Abstract

The optical constants of molybdenum, tantalum, tungsten, and rhenium have been measured at wavelengths from 537 through 5770 Å by the reflectance vs angle of incidence method. The spectra for the two parts of the complex dielectric constant exhibit structural similarities among the four metals, consisting of three broad, partially overlapping absorption bands situated in the approximate photon-energy regions between 13 and 26 eV, between 7 and 15 eV, and below 10 eV. The latter band generally has one or more narrower absorption resonances superimposed on it. The observed structure bears a resemblance to the level separations calculated by Mattheiss for tungsten and rhenium, but correlation with specific transitions has not been pursued in detail. The f-sum rule applied to the imaginary part of the dielectric constant yields appropriate values of 5 and 7 electrons/atom for tantalum and rhenium. For molybdenum and tungsten the corresponding values are near 8, rather than the anticipated 6, electrons/atom.

© 1968 Optical Society of America

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References

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  1. L. J. LeBlanc, J. S. Farrell, and D. W. Juenker, J. Opt. Soc. Am. 54, 956 (1964).
    [CrossRef]
  2. S. Roberts, Phys. Rev. 114, 104 (1959).
    [CrossRef]
  3. A. P. Lenham, J. Opt. Soc. Am. 57, 473 (1967).
    [CrossRef] [PubMed]
  4. D. W. Juenker, J. Opt. Soc. Am. 55, 295 (1965).
    [CrossRef]
  5. L. F. Mattheiss, Phys. Rev. 139, A1893 (1965); L. F. Mattheiss and R. E. Watson, Phys. Rev. Letters 13, 527 (1964).
    [CrossRef]
  6. L. F. Mattheiss, Phys. Rev. 151, 450 (1966).
    [CrossRef]
  7. T. L. Loucks, Phys. Rev. 139, A1181 (1965).
    [CrossRef]
  8. T. L. Loucks, Phys. Rev. 139, A1333 (1965).
    [CrossRef]
  9. T. L. Loucks, Phys. Rev. 143, 506 (1966).
    [CrossRef]
  10. P. L. Hartman, J. Opt. Soc. Am. 51, 113 (1961).
    [CrossRef]
  11. J. P. Waldron and D. W. Juenker, J. Opt. Soc. Am. 54, 204 (1964).
    [CrossRef]
  12. A single such exception occurred in molybdenum, two each in tantalum and tungsten, and five in rhenium. The somewhat poorer surface finish of the rhenium samples was probably responsible for its excessive data scatter, although a slight anisotropy of the optical properties of its hcp lattice is a possible source of the discrepancies.
  13. W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
    [CrossRef]
  14. A lorentzian function might have been preferable; cf. N. Swanson, J. Opt. Soc. Am. 54, 1130 (1964).
    [CrossRef]
  15. See, for example, F. Stern, in Solid State Physics (Academic Press Inc., New York, 1963), Vol. 15, p. 300.
    [CrossRef]
  16. M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939).
    [CrossRef]
  17. L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.
  18. L. J. Haworth, Phys. Rev. 48, 88 (1935); Phys. Rev. 50, 216 (1936).
    [CrossRef]
  19. V. W. Kleinn, Optik 11, 226 (1954).
  20. J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

1967 (1)

1966 (2)

L. F. Mattheiss, Phys. Rev. 151, 450 (1966).
[CrossRef]

T. L. Loucks, Phys. Rev. 143, 506 (1966).
[CrossRef]

1965 (5)

T. L. Loucks, Phys. Rev. 139, A1181 (1965).
[CrossRef]

T. L. Loucks, Phys. Rev. 139, A1333 (1965).
[CrossRef]

D. W. Juenker, J. Opt. Soc. Am. 55, 295 (1965).
[CrossRef]

L. F. Mattheiss, Phys. Rev. 139, A1893 (1965); L. F. Mattheiss and R. E. Watson, Phys. Rev. Letters 13, 527 (1964).
[CrossRef]

W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
[CrossRef]

1964 (3)

1961 (1)

1959 (1)

S. Roberts, Phys. Rev. 114, 104 (1959).
[CrossRef]

1954 (1)

V. W. Kleinn, Optik 11, 226 (1954).

1939 (1)

M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939).
[CrossRef]

1935 (1)

L. J. Haworth, Phys. Rev. 48, 88 (1935); Phys. Rev. 50, 216 (1936).
[CrossRef]

Chodorow, M. I.

M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939).
[CrossRef]

Dimmock, J. O.

J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

Farrell, J. S.

Freeman, A. J.

J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

Hartman, P. L.

Haworth, L. J.

L. J. Haworth, Phys. Rev. 48, 88 (1935); Phys. Rev. 50, 216 (1936).
[CrossRef]

Hunter, W. R.

Juenker, D. W.

Kleinn, V. W.

V. W. Kleinn, Optik 11, 226 (1954).

LeBlanc, L. J.

Leder, L. B.

L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.

Lenham, A. P.

Loucks, T. L.

