Abstract

An experimental method is introduced to measure the refractive index and its temperature dependence for wafer-shaped infrared materials over a continuous temperature range. Using a combination of Michelson interferometry, Fabry–Perot interferometry, and a temperature-controlled cryostat in a laser micrometer, refractive index values and their temperature coefficients can be measured for any specific temperature within a desired temperature range. Measurements arereported for InAs and InSb for a laser wavelength of 10.59μm.

© 2008 Optical Society of America

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References

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  1. R. N. Singh, D. P. Juyal, J. S. Bharguva, K. M. Mathur, O. S. Nagar, and A. N. Bhattacharyya, "An accurate visual method for refractive index measurement in near infrared," J. Phys. E 4, 2054-2058 (2004).
  2. D. E. Zelmon, E. A. Hanning, and P. G. Schunemann, "Refractive-index measurements and Sellmeier coefficients for zinc germanium phosphide from 2 to 9 μm with implications for phase matching in optical frequency-conversion devices," J. Opt. Soc. Am. B 18, 1307-1310 (2001).
    [CrossRef]
  3. D. E. Aspnes and A. A. Studna, "Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV," Phys. Rev. B 27, 985-1009 (1983).
    [CrossRef]
  4. Z. Huang and J. Chu, "The refractive index dispersion of Hg1-xCdxTe by infrared spectroscopic ellipsometry," Infrared Phys. 42, 77-80 (2001).
    [CrossRef]
  5. S. Su, "A rapid and accurate procedure for the determination of refractive indices of regulated asbestos minerals," Am. Mineral. 88, 1979-1982 (2003).
  6. M. Deetlefs, K. R. Sedden, and M. Shara, "Neoteric optical media for refractive index determination of gems and minerals," New J. Chem. 30, 317-326 (2006).
    [CrossRef]
  7. G. D. Gillen and S. Guha, "Refractive-index measurements of zinc germanium diphosphide at 300 K and 77 K by use of a modified Michelson interferometer," Appl. Opt. 43, 2054-2058 (2004).
    [CrossRef] [PubMed]
  8. G. D. Gillen and S. Guha, "Use of Michelson and Fabry-Perot interferometry for independent determination of the refractive index and physical thickness of wafers," Appl. Opt. 44, 344-347 (2005).
    [CrossRef] [PubMed]
  9. P. Yu and M. Cardona, "Temperature coefficient of the refractive index of diamond- and zinc-blende-type semiconductors," Phys. Rev. B 2, 3193-3197 (1970).
    [CrossRef]
  10. P. J. L. Hervé and L. K. J. Vandamme, "Emperical temperature dependence of the refractive index of semiconductors," J. Appl. Phys. 77, 5476-5477 (1995).
    [CrossRef]
  11. H. W. Icenogle, B. C. Platt, and W. L. Wolfe, "Refractive indexes and temperature coefficients of germanium and silicon," Appl. Opt. 15, 2348-2351 (1976).
    [CrossRef] [PubMed]
  12. M. Levinshtein, S. Rumyantsev, and M. Shur, Handbook Series on Semiconductor Parameters (World Scientific, 1996), Vol. 1.
    [CrossRef]
  13. G. Ghosh, "Temperature dispersion of refractive indices in semiconductors," J. Appl. Phys. 79, 9388-9389 (1996).
    [CrossRef]

2006 (1)

M. Deetlefs, K. R. Sedden, and M. Shara, "Neoteric optical media for refractive index determination of gems and minerals," New J. Chem. 30, 317-326 (2006).
[CrossRef]

2005 (1)

2004 (2)

G. D. Gillen and S. Guha, "Refractive-index measurements of zinc germanium diphosphide at 300 K and 77 K by use of a modified Michelson interferometer," Appl. Opt. 43, 2054-2058 (2004).
[CrossRef] [PubMed]

R. N. Singh, D. P. Juyal, J. S. Bharguva, K. M. Mathur, O. S. Nagar, and A. N. Bhattacharyya, "An accurate visual method for refractive index measurement in near infrared," J. Phys. E 4, 2054-2058 (2004).

2003 (1)

S. Su, "A rapid and accurate procedure for the determination of refractive indices of regulated asbestos minerals," Am. Mineral. 88, 1979-1982 (2003).

