Abstract

A method for the determination of the optical constants of thin films based on the combination of a waveguide measurement procedure with the spectroscopic measurements made from the UV to the IR is presented. As a test material AlN thin film on sapphire substrates is investigated.

© 2006 Optical Society of America

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References

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  1. P. Arndt, R. M. A. Azzam, J. M. Bennett, J. P. Borgogno, C. K. Carniglia, W. E. Case, J. A. Dobrowolski, U. J. Gibson, T. Tuttle Hart, F. C. Ho, V. A. Hodgkin, W. P. Klapp, H. A. Macleod, E. Pelletier, M. K. Purvis, D. M. Quinn, D. H. Strome, R. Swenson, P. A. Temple, and T. F. Thonn, "Multiple determination of the optical constants of thin-film coating materials," Appl. Opt. 23, 3571-3596 (1984).
    [CrossRef] [PubMed]
  2. H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry (J. Wiley, 1999).
  3. D. Poelman and P. F. Smet, "Methods for the determination of the optical constants of thin films from single transmission measurement: a critical review," J. Phys. D 36, 1850-1857 (2003).
    [CrossRef]
  4. R. Ulrich and R. Torge, "Measurement of thin film parameters with a prism coupler," Appl. Opt. 12, 2901-2908 (1973).
    [CrossRef] [PubMed]
  5. M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin film," Appl. Phys. Lett. 16, 523-525 (1970).
    [CrossRef]
  6. E. Pelletier, F. Flory, and Y. Hu, "Optical characterization of thin films by guided modes," Appl. Opt. 28, 2918-2924 (1989).
    [CrossRef] [PubMed]
  7. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  8. R. Swanepoel, "Determination of the thickness and optical constants of amorphous silicon," J. Phys. E 16, 1214-1222 (1983).
    [CrossRef]
  9. D. A. Minkov, "Method for determining the optical constants of a thin film on a transparent substrate," J. Phys. D 22, 199-205 (1989).
    [CrossRef]

2003 (1)

D. Poelman and P. F. Smet, "Methods for the determination of the optical constants of thin films from single transmission measurement: a critical review," J. Phys. D 36, 1850-1857 (2003).
[CrossRef]

1989 (2)

D. A. Minkov, "Method for determining the optical constants of a thin film on a transparent substrate," J. Phys. D 22, 199-205 (1989).
[CrossRef]

E. Pelletier, F. Flory, and Y. Hu, "Optical characterization of thin films by guided modes," Appl. Opt. 28, 2918-2924 (1989).
[CrossRef] [PubMed]

1984 (1)

1983 (1)

R. Swanepoel, "Determination of the thickness and optical constants of amorphous silicon," J. Phys. E 16, 1214-1222 (1983).
[CrossRef]

1973 (1)

1970 (1)

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin film," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

Arndt, P.

Azzam, R. M. A.

Bennett, J. M.

Borgogno, J. P.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Carniglia, C. K.

Case, W. E.

Dakss, M. L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin film," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

Dobrowolski, J. A.

Flory, F.

Gibson, U. J.

Hart, T. Tuttle

Heidrich, P. F.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin film," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

Ho, F. C.

Hodgkin, V. A.

Hu, Y.

Klapp, W. P.

Kuhn, L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin film," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

Macleod, H. A.

McGahan, W. A.

H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry (J. Wiley, 1999).

Minkov, D. A.

D. A. Minkov, "Method for determining the optical constants of a thin film on a transparent substrate," J. Phys. D 22, 199-205 (1989).
[CrossRef]

Pelletier, E.

Poelman, D.

D. Poelman and P. F. Smet, "Methods for the determination of the optical constants of thin films from single transmission measurement: a critical review," J. Phys. D 36, 1850-1857 (2003).
[CrossRef]

Purvis, M. K.

Quinn, D. M.

Scott, B. A.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin film," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

Smet, P. F.

D. Poelman and P. F. Smet, "Methods for the determination of the optical constants of thin films from single transmission measurement: a critical review," J. Phys. D 36, 1850-1857 (2003).
[CrossRef]

Strome, D. H.

Swanepoel, R.

R. Swanepoel, "Determination of the thickness and optical constants of amorphous silicon," J. Phys. E 16, 1214-1222 (1983).
[CrossRef]

Swenson, R.

Temple, P. A.

Thonn, T. F.

Tompkins, H. G.

H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry (J. Wiley, 1999).

Torge, R.

Ulrich, R.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

Appl. Opt. (3)

Appl. Phys. Lett. (1)

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin film," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

J. Phys. D (2)

D. Poelman and P. F. Smet, "Methods for the determination of the optical constants of thin films from single transmission measurement: a critical review," J. Phys. D 36, 1850-1857 (2003).
[CrossRef]

D. A. Minkov, "Method for determining the optical constants of a thin film on a transparent substrate," J. Phys. D 22, 199-205 (1989).
[CrossRef]

J. Phys. E (1)

R. Swanepoel, "Determination of the thickness and optical constants of amorphous silicon," J. Phys. E 16, 1214-1222 (1983).
[CrossRef]

Other (2)

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).

H. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry (J. Wiley, 1999).

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Figures (7)

Fig. 1
Fig. 1

Typical angular dependence for a grating-coupled AlN waveguide at λ = 0.6328   μm for sample 1 [ sin   θ = ( l λ / Λ ) n * ] . θ, incidence angle; l, diffraction order; λ, wavelength; Λ, grating period; n * , effective refractive index.

Fig. 2
Fig. 2

Determining index and thickness of for an AlN waveguide (sample 1). λ = 632.8   nm , n c = 1.0003 , n s = 1.7659 , M = 3 , n 0 * = 2.122 , n 1 * = 2.083 , and n 2 * = 2.000 .

Fig. 3
Fig. 3

Determination of the refractive index of an AlN waveguide (sample 2) at a wavelength of λ = 632.8   nm . n f = 2.0743 ± 0.0001 .

Fig. 4
Fig. 4

Propagation of an electromagnetic wave through a homogeneous film.

Fig. 5
Fig. 5

Reflection measurements in the 175 3300   nm area.

Fig. 6
Fig. 6

Calibrated curve for AlN film in the 350 3300   nm region.

Fig. 7
Fig. 7

(a) Reflection from model thin film with n f = 2.05 and t = 4.08 . (b) n f t dependence in the case of 0.05 % error for reflection measurement.

Equations (11)

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t = λ 2 π n f 2 n * 2 × ( arctan n * 2 n c 2 n f 2 n * 2 + arctan n * 2 n s 2 n f 2 n * 2 + m π ) ,
t av = 1 M m = 0 M 1 t m ,
δ t ( n f ) = 1 M m = 0 M 1 ( t m t av ) 2 ,
R = r cf 2 + r fs 2 + 2 r cf r fs cos 2 β 1 + r cf 2 r fs 2 + 2 r cf r fs cos 2 β ,
r c f = n c cos θ 1 n f cos θ 2 n c cos θ 1 + n f cos θ 2 ,
r f s = n f cos θ 2 n s cos θ 3 n f cos θ 2 + n s cos θ 3 ,
β = 2 π λ n f t cos θ 2 .
r cf = n c - n f n c + n f , r fs = n f - n s n f + n s ,
maximum ,   if   ( 1 ) p ( n c n f ) ( n f n s ) > 0 ,
minimum , if ( 1 ) p ( n c n f ) ( n f n s ) < 0 .
ε ( n 2 , t ) = 1 ν 2 ν 1 ν 1 ν 2 [ R s ( n f , t , ν ) R 0 ( ν ) ] 2 d ν .

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