Abstract

The authors have attempted to assess the disagreement of various investigators on the optical properties of germanium in the far uv. The analyis subjected the reported data, out to about 25 eV, to the following tests: (1) an internal consistency check when possible by applying the Kronig–Kramers dispersion relations to the optical constants; (2) an evaluation of the optical oscillator strength distribution for the spectrum under study; (3) correlation of the values of Im(1/*) from the optical data with the characteristic electron energy loss spectrum for the material; and (4) evaluation of the oscillator strength sum for the electron energy loss distribution. A set of optical constants derived from the characteristic electron energy loss data is presented and discussed. Also, an estimate of the source of errors incurred in the application of the Kronig–Kramers dispersion relations are given and discussed in terms of optical data.

© 1967 Optical Society of America

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References

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  1. Om P. Rustigi, J. S. Nodvik, G. L. Weissler, Phys. Rev. 122, 1131 (1961).
    [CrossRef]
  2. S. Robin-Kandare, thesis, University of Paris (1959).
  3. R. P. Madden, Physics of Thin Films, G. Hass, Ed. (Academic Press, New York, 1962), Vol. 1, p. 123.
  4. T. Sasaki, J. Phys. Soc. Japan 18, 700 (1963).
  5. H. R. Philipp, H. E. Ehrenreich, Phys. Rev. 129, 1550 (1963).
    [CrossRef]
  6. R. de L. Kronig, J. Opt. Soc. Am. 12, 547 (1926); Ned. Tijdschr. Natnurk 9, 402 (1942); H. A. Kramers, in Atti del Congresso Internazionale di Fisici, 11–20 Settembre 1927, Como–Pavia–Roma (N. Zanichelli, Bologna, 1928), Vol. 2, p. 545.
    [CrossRef]
  7. R. E. LaVilla, H. Mendlowitz, J. Phys. 25, 114 (1964).
    [CrossRef]
  8. R. E. LaVilla, H. Mendlowitz, Phys. Rev. Letters 9, 149 (1962).
    [CrossRef]
  9. H. J. Bowlden, J. K. Wilmshurst, J. Opt. Soc. Am. 53, 1073 (1963).
    [CrossRef]
  10. D. M. Roessler, Brit. J. Appl. Phys. 16, 1119 (1965).
    [CrossRef]
  11. G. Andermann, A. Caron, D. A. Dows, J. Opt. Soc. Am. 55, 1210 (1965).
    [CrossRef]
  12. K. Kozima, W. Suëtaka, P. N. Schatz, J. Opt. Soc. Am. 56, 181 (1966).
    [CrossRef]
  13. R. E. LaVilla, H. Mendlowitz, Appl. Opt. 4, 955 (1965).
    [CrossRef]
  14. D. Beaglehole, Proc. Phys. Soc. 85, 1007 (1965).
    [CrossRef]
  15. H. R. Philipp, E. A. Taft, Phys. Rev. 113, 1002 (1959).
    [CrossRef]
  16. U. Fano, Phys. Rev. 103, 1202 (1956).
    [CrossRef]
  17. L. Marton, L. Leder, H. Mendlowitz, Advan. Electron. Electron Phys. 7, 183 (1955); H. Fröhlich, H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955); H. Hubbard, Proc. Phys. Soc. (London) A68, 441 (1955).
    [CrossRef]
  18. C. B. Wilson, Proc. Phys. Soc. (London) 76, 481 (1960).
    [CrossRef]
  19. The characteristic electron energy loss data of germanium used in this analysis is taken from N. Swanson, J. Opt. Soc. Am. 54, 1130 (1964).
    [CrossRef]
  20. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959).
  21. H. Mendlowitz, J. Opt. Soc. Am. 50, 739 (1960).
    [CrossRef]
  22. W. R. Hunter, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland Publishing Co., Amsterdam, 1966), p. 136.
  23. J. Toots, L. L. Marton (private communication) have informed us of some recent optical measurements on evaporated germanium films from about 10–25 eV Their nand kvalues are lower than those previously reported and tend to substantiate our analysis.
  24. G. S. Koster, J. C. Slater, Phys. Rev. 96, 1208 (1954).
    [CrossRef]

1966

1965

1964

1963

T. Sasaki, J. Phys. Soc. Japan 18, 700 (1963).

H. R. Philipp, H. E. Ehrenreich, Phys. Rev. 129, 1550 (1963).
[CrossRef]

H. J. Bowlden, J. K. Wilmshurst, J. Opt. Soc. Am. 53, 1073 (1963).
[CrossRef]

1962

R. E. LaVilla, H. Mendlowitz, Phys. Rev. Letters 9, 149 (1962).
[CrossRef]

1961

Om P. Rustigi, J. S. Nodvik, G. L. Weissler, Phys. Rev. 122, 1131 (1961).
[CrossRef]

