Abstract

The dispersive refractive index n(λ) and thickness d of thin films are usually determined from measurements of both transmission and wavelength values. Many factors can influence transmission values, leading to large errors in the calculated values of n(λ) and d. A method is presented to determine n(λ) and d in the region where k2n2 from wavelength values only. This entails obtaining two spectra, one at normal incidence and another at oblique incidence. The method yields values of n(λ) and d to an accuracy better than 1%.

© 1985 Optical Society of America

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References

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  1. A. H. Clark, in Polycrystalline and Amorphous Thin Film Devices, L. L. Kazmerski, ed. (Academic, New York, 1980), p. 135.
  2. O. S. Heavens, in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964), Vol. 2, p. 193.
  3. M. M. Koltun, Selective Optical Surfaces for Solar Energy Converters (Allerton, New York, 1981), p. 9.
  4. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing film,” J. Phys. E 9, 1002–1004 (1976).
    [CrossRef]
  5. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983).
    [CrossRef]
  6. R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
    [CrossRef]
  7. F. S. Crawford, Waves (McGraw-Hill, New York, 1968), p. 182.
  8. A. Nussbaum, R. A. Phillips, Contemporary Optics for Scientists and Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1976), p. 168.
  9. G. R. Fowles, Introduction to Modern Optics (Holt, Rinehart and Winston, New York, 1975), p. 44.

1984

R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
[CrossRef]

1983

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

1976

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Clark, A. H.

A. H. Clark, in Polycrystalline and Amorphous Thin Film Devices, L. L. Kazmerski, ed. (Academic, New York, 1980), p. 135.

Crawford, F. S.

F. S. Crawford, Waves (McGraw-Hill, New York, 1968), p. 182.

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics (Holt, Rinehart and Winston, New York, 1975), p. 44.

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Heavens, O. S.

O. S. Heavens, in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964), Vol. 2, p. 193.

Koltun, M. M.

M. M. Koltun, Selective Optical Surfaces for Solar Energy Converters (Allerton, New York, 1981), p. 9.

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

Nussbaum, A.

A. Nussbaum, R. A. Phillips, Contemporary Optics for Scientists and Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1976), p. 168.

Phillips, R. A.

A. Nussbaum, R. A. Phillips, Contemporary Optics for Scientists and Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1976), p. 168.

Swanepoel, R.

R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
[CrossRef]

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

J. Phys. E

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A simple method for the determination of the optical constants n, k and the thickness of a weakly absorbing film,” J. Phys. E 9, 1002–1004 (1976).
[CrossRef]

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

R. Swanepoel, “Determination of surface roughness and optical constants of inhomogeneous amorphous silicon films,” J. Phys. E 17, 896–903 (1984).
[CrossRef]

Other

F. S. Crawford, Waves (McGraw-Hill, New York, 1968), p. 182.

A. Nussbaum, R. A. Phillips, Contemporary Optics for Scientists and Engineers (Prentice-Hall, Englewood Cliffs, N.J., 1976), p. 168.

G. R. Fowles, Introduction to Modern Optics (Holt, Rinehart and Winston, New York, 1975), p. 44.

A. H. Clark, in Polycrystalline and Amorphous Thin Film Devices, L. L. Kazmerski, ed. (Academic, New York, 1980), p. 135.

O. S. Heavens, in Physics of Thin Films, G. Hass, R. E. Thun, eds. (Academic, New York, 1964), Vol. 2, p. 193.

M. M. Koltun, Selective Optical Surfaces for Solar Energy Converters (Allerton, New York, 1981), p. 9.

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Figures (2)

Fig. 1
Fig. 1

Transmission spectra of a 1-μm film of α-Si:H on a glass substrate for normal incidence (solid line) and an angle of incidence of 30° (broken line).

Fig. 2
Fig. 2

Plot of nii versus l/2 + Δm (○) and n00 versus l/2 (●) to determine the thickness of the film d.

Tables (1)

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Table 1 Calculations for Refractive Index

Equations (38)

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n 2 = P + ( P 2 s 2 ) 1 / 2 ,
P = 2 s T M T m T M T m + s 2 + 1 2 .
n 2 = a λ x + b .
n = b .
2 n 0 d = m λ 0 .
2 n i d cos r = m λ i ,
2 n i d = ( m + Δ m ) λ i .
cos r = m m + Δ m ,
n i = sin i sin r .
m 1 = n 01 λ 02 2 ( n 02 λ 01 n 01 λ 02 ) .
M = λ 02 2 ( λ 01 λ 02 ) ,
M = C λ 0 ( 1 + D λ 0 y ) .
m C λ 0 .
M λ 0 = D λ 0 y + C .
Δ m 1 2 λ 02 ( λ i λ 01 ) λ i ( λ 02 λ 01 ) .
m 2 λ 0 2 = A λ 0 x + B ,
A = 4 a d 2 , B = 4 b d 2 .
Δ m = [ m 2 λ 0 2 λ i 2 + A λ i 2 ( 1 λ i x 1 λ 0 x ) ] 1 / 2 m .
( l 2 + Δ m ) = 2 d n i λ i m 1 ,
n i cos r = n 0 λ i λ 0 .
cos r = λ i λ 0 ,
n i 2 ( 1 sin 2 r ) = n 0 2 λ i 2 λ 0 2 .
n i 2 n 0 2 λ i 2 λ 0 2 = sin 2 i .
n i 2 = n 0 2 + a x λ 0 x + 1 ( λ 0 λ i ) .
n 0 2 = N 2 a x λ 0 x 1 ( λ 0 + λ i ) ,
N 2 = λ 0 2 sin 2 i λ 0 2 λ i 2 .
N 2 = E λ x + b .
E a = ( 1 + x ) λ 0 + λ i λ 0 + λ i 1 + x 2 .
l 2 = 2 d n 0 λ 0 m 1 .
M λ 0 = 9.726 × 10 15 / λ 0 4.5 + 5709 .
m 2 λ 0 2 = A / λ 0 4.2 + B , A = 3.027 × 10 18 , B = 2.962 × 10 7 .
n 2 = 7.016 × 10 11 λ 4.2 + 6.865 .
N 2 = 7.952 × 10 12 λ 4.4 + 6.947 .
E / a = 3.215 .
n 2 = 2.473 × 10 12 λ 4.4 + 6.947 .
d = 1036 nm .
d = 1040 nm .
n 2 = 1.319 × 10 12 λ 4.3 + 6.890 .

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