2001 (2)

1996 (1)

G. Ghosh, "Temperature dispersion of refractive indices in semiconductors," J. Appl. Phys. 79, 9388-9389 (1996).
[CrossRef]

1995 (1)

P. J. L. Hervé and L. K. J. Vandamme, "Emperical temperature dependence of the refractive index of semiconductors," J. Appl. Phys. 77, 5476-5477 (1995).
[CrossRef]

1983 (1)

D. E. Aspnes and A. A. Studna, "Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV," Phys. Rev. B 27, 985-1009 (1983).
[CrossRef]

1976 (1)

1970 (1)

P. Yu and M. Cardona, "Temperature coefficient of the refractive index of diamond- and zinc-blende-type semiconductors," Phys. Rev. B 2, 3193-3197 (1970).
[CrossRef]

Am. Mineral. (1)

S. Su, "A rapid and accurate procedure for the determination of refractive indices of regulated asbestos minerals," Am. Mineral. 88, 1979-1982 (2003).

Appl. Opt. (3)

Infrared Phys. (1)

Z. Huang and J. Chu, "The refractive index dispersion of Hg1-xCdxTe by infrared spectroscopic ellipsometry," Infrared Phys. 42, 77-80 (2001).
[CrossRef]

J. Appl. Phys. (2)

P. J. L. Hervé and L. K. J. Vandamme, "Emperical temperature dependence of the refractive index of semiconductors," J. Appl. Phys. 77, 5476-5477 (1995).
[CrossRef]

G. Ghosh, "Temperature dispersion of refractive indices in semiconductors," J. Appl. Phys. 79, 9388-9389 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. E (1)

R. N. Singh, D. P. Juyal, J. S. Bharguva, K. M. Mathur, O. S. Nagar, and A. N. Bhattacharyya, "An accurate visual method for refractive index measurement in near infrared," J. Phys. E 4, 2054-2058 (2004).

New J. Chem. (1)

M. Deetlefs, K. R. Sedden, and M. Shara, "Neoteric optical media for refractive index determination of gems and minerals," New J. Chem. 30, 317-326 (2006).
[CrossRef]

Phys. Rev. B (2)

D. E. Aspnes and A. A. Studna, "Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV," Phys. Rev. B 27, 985-1009 (1983).
[CrossRef]

P. Yu and M. Cardona, "Temperature coefficient of the refractive index of diamond- and zinc-blende-type semiconductors," Phys. Rev. B 2, 3193-3197 (1970).
[CrossRef]

Other (1)

M. Levinshtein, S. Rumyantsev, and M. Shur, Handbook Series on Semiconductor Parameters (World Scientific, 1996), Vol. 1.
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of the angle-dependent Michelson interferometry setup (top) and the temperature-dependent Fabry–Perot interferometry setup (bottom).

Fig. 2
Fig. 2

Temperature-dependent absolute refractive index for germanium and silicon (calibration materials), as well as InAs and InSb.

Fig. 3
Fig. 3

Temperature-dependent absolute refractive index for InAs from 102 to 357   K .

Fig. 4
Fig. 4

Temperature-dependent absolute refractive index for InSb from 104 to 222   K .

Tables (3)

Tables Icon

Table 1 Polynomial Fits to the Measured Temperature-Dependent Refractive Indices of Ge, Si, InAs, and InSb, Where the Temperature is in Kelvins

Tables Icon

Table 2 Calculated (1∕ n )(d n ∕d T ) Temperature Coefficients Using Measured Refractive Index Measurements over a Continuous Temperature Range, Where the Temperature is in Kelvins

Tables Icon

Table 3 Comparison of 2 n (d n ∕d T ) ValuesReported Here and Values Predicted by Ghosh [13] for Ge, Si, and InAs at a Temperature of 300 K

Equations (4)

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ϕ m ( θ ) = 4 π L λ ( n 2 sin 2 θ + 1 cos   θ ) ,
ϕ f ( θ ) = 4 π L λ n 2 sin 2 θ .
ϕ m ( θ ) ϕ f ( θ ) = 4 π L λ ( 1 cos   θ ) ,
ϕ f ( T ) = 4 π n ( T ) L ( T ) λ .

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