1960

H. Mendlowitz, J. Opt. Soc. Am. 50, 739 (1960).
[CrossRef]

C. B. Wilson, Proc. Phys. Soc. (London) 76, 481 (1960).
[CrossRef]

1959

H. R. Philipp, E. A. Taft, Phys. Rev. 113, 1002 (1959).
[CrossRef]

1956

U. Fano, Phys. Rev. 103, 1202 (1956).
[CrossRef]

1955

L. Marton, L. Leder, H. Mendlowitz, Advan. Electron. Electron Phys. 7, 183 (1955); H. Fröhlich, H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955); H. Hubbard, Proc. Phys. Soc. (London) A68, 441 (1955).
[CrossRef]

1954

G. S. Koster, J. C. Slater, Phys. Rev. 96, 1208 (1954).
[CrossRef]

1926

Andermann, G.

Beaglehole, D.

D. Beaglehole, Proc. Phys. Soc. 85, 1007 (1965).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959).

Bowlden, H. J.

Caron, A.

Dows, D. A.

Ehrenreich, H. E.

H. R. Philipp, H. E. Ehrenreich, Phys. Rev. 129, 1550 (1963).
[CrossRef]

Fano, U.

U. Fano, Phys. Rev. 103, 1202 (1956).
[CrossRef]

Hunter, W. R.

W. R. Hunter, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland Publishing Co., Amsterdam, 1966), p. 136.

Koster, G. S.

G. S. Koster, J. C. Slater, Phys. Rev. 96, 1208 (1954).
[CrossRef]

Kozima, K.

Kronig, R. de L.

LaVilla, R. E.

R. E. LaVilla, H. Mendlowitz, Appl. Opt. 4, 955 (1965).
[CrossRef]

R. E. LaVilla, H. Mendlowitz, J. Phys. 25, 114 (1964).
[CrossRef]

R. E. LaVilla, H. Mendlowitz, Phys. Rev. Letters 9, 149 (1962).
[CrossRef]

Leder, L.

L. Marton, L. Leder, H. Mendlowitz, Advan. Electron. Electron Phys. 7, 183 (1955); H. Fröhlich, H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955); H. Hubbard, Proc. Phys. Soc. (London) A68, 441 (1955).
[CrossRef]

Madden, R. P.

R. P. Madden, Physics of Thin Films, G. Hass, Ed. (Academic Press, New York, 1962), Vol. 1, p. 123.

Marton, L.

L. Marton, L. Leder, H. Mendlowitz, Advan. Electron. Electron Phys. 7, 183 (1955); H. Fröhlich, H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955); H. Hubbard, Proc. Phys. Soc. (London) A68, 441 (1955).
[CrossRef]

Marton, L. L.

J. Toots, L. L. Marton (private communication) have informed us of some recent optical measurements on evaporated germanium films from about 10–25 eV Their nand kvalues are lower than those previously reported and tend to substantiate our analysis.

Mendlowitz, H.

R. E. LaVilla, H. Mendlowitz, Appl. Opt. 4, 955 (1965).
[CrossRef]

R. E. LaVilla, H. Mendlowitz, J. Phys. 25, 114 (1964).
[CrossRef]

R. E. LaVilla, H. Mendlowitz, Phys. Rev. Letters 9, 149 (1962).
[CrossRef]

H. Mendlowitz, J. Opt. Soc. Am. 50, 739 (1960).
[CrossRef]

L. Marton, L. Leder, H. Mendlowitz, Advan. Electron. Electron Phys. 7, 183 (1955); H. Fröhlich, H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955); H. Hubbard, Proc. Phys. Soc. (London) A68, 441 (1955).
[CrossRef]

Nodvik, J. S.

Om P. Rustigi, J. S. Nodvik, G. L. Weissler, Phys. Rev. 122, 1131 (1961).
[CrossRef]

Philipp, H. R.

H. R. Philipp, H. E. Ehrenreich, Phys. Rev. 129, 1550 (1963).
[CrossRef]

H. R. Philipp, E. A. Taft, Phys. Rev. 113, 1002 (1959).
[CrossRef]

Robin-Kandare, S.

S. Robin-Kandare, thesis, University of Paris (1959).

Roessler, D. M.

D. M. Roessler, Brit. J. Appl. Phys. 16, 1119 (1965).
[CrossRef]

Rustigi, Om P.

Om P. Rustigi, J. S. Nodvik, G. L. Weissler, Phys. Rev. 122, 1131 (1961).
[CrossRef]

Sasaki, T.

T. Sasaki, J. Phys. Soc. Japan 18, 700 (1963).

Schatz, P. N.

Slater, J. C.

G. S. Koster, J. C. Slater, Phys. Rev. 96, 1208 (1954).
[CrossRef]

Suëtaka, W.

Swanson, N.

Taft, E. A.

