Abstract

A method for routine, but precise measurements of refractive index is described. The method is fast and accurate. It is based on the analysis of interference fringes, and uses positions of the fringe maxima and/or minima and a precise measurement of sample thickness to extract refractive index. An extremely dense dataset of refractive index values over the entire spectral range of interest can be routinely obtained.

© 2013 Optical Society of America

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References

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  1. S. W. King and M. Milosevic, “A method to extract absorption coefficient of thin films from transmission spectra of the films on thick substrates,” J. Appl. Phys. 111, 073109 (2012).
    [CrossRef]
  2. H. B. Briggs, “Optical effects in bulk silicon and germanium,” Phys. Rev. 77, 287 (1950).
    [CrossRef]
  3. C. D. Salzburg and J. J. Villa, “Infrared refractive indexes of silicon germanium and modified selenium glass,” J. Opt. Soc. Am. 47, 244–246 (1957).
    [CrossRef]
  4. M. Cardona, W. Paul, and H. Brooks, “Dielectric constant of germanium and silicon as a function of volume,” Phys. Chem. Solids 8, 204–206 (1959).
    [CrossRef]
  5. W. Primak, “Refractive index of silicon,” Appl. Opt. 10, 759–763 (1971).
    [CrossRef]
  6. J. J. Villa, “Additional data on the refractive index of silicon,” Appl. Opt. 11, 2102–2103 (1972).
    [CrossRef]
  7. 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]
  8. B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” NASA preprint, unpublished.
  9. S. G. Kaplan, L. M. Hanssen, U. Griesman, and R. Gupta, “Fourier transform refractometry,” Proc. SPIE 3425, 203–212 (1998).
    [CrossRef]
  10. J. Cisowski, B. Jarzabek, J. Jurisik, and M. Domanski, “Direct determination of the refraction index normal dispersion for thin films of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA),” Opt. Appl. 42, 181–192 (2012).
  11. M. Milosevic, Internal Reflection and ATR Spectroscopy (Wiley, 2012).
  12. B. Tatian, “Fitting refractive-index data with the Sellmeier dispersion formula,” Appl. Opt. 23, 4477–4485 (1984).
    [CrossRef]
  13. http://RefractiveIndex.info .

2012

S. W. King and M. Milosevic, “A method to extract absorption coefficient of thin films from transmission spectra of the films on thick substrates,” J. Appl. Phys. 111, 073109 (2012).
[CrossRef]

J. Cisowski, B. Jarzabek, J. Jurisik, and M. Domanski, “Direct determination of the refraction index normal dispersion for thin films of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA),” Opt. Appl. 42, 181–192 (2012).

1998

S. G. Kaplan, L. M. Hanssen, U. Griesman, and R. Gupta, “Fourier transform refractometry,” Proc. SPIE 3425, 203–212 (1998).
[CrossRef]

1984

1976

1972

1971

1959

M. Cardona, W. Paul, and H. Brooks, “Dielectric constant of germanium and silicon as a function of volume,” Phys. Chem. Solids 8, 204–206 (1959).
[CrossRef]

1957

1950

H. B. Briggs, “Optical effects in bulk silicon and germanium,” Phys. Rev. 77, 287 (1950).
[CrossRef]

Briggs, H. B.

H. B. Briggs, “Optical effects in bulk silicon and germanium,” Phys. Rev. 77, 287 (1950).
[CrossRef]

Brooks, H.

M. Cardona, W. Paul, and H. Brooks, “Dielectric constant of germanium and silicon as a function of volume,” Phys. Chem. Solids 8, 204–206 (1959).
[CrossRef]

Cardona, M.

M. Cardona, W. Paul, and H. Brooks, “Dielectric constant of germanium and silicon as a function of volume,” Phys. Chem. Solids 8, 204–206 (1959).
[CrossRef]

Cisowski, J.

J. Cisowski, B. Jarzabek, J. Jurisik, and M. Domanski, “Direct determination of the refraction index normal dispersion for thin films of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA),” Opt. Appl. 42, 181–192 (2012).

Domanski, M.

J. Cisowski, B. Jarzabek, J. Jurisik, and M. Domanski, “Direct determination of the refraction index normal dispersion for thin films of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA),” Opt. Appl. 42, 181–192 (2012).

Frey, B. J.

B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” NASA preprint, unpublished.

Griesman, U.

S. G. Kaplan, L. M. Hanssen, U. Griesman, and R. Gupta, “Fourier transform refractometry,” Proc. SPIE 3425, 203–212 (1998).
[CrossRef]

Gupta, R.

S. G. Kaplan, L. M. Hanssen, U. Griesman, and R. Gupta, “Fourier transform refractometry,” Proc. SPIE 3425, 203–212 (1998).
[CrossRef]

Hanssen, L. M.

S. G. Kaplan, L. M. Hanssen, U. Griesman, and R. Gupta, “Fourier transform refractometry,” Proc. SPIE 3425, 203–212 (1998).
[CrossRef]

Icenogle, H. W.

Jarzabek, B.

