Abstract

In the spectral range 0.5<hv<11.9 eV, reflectance data were obtained from molybdenum and ruthenium films, vapor deposited in ultra-high vacuum and extended to 14 eV using the reflectance of a polished bulk sample. The Mo data are different from previously reported data. The optical constants are obtained by a Kramers–Kronig analysis of the normal-incidence reflectance. In the analysis for hv>14 eV (23 eV for Mo) the reflectance was represented by an inverse power function where the exponent was determined with the aid of the reflectance measured at 50° incidence for hv<11.9 eV. The imaginary part of the dielectric constant, 2, has shoulders at about 2.2 and 4.0 eV for Mo and 1.6 eV for Ru. The loss functions Im[1/] and Im [1/(1+)] have peaks at 10.8 and 9.9 eV, respectively, for Mo, and 10.2 and 8.7 eV, respectively, for Ru. Interband transitions dominate for 0.5≲hv≲10.0 eV.

© 1970 Optical Society of America

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References

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  1. D. W. Juenker, L. J. LeBlanc, and C. R. Martin, J. Opt. Soc. Am. 58, 164 (1968).
    [Crossref]
  2. K. A. Kress and G. J. Lapeyre, Proc. 3rd IMR Symposium, Electronic Density of States, Nat. Bur. Std. (U.S.), Spec. Publ. 323 (U. S. Govt. Printing Office, Washington, D. C., 1970).
  3. K. A. Kress and G. J. Lapeyre, Phys. Rev. 2, 2532 (1970).
    [Crossref]
  4. Because the center of rotation of the substrate was slightly off the optic axis, the optical path of the reflected light increased, with angle of reflectance. As a consequence, the apparent reflectance decreased slightly as the reflectance angle increased. The effect becomes appreciable for angles ≳60°.
  5. Details of the numerical analysis are found in the thesis by K. A. Kress, Montana State University, 1969.
  6. For example, see J. Feinleib, W. J. Scouler, and A. Ferretti, Phys. Rev. 165, 765 (1968).
    [Crossref]
  7. W. R. Hunter, J. Opt. Soc. Am. 55, 1197 (1965).
    [Crossref]
  8. D. W. Vance, Phys. Rev. 164, 372 (1967).
    [Crossref]
  9. V. W. Kleiner, Optiks 11, 226 (1954).
  10. L. J. Haworth, Phys. Rev. 48, 88 (1935).
    [Crossref]
  11. L. J. Haworth, Phys. Rev. 50, 216 (1936).
    [Crossref]
  12. For example, see S. Robin, in Optical Properties and Electronic Structure of Metal and Alloys, edited by F. Abelès (North-Holland, Amsterdam, 1966), pp. 202–209.
  13. H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
    [Crossref]
  14. N. V. Smith and W. C. Spicer, in Ref. 2.
  15. J. F. Janals, D. C. Eastman, and A. R. Williams, in Ref. 2.

1970 (1)

K. A. Kress and G. J. Lapeyre, Phys. Rev. 2, 2532 (1970).
[Crossref]

1968 (2)

For example, see J. Feinleib, W. J. Scouler, and A. Ferretti, Phys. Rev. 165, 765 (1968).
[Crossref]

D. W. Juenker, L. J. LeBlanc, and C. R. Martin, J. Opt. Soc. Am. 58, 164 (1968).
[Crossref]

1967 (1)

D. W. Vance, Phys. Rev. 164, 372 (1967).
[Crossref]

1965 (1)

1962 (1)

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

1954 (1)

V. W. Kleiner, Optiks 11, 226 (1954).

1936 (1)

L. J. Haworth, Phys. Rev. 50, 216 (1936).
[Crossref]

1935 (1)

L. J. Haworth, Phys. Rev. 48, 88 (1935).
[Crossref]

Eastman, D. C.

J. F. Janals, D. C. Eastman, and A. R. Williams, in Ref. 2.

Ehrenreich, H.

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

Feinleib, J.

For example, see J. Feinleib, W. J. Scouler, and A. Ferretti, Phys. Rev. 165, 765 (1968).
[Crossref]

Ferretti, A.

For example, see J. Feinleib, W. J. Scouler, and A. Ferretti, Phys. Rev. 165, 765 (1968).
[Crossref]

Haworth, L. J.

L. J. Haworth, Phys. Rev. 50, 216 (1936).
[Crossref]

L. J. Haworth, Phys. Rev. 48, 88 (1935).
[Crossref]

Hunter, W. R.

Janals, J. F.

J. F. Janals, D. C. Eastman, and A. R. Williams, in Ref. 2.

Juenker, D. W.

Kleiner, V. W.