H. R. Philipp, E. A. Taft, Phys. Rev. 113, 1002 (1959).
[CrossRef]

Toots, J.

J. Toots, L. L. Marton (private communication) have informed us of some recent optical measurements on evaporated germanium films from about 10–25 eV Their nand kvalues are lower than those previously reported and tend to substantiate our analysis.

Weissler, G. L.

Om P. Rustigi, J. S. Nodvik, G. L. Weissler, Phys. Rev. 122, 1131 (1961).
[CrossRef]

Wilmshurst, J. K.

Wilson, C. B.

C. B. Wilson, Proc. Phys. Soc. (London) 76, 481 (1960).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959).

Advan. Electron. Electron Phys.

L. Marton, L. Leder, H. Mendlowitz, Advan. Electron. Electron Phys. 7, 183 (1955); H. Fröhlich, H. Pelzer, Proc. Phys. Soc. (London) A68, 525 (1955); H. Hubbard, Proc. Phys. Soc. (London) A68, 441 (1955).
[CrossRef]

Appl. Opt.

Brit. J. Appl. Phys.

D. M. Roessler, Brit. J. Appl. Phys. 16, 1119 (1965).
[CrossRef]

J. Opt. Soc. Am.

J. Phys.

R. E. LaVilla, H. Mendlowitz, J. Phys. 25, 114 (1964).
[CrossRef]

J. Phys. Soc. Japan

T. Sasaki, J. Phys. Soc. Japan 18, 700 (1963).

Phys. Rev.

H. R. Philipp, H. E. Ehrenreich, Phys. Rev. 129, 1550 (1963).
[CrossRef]

Om P. Rustigi, J. S. Nodvik, G. L. Weissler, Phys. Rev. 122, 1131 (1961).
[CrossRef]

H. R. Philipp, E. A. Taft, Phys. Rev. 113, 1002 (1959).
[CrossRef]

U. Fano, Phys. Rev. 103, 1202 (1956).
[CrossRef]

G. S. Koster, J. C. Slater, Phys. Rev. 96, 1208 (1954).
[CrossRef]

Phys. Rev. Letters

R. E. LaVilla, H. Mendlowitz, Phys. Rev. Letters 9, 149 (1962).
[CrossRef]

Proc. Phys. Soc.

D. Beaglehole, Proc. Phys. Soc. 85, 1007 (1965).
[CrossRef]

Proc. Phys. Soc. (London)

C. B. Wilson, Proc. Phys. Soc. (London) 76, 481 (1960).
[CrossRef]

Other

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959).

S. Robin-Kandare, thesis, University of Paris (1959).

R. P. Madden, Physics of Thin Films, G. Hass, Ed. (Academic Press, New York, 1962), Vol. 1, p. 123.

W. R. Hunter, Optical Properties and Electronic Structure of Metals and Alloys, F. Abeles, Ed. (North Holland Publishing Co., Amsterdam, 1966), p. 136.

J. Toots, L. L. Marton (private communication) have informed us of some recent optical measurements on evaporated germanium films from about 10–25 eV Their nand kvalues are lower than those previously reported and tend to substantiate our analysis.

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Figures (5)

Fig. 1
Fig. 1

A comparison of the k values of germanium, The curves:—●— was taken from Sasaki4, —○— from Philipp and Ehrenreich5, — – — from Philipp and Taft15, and the △ from Madden.3 The dashed curves are the extrapolations used and the solid curve is derived from the values calculated from the characteristic electron energy loss data. The k values beyond about 25 eV are merely shown for purposes of consistency in our computations. Their interpretation is discussed in the text.

Fig. 2
Fig. 2

A comparison of the reported n values and those calculated from the k values in Fig. 1. The solid curve is obtained from the n values calculated from the k values of P&E5 and are to be compared with their reported n values, the —○— curve. The dashed curve is obtained from the n values calculated from the composite k values of SPE and are to be compared with Sasaki’s4 reported n values, the —●— curve. The — – — curve is from the reported n values of Philipp and Taft.15

Fig. 3
Fig. 3

The comparison of the electron oscillator strength distribution, ħω Im(1/*), as a function of ΔE = (ħω). The solid circles and open circles are respectively from Sasaki4, and Philipp and Ehrenreich.5 The dashed curve is the extrapolation of these data to 35 eV. The solid curve is the characteristic electron energy loss spectrum, extrapolated to 50 eV, that was used in this computation.

Fig. 4
Fig. 4

The optical properties calculated from the characteristic electron energy loss spectrum shown in Fig. 3. The values beyond about 25 eV are merely shown for purposes of consistency in our computations. Their interpretation is discussed in the text.