T. L. Loucks, Phys. Rev. 143, 506 (1966).
[CrossRef]

T. L. Loucks, Phys. Rev. 139, A1181 (1965).
[CrossRef]

T. L. Loucks, Phys. Rev. 139, A1333 (1965).
[CrossRef]

Manning, M. F.

M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939).
[CrossRef]

Marton, L.

L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.

Mattheiss, L. F.

L. F. Mattheiss, Phys. Rev. 151, 450 (1966).
[CrossRef]

L. F. Mattheiss, Phys. Rev. 139, A1893 (1965); L. F. Mattheiss and R. E. Watson, Phys. Rev. Letters 13, 527 (1964).
[CrossRef]

Mendlowitz, H.

L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.

Roberts, S.

S. Roberts, Phys. Rev. 114, 104 (1959).
[CrossRef]

Stern, F.

See, for example, F. Stern, in Solid State Physics (Academic Press Inc., New York, 1963), Vol. 15, p. 300.
[CrossRef]

Swanson, N.

Waldron, J. P.

Watson, R. E.

J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

J. Opt. Soc. Am. (7)

Optik (1)

V. W. Kleinn, Optik 11, 226 (1954).

Phys. Rev. (8)

L. J. Haworth, Phys. Rev. 48, 88 (1935); Phys. Rev. 50, 216 (1936).
[CrossRef]

M. F. Manning and M. I. Chodorow, Phys. Rev. 56, 787 (1939).
[CrossRef]

S. Roberts, Phys. Rev. 114, 104 (1959).
[CrossRef]

L. F. Mattheiss, Phys. Rev. 139, A1893 (1965); L. F. Mattheiss and R. E. Watson, Phys. Rev. Letters 13, 527 (1964).
[CrossRef]

L. F. Mattheiss, Phys. Rev. 151, 450 (1966).
[CrossRef]

T. L. Loucks, Phys. Rev. 139, A1181 (1965).
[CrossRef]

T. L. Loucks, Phys. Rev. 139, A1333 (1965).
[CrossRef]

T. L. Loucks, Phys. Rev. 143, 506 (1966).
[CrossRef]

Other (4)

A single such exception occurred in molybdenum, two each in tantalum and tungsten, and five in rhenium. The somewhat poorer surface finish of the rhenium samples was probably responsible for its excessive data scatter, although a slight anisotropy of the optical properties of its hcp lattice is a possible source of the discrepancies.

L. Marton, L. B. Leder, and H. Mendlowitz, in Advances in Electronics and Electron Physics, L. Marton, Ed. (Academic Press Inc., New York, 1955), Vol. 7.

See, for example, F. Stern, in Solid State Physics (Academic Press Inc., New York, 1963), Vol. 15, p. 300.
[CrossRef]

J. O. Dimmock, A. J. Freeman, and R. E. Watson, in Proc. Int. Colloq. on Optical Properties and Electronics Structure of Metals and Alloys, F. Abelès, Ed. (North-Holland Publishing Co., Amsterdam, 1966), p. 237.

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Figures (11)

Fig. 1
Fig. 1

Reflectometer for measurements in the extreme uv.

Fig. 2
Fig. 2

Index of refraction and normal-incidence reflectance for molybdenum. Data points and solid curves are from the present experiment. Dashed curves were reported previously.

Fig. 3
Fig. 3

Index of refraction and reflectance for tantalum.

Fig. 4
Fig. 4

Index of refraction and reflectance for tungsten.

Fig. 5
Fig. 5

Index of refraction and reflectance for rhenium.

Fig. 6
Fig. 6

Real and imaginary parts of the dielectric constant of molybdenum. The solid curves are from a polished sample.

Fig. 7
Fig. 7

The dielectric constant of tantalum.

Fig. 8
Fig. 8

The dielectric constant of tungsten.

Fig. 9
Fig. 9

The dielectric constant of rhenium.

Fig. 10
Fig. 10

The loss function. Data are represented collectively by solid curves where the density of measurements was high, and as individual points elsewhere. The dashed curves are gaussian functions matched to the data at the higher energies.

Fig. 11
Fig. 11

The absorption function EK2 for tungsten. Circles are from Roberts’s data and squares from the present results. The arrows mark the minor absorption peaks listed in Table I. The dashed lines approximate the data for the purpose of integration.

Tables (2)

Tables Icon

Table I Location, in eV, of structural features in the dielectric constant. The numbers in each triad refer to a successive minimum, null, and maximum second derivative in K1. Estimated positions for features that are poorly defined, or occur in a data gap, are given in italics. Entries in parentheses are adapted from Ref. 2.

Tables Icon

Table II Plasma oscillation energies in eV as inferred from optical data. Ep1 was obtained from gaussian extrapolations of Im(−K−1) data at high photon energies, and Ep2 from the sum rule on EK2. Ep0 is calculated on the basis of 5 electrons/atom for tantalum, 6 for molybdenum and tungsten, and 7 for rhenium.

Equations (2)

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0 E Im ( - K - 1 ) d E = π E p 2 / 2 ,
0 E K 2 d E = π E p 2 / 2 N ,