V. W. Kleiner, Optiks 11, 226 (1954).

Kress, K. A.

K. A. Kress and G. J. Lapeyre, Phys. Rev. 2, 2532 (1970).
[Crossref]

K. A. Kress and G. J. Lapeyre, Proc. 3rd IMR Symposium, Electronic Density of States, Nat. Bur. Std. (U.S.), Spec. Publ. 323 (U. S. Govt. Printing Office, Washington, D. C., 1970).

Details of the numerical analysis are found in the thesis by K. A. Kress, Montana State University, 1969.

Lapeyre, G. J.

K. A. Kress and G. J. Lapeyre, Phys. Rev. 2, 2532 (1970).
[Crossref]

K. A. Kress and G. J. Lapeyre, Proc. 3rd IMR Symposium, Electronic Density of States, Nat. Bur. Std. (U.S.), Spec. Publ. 323 (U. S. Govt. Printing Office, Washington, D. C., 1970).

LeBlanc, L. J.

Martin, C. R.

Philipp, H. R.

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

Robin, S.

For example, see S. Robin, in Optical Properties and Electronic Structure of Metal and Alloys, edited by F. Abelès (North-Holland, Amsterdam, 1966), pp. 202–209.

Scouler, W. J.

For example, see J. Feinleib, W. J. Scouler, and A. Ferretti, Phys. Rev. 165, 765 (1968).
[Crossref]

Smith, N. V.

N. V. Smith and W. C. Spicer, in Ref. 2.

Spicer, W. C.

N. V. Smith and W. C. Spicer, in Ref. 2.

Vance, D. W.

D. W. Vance, Phys. Rev. 164, 372 (1967).
[Crossref]

Williams, A. R.

J. F. Janals, D. C. Eastman, and A. R. Williams, in Ref. 2.

J. Opt. Soc. Am. (2)

Optiks (1)

V. W. Kleiner, Optiks 11, 226 (1954).

Phys. Rev. (6)

L. J. Haworth, Phys. Rev. 48, 88 (1935).
[Crossref]

L. J. Haworth, Phys. Rev. 50, 216 (1936).
[Crossref]

K. A. Kress and G. J. Lapeyre, Phys. Rev. 2, 2532 (1970).
[Crossref]

D. W. Vance, Phys. Rev. 164, 372 (1967).
[Crossref]

H. Ehrenreich and H. R. Philipp, Phys. Rev. 128, 1622 (1962).
[Crossref]

For example, see J. Feinleib, W. J. Scouler, and A. Ferretti, Phys. Rev. 165, 765 (1968).
[Crossref]

Other (6)

N. V. Smith and W. C. Spicer, in Ref. 2.

J. F. Janals, D. C. Eastman, and A. R. Williams, in Ref. 2.

Because the center of rotation of the substrate was slightly off the optic axis, the optical path of the reflected light increased, with angle of reflectance. As a consequence, the apparent reflectance decreased slightly as the reflectance angle increased. The effect becomes appreciable for angles ≳60°.

Details of the numerical analysis are found in the thesis by K. A. Kress, Montana State University, 1969.

K. A. Kress and G. J. Lapeyre, Proc. 3rd IMR Symposium, Electronic Density of States, Nat. Bur. Std. (U.S.), Spec. Publ. 323 (U. S. Govt. Printing Office, Washington, D. C., 1970).

For example, see S. Robin, in Optical Properties and Electronic Structure of Metal and Alloys, edited by F. Abelès (North-Holland, Amsterdam, 1966), pp. 202–209.

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Figures (7)

Fig. 1
Fig. 1

Schematic of reflectometer; D, LiF W, S, GW, P, and E are the detector, LiF window, substrate, glass window, 250-liter/s ion pump, and electron-beam evaporator, respectively.

Fig. 2
Fig. 2

Spectral reflectance of molybdenum; i is the angle of incidence.

Fig. 3
Fig. 3

Spectral dependence of the real and imaginary parts of the dielectric constant of molybdenum.

Fig. 4
Fig. 4

Volume- and surface-loss functions for molybdenum as a function of spectral energy.

Fig. 5
Fig. 5

Spectral reflectance of ruthenium; i is the angle of incidence.

Fig. 6
Fig. 6

Spectral dependence of the real and imaginary parts of the dielectric function of ruthenium.

Fig. 7
Fig. 7

Surface- and volume-loss functions of ruthenium as a function of spectral energy.

Equations (2)

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( n - k - i k ) / ( n + 1 - i k ) = R 1 2 e i θ .
θ ( h ν ) = h ν π 0 ln [ R ( E ) / R ( h ν ) ] d E E 2 - ( h ν ) 2 .