Fig. 5
Fig. 5

A comparison of the n values of germanium. The curves: —●— was taken from Sasaki4, —○— from Philipp and Ehrenreich5,— – — from Philipp and Taft15, and the △ from Madden.3 The solid curve is derived from the values calculated from the characteristic electron energy loss data. The n values beyond about 25 eV are merely shown for purposes of consistency in our computations. Their interpretation is discussed in the text.

Equations (25)

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R e f = A - 2 π P 0 ω I m f d ω ω 2 - ω 0 2 ,
2 0 ω f ω I m d ω = π 2 2 ω p 2 ; ω p 2 = 4 π N e 2 m * ,
y ( ω 0 ) = 2 ω 0 π P 0 x d ω ω 2 - ω 0 2
x ( ω 0 ) = x ( ) - 2 π P 0 y ω d ω ω 2 - ω 0 2 ,
y ( ω 0 ) - y ( ω 0 ) = Δ y 0 = 2 ω 0 π Δ x P ω 0 - Δ ω ω 0 + Δ ω d ω ω 2 - ω 0 2 = lim 0 2 ω 0 π Δ x [ ω 0 - Δ ω ω 0 - + ω 0 + ω 0 + Δ ω ] d ω ω 2 - ω 0 2 - ( Δ x / π ) ln [ 1 + ( Δ ω / 2 ω 0 ) / 1 - ( Δ ω / 2 ω 0 ) ] ( - Δ x / ω 0 ) ( Δ ω / π ) for Δ ω ω 0 .
x ( ω 0 ) - x ( ω 0 ) = Δ x 0 = - 2 π Δ y P ω 0 - Δ ω ω 0 + Δ ω ω d ω ( ω 2 - ω 0 2 ) = - 2 π Δ y P ω 0 - Δ ω ω 0 + Δ ω d ln ( ω 2 - ω 0 2 )
= lim 0 - Δ y π [ ω 0 - Δ ω ω 0 - + ω 0 + ω 0 - Δ ω ] d ln ( ω 2 - ω 0 2 )
- ( Δ y / π ) ( Δ ω / ω 0 ) for Δ ω ω 0 .
Δ x 0 / Δ y 0 = Δ y / Δ x
Δ y 0 = 2 ω 0 π Δ x 0 ω 1 d ω ω 2 - ω 0 2 = Δ x π ln ( ω - ω 0 ω + ω 0 ) | 0 ω 1
- Δ x π 2 ω 1 ω 0 for ω 1 ω 0 .
Δ x 0 = - 2 Δ y π 0 ω 1 1 2 d ln ( ω 2 - ω 0 2 ) = - Δ y π ln ( ω 0 2 - ω 1 2 ω 0 2 )
+ ( Δ y / π ) ( ω 1 2 / ω 0 2 ) for ω 1 ω 0 .
Δ x 0 / Δ y 0 = ( Δ y / Δ x ) ( ω 1 / 2 ω 0 ) .
x = 1 - [ ( ω p 2 τ 2 ) / ( 1 + ω 2 τ 2 ) ] , y = ( 1 / ω ) [ ( ω p 2 τ ) / ( 1 + ω 2 τ 2 ) ] ,
Δ y 0 ( 4 ω p 2 τ / π ) ( Δ τ ω 1 / ω 0 )
Δ x 0 - ( 2 ω p 2 / π ) ( Δ τ ω 1 / ω 0 2 ) .
Δ x 0 / Δ y 0 = ( 2 ω 0 τ ) - 1 ,
Δ y 0 = 2 ω 0 π Δ x ω 2 ω 3 d ω ω 2 - ω 0 2 = 2 ω 0 π Δ x 2 ω 0 ln ( ω - ω 0 ω + ω 0 ) | ω 2 ω 3
2 ( Δ x / π ) ω 0 [ ( ω 3 - ω 2 ) / ω 3 ω 2 ] for ω 0 ω 2
Δ x 0 = 2 Δ y π ω 2 ω 3 1 2 d [ ln ( ω 2 - ω 0 2 ) ] = - Δ y π { ln [ 1 - ( ω 0 2 / ω 3 2 ) ] - ln [ 1 - ( ω 0 2 / ω 2 2 ) ] + 2 ln ( ω 3 / ω 2 ) } .
Δ x 0 Δ y / π { ω 0 2 [ ( ω 3 2 ) - 1 - ( ω 2 2 ) - 1 - 2 ln ( ω 3 / ω 2 ) } = Δ y / π { ω 0 2 [ ( ω 2 2 - ω 3 2 ) / ω 2 2 ω 3 2 ] - 2 ln ( ω 3 / ω 2 ) } .
Δ x 0 - 2 ( Δ y / π ) ( Δ ω / ω 2 ) [ 1 + ( ω 0 2 / ω 2 2 ) ] .
Δ x 0 ( 2 Δ y / π ) ( Δ ω / ω 2 )
Δ y 0 2 ( Δ x / π ) ( ω 0 Δ ω / ω 2 2 ) .

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