bösenberg, Phys. Lett. 41A, 185 (1972).

Phys. Rev. B (2)

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 6, 2109 (1972).
[CrossRef]

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. B 5, 2118 (1972).
[CrossRef]

Phys. Rev. Lett. (2)

U. S. Whang, E. T. Arakawa, and T. A. Callcott, Phys. Rev. Lett. 25, 646 (1970); J. Opt. Soc. Am. 61, 740 (1971).
[CrossRef]

W. Y. Ching and J. Calloway, Phys. Rev. Lett. 30, 441 (1973).
[CrossRef]

Phys. Stat. Sol. (1)

C. Macek, A. Otto, and W. Steinmann, Phys. Stat. Sol. 51, K59 (1972).
[CrossRef]

Z. Phys. (2)

C. Kunz, Z. Phys. 196, 311 (1966).
[CrossRef]

A. Otto, Z. Phys. 216, 398 (1968); Phys. Stat. Sol. 42, K37 (1970); also see E. Kretschmann. Z. Phys. 241, 313 (1971).
[CrossRef]

Other (1)

J. N. Hodgson, in Optical Properties and Electronic Structure of Metals and Alloys, edited by F. Abelès (North–Holland, Amsterdam, 1966), p. 60.

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Figures (7)

Fig. 1
Fig. 1

Index of refraction vs photon energy for Li films on MgF2 substrate derived from R(θ) measurements. Filled circles, filled circles with vertical lines, filled circles with horizontal lines, and filled squares are values for light incident through substrate and open circles and triangles are values for light incident from vacuum.

Fig. 2
Fig. 2

Absorption coefficient vs photon energy for Li films on MgF2 substrate derived from R(θ) measurements. Filled circles, filled circles with vertical lines, and filled circles with horizontal lines are values for light incident through substrate and open circles and triangles are values for light incident from vacuum.

Fig. 3
Fig. 3

Angular reflectance curves for 3-eV polarized light incident through the substrate. P-polarized light shows the plasmon dip at about 50°.

Fig. 4
Fig. 4

Index of refraction vs photon energy for Li showing inconsistency of results obtained with different techniques for photon energies below 6 eV: ●–●–● for thick films on MgF2, light through substrate; ○–○–○ for thick films on MgF2, light from vacuum; — – — – for thin films on MgF2, s-polarized light through substrate; — — —, for thin films on MgF2, p-polarized light through substrate; –□–□–□– Bösenberg’s data (Ref. 14); and △–△–△ Hodgson’s data (Ref. 15).

Fig. 5
Fig. 5

Absorption coefficient vs photon energy for Li, showing inconsistency of results obtained with different techniques for photon energies below 6 eV. Curves have same identification as for Fig. 4.

Fig. 6
Fig. 6

Dielectric functions 1 and 2 and the energy-loss function −Im(1/) for photon energies from 6 to 10.7 eV. Plasma frequencies shown for condition where 1 = 0 (6.7 eV) and for maximum in energy-loss function (7.1 eV).

Fig. 7
Fig. 7

Plot of 1 vs λ2 used to deduce free-carrier parameters.

Tables (1)

Tables Icon

Table I Optical and dielectric constants of Li for photon energies from 6 to 10.7 eV.

Equations (2)

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1 = 1 + 4 π N α - ω a 2 ω 2 + δ 1 ,
1 = 1 + 4 π N α - 4 π N e 2 m opt 1 ω 2 .