J. Cisowski, B. Jarzabek, J. Jurisik, and M. Domanski, “Direct determination of the refraction index normal dispersion for thin films of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA),” Opt. Appl. 42, 181–192 (2012).

Jurisik, J.

J. Cisowski, B. Jarzabek, J. Jurisik, and M. Domanski, “Direct determination of the refraction index normal dispersion for thin films of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA),” Opt. Appl. 42, 181–192 (2012).

Kaplan, S. G.

S. G. Kaplan, L. M. Hanssen, U. Griesman, and R. Gupta, “Fourier transform refractometry,” Proc. SPIE 3425, 203–212 (1998).
[CrossRef]

King, S. W.

S. W. King and M. Milosevic, “A method to extract absorption coefficient of thin films from transmission spectra of the films on thick substrates,” J. Appl. Phys. 111, 073109 (2012).
[CrossRef]

Leviton, D. B.

B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” NASA preprint, unpublished.

Madison, T. J.

B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” NASA preprint, unpublished.

Milosevic, M.

S. W. King and M. Milosevic, “A method to extract absorption coefficient of thin films from transmission spectra of the films on thick substrates,” J. Appl. Phys. 111, 073109 (2012).
[CrossRef]

M. Milosevic, Internal Reflection and ATR Spectroscopy (Wiley, 2012).

Paul, W.

M. Cardona, W. Paul, and H. Brooks, “Dielectric constant of germanium and silicon as a function of volume,” Phys. Chem. Solids 8, 204–206 (1959).
[CrossRef]

Platt, B. C.

Primak, W.

Salzburg, C. D.

Tatian, B.

Villa, J. J.

Wolfe, W. L.

Appl. Opt.

J. Appl. Phys.

S. W. King and M. Milosevic, “A method to extract absorption coefficient of thin films from transmission spectra of the films on thick substrates,” J. Appl. Phys. 111, 073109 (2012).
[CrossRef]

J. Opt. Soc. Am.

Opt. Appl.

J. Cisowski, B. Jarzabek, J. Jurisik, and M. Domanski, “Direct determination of the refraction index normal dispersion for thin films of 3, 4, 9, 10-perylene tetracarboxylic dianhydride (PTCDA),” Opt. Appl. 42, 181–192 (2012).

Phys. Chem. Solids

M. Cardona, W. Paul, and H. Brooks, “Dielectric constant of germanium and silicon as a function of volume,” Phys. Chem. Solids 8, 204–206 (1959).
[CrossRef]

Phys. Rev.

H. B. Briggs, “Optical effects in bulk silicon and germanium,” Phys. Rev. 77, 287 (1950).
[CrossRef]

Proc. SPIE

S. G. Kaplan, L. M. Hanssen, U. Griesman, and R. Gupta, “Fourier transform refractometry,” Proc. SPIE 3425, 203–212 (1998).
[CrossRef]

Other

M. Milosevic, Internal Reflection and ATR Spectroscopy (Wiley, 2012).

http://RefractiveIndex.info .

B. J. Frey, D. B. Leviton, and T. J. Madison, “Temperature-dependent refractive index of silicon and germanium,” NASA preprint, unpublished.

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Figures (6)

Fig. 1.
Fig. 1.

Transmission spectrum of silicon wafer exhibits a strong high-frequency interference fringe. Note the absorption pattern characteristic of silicon embedded into the envelope of the fringe. See [1] for the spectrum of the same Si wafer without fringes.

Fig. 2.
Fig. 2.

Portion of the high-resolution spectrum of silicon wafer from Fig. 1 showing interference fringes.

Fig. 3.
Fig. 3.

Graphical extrapolation of the values from Table 1 to determine the absolute fringe ordinal number. The heavier line is a dense collection of measured data points and the thin line is the quadratic fit extrapolated down to zero frequency. The best fit is achieved for the fringe numbering choice shown in Table 1.

Fig. 4.
Fig. 4.

Graph of experimental points for refractive index of silicon (appears as solid line). The large squares represent the values of the refractive index of silicon from [3]. To minimize noise the refractive index data were averaged over seven consecutive data points and the average value was assigned to the frequency of the central data point.

Fig. 5.
Fig. 5.

Transmittance values at fringe maxima.

Fig. 6.
Fig. 6.

Zoom into the portion of the graph from Fig. 4 showing the refractive index of silicon with an unexpected level of detail. Quadratic fit based on the full spectral range from 400cm1 to 7000cm1 is also shown. The equation of the curve and the correlation coefficient for the fit are also displayed. Literature values are shown as squares, experimental data form a wiggly line and the quadratic fit is a smooth line.

Tables (1)

Tables Icon

Table 1. List of the Positions of the First Few Fringe Minima

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

T(k)=11+Fsin22πνn(ν)d,
F=4|r|2(1|r|2)2,
|r|2=(n(ν)1n(ν)+1)2,
n(ν)ddn2(ν)nAir2(ν)sin2(θ),
2πνmn(νm)d=mπ,
n(νm)=m2νmd.
n(νi)=n(νi3)+n(νi2)+n(νi1)+n(νi)+n(νi+1)+n(νi+2)+n(νi+3)7.

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