Abstract

Room-temperature transmittance measurements at 10.6 μm were made of germanium single-crystal samples. The samples were cut from very large doped single-crystal slabs that had been grown from +40-Ω-cm charge material of unknown purity for use as infrared windows and image-forming elements. The dependence of the absorption coefficient on sample resistivity was calculated from measured transmittances of ninety-two samples with resistivities ranging from 0.9 Ω-cm to 57 Ω-cm. Maximum transmittance at 10.6 μm was obtained for the samples that were doped to a resistivity of 5–10 Ω-cm and n-type conductivity.

© 1973 Optical Society of America

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References

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  1. P. A. Young, Appl. Opt. 10, 638 (1971).
    [Crossref] [PubMed]
  2. F. Horrigan, C. Klein, R. Rudko, D. Wilson, Microwave Mag.68 (1969).
  3. T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959), p. 6.
  4. P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 139.
  5. C. D. Salzberg, J. J. Villa, J. Opt. Soc. Am. 47, 244 (1957).
    [Crossref]

1971 (1)

1969 (1)

F. Horrigan, C. Klein, R. Rudko, D. Wilson, Microwave Mag.68 (1969).

1957 (1)

Horrigan, F.

F. Horrigan, C. Klein, R. Rudko, D. Wilson, Microwave Mag.68 (1969).

Klein, C.

F. Horrigan, C. Klein, R. Rudko, D. Wilson, Microwave Mag.68 (1969).

Kruse, P. W.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 139.

McGlauchlin, L. D.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 139.

McQuistan, R. B.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 139.

Moss, T. S.

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959), p. 6.

Rudko, R.

F. Horrigan, C. Klein, R. Rudko, D. Wilson, Microwave Mag.68 (1969).

Salzberg, C. D.

Villa, J. J.

Wilson, D.

F. Horrigan, C. Klein, R. Rudko, D. Wilson, Microwave Mag.68 (1969).

Young, P. A.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Microwave Mag. (1)

F. Horrigan, C. Klein, R. Rudko, D. Wilson, Microwave Mag.68 (1969).

Other (2)

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959), p. 6.

P. W. Kruse, L. D. McGlauchlin, R. B. McQuistan, Elements of Infrared Technology (Wiley, New York, 1962), p. 139.

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Figures (2)

Fig. 1
Fig. 1

Absorption coefficient resistivity at 10.6 μm for antimony-doped germanium single crystals grown by the natural freeze method. The triangles, open circles, shaded circles, daggers, and crosses represent samples wafered from different single-crystal bars for which the ranges of resistivities overlapped. Conductivity type was determined by a cold-probe method at liquid nitrogen temperature. Below 40 Ω-cm the samples were n-type; above 48 Ω-cm the samples were p-type. From near 42 Ω-cm to near 48 Ω-cm, the samples were neither clearly n-type nor clearly p-type. The vertical bars indicate calculated uncertainties in the absorption coefficient due to an uncertainty of ±0.1% in the transmittance on the 0–100% scale. The solid line is a hand-drawn curve that is presumed to be a reasonable fit to the data.

Fig. 2
Fig. 2

Absorption coefficient vs resistivity at 10.6 μm for stock samples of p-type conductivity. The circles represent gallium-doped samples grown by the horizontal-zone-level method; the triangles represent samples taken from several undoped single crystals grown by the horizontal-zone-level method; the squares represent several undoped samples grown by the Czochralski method. Conductivity type was determined by a cold-probe method at liquid nitrogen temperature. The lower curve has been transferred from Fig. 1, and the upper curve is presumed to be a reasonable fit to the data for the p-type crystals.

Equations (6)

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r = [ ( n - 1 ) 2 + k 2 ] / [ ( n + 1 ) 2 + k 2 ] ,
I = ( 1 - r ) 2 e - α t / ( 1 - r 2 e - 2 α t ) ,
R = r + [ ( 1 - r ) 2 r e - 2 α t / ( 1 - r 2 e - 2 α t ) ] ,
A = [ ( 1 - r ) ( 1 - e - α t ) / ( 1 - r e - α t ) ] .
α = - ( 1 / t ) ln { [ ( 1 - r ) 4 4 r 4 T 2 + 1 r 2 ] 1 / 2 - ( 1 - r ) 2 2 r 2 T } ,
r = e 2 α t + 1 2 ( 2 - R ) ± [ ( e 2 α t + 1 ) 2 4 ( 2 - R ) 2 - Re 2 α t ( 2 - R ) ] 1 / 2 .

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