Abstract

The refractive index and extinction coefficient of purple K3Sb film prepared on a quartz substrate were determined from the transmittance data in the photon-energy region 0.5–6.2 eV through the Kramers–Kronig (KK) dispersion analysis. The interference effect due to the internal reflection of the light in the substrate was eliminated by taking the average value over the substrate thickness. The refractive index in the low-photon-energy region is nearly equal to 2.0, e.g., 1.97 at 0.5 eV and 2.17 at 0.9 eV. The static refractive index evaluated from the KK integral of the imaginary part of complex dielectric constant up to 10 eV is 1.98. The spectrum of the refractive index shows some structures corresponding to the structure in the transmission spectrum; the peak at 1.05 eV corresponds to the start of the fundamental absorption, the sharp decrease from the shoulder at 2.1 eV to the minimum at 2.75 eV corresponds to the first strong absorption band, and the well-defined peak at 3.35 eV corresponds to the sharp increase of the absorption. Calculated reflectivity using the refractive index and extinction coefficient obtained from the KK dispersion analysis explains quite well the features of the measured reflectivity in the 2.7–5.8-eV range.

© 1972 Optical Society of America

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References

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  1. A. H. Sommer, Photoemissive Materials (Wiley, New York, 1968).
  2. W. E. Spicer, Phys. Rev. 112, 114 (1958).
    [CrossRef]
  3. E. A. Taft and H. R. Philipp, Phys. Rev. 115, 1583 (1959).
    [CrossRef]
  4. See, for example, W. F. Krolikowski, Phys. Rev. 185, 882 (1969).
    [CrossRef]
  5. J. A. Van Vechten, Phys. Rev. 182, 891 (1969).
    [CrossRef]
  6. S. H. Wemple and M. DiDomenico, Phys. Rev. B 3, 1338 (1971).
    [CrossRef]
  7. P. O. Nilsson, Appl. Opt. 7, 435 (1968).
    [CrossRef] [PubMed]
  8. J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), p. 511.
  9. T. S. Moss, Optical Properties of Semi-Conductors (Butterworths, London, 1959), p. 11.
  10. F. Abelès and M. L. Thèye, Surface Sci. 5, 325 (1966).
    [CrossRef]
  11. A. H. Sommer and W. H. McCarroll, J. Appl. Phys. 37, 174 (1966).
    [CrossRef]
  12. M. Hagino and T. Takahashi, J. Appl. Phys. 37, 3741 (1966).
    [CrossRef]
  13. R. J. Powell and W. E. Spicer, Phys. Rev. B 2, 2182 (1970).
    [CrossRef]
  14. H. Miyazawa, J. Phys. Soc. Japan 8, 169 (1953).
    [CrossRef]
  15. H. Shiraki, Japan. J. Appl. Phys. 4, 238 (1965).
    [CrossRef]
  16. G. Wallis, Ann. Phys. (N. Y.) 6, 401 (1956).

1971 (1)

S. H. Wemple and M. DiDomenico, Phys. Rev. B 3, 1338 (1971).
[CrossRef]

1970 (1)

R. J. Powell and W. E. Spicer, Phys. Rev. B 2, 2182 (1970).
[CrossRef]

1969 (2)

See, for example, W. F. Krolikowski, Phys. Rev. 185, 882 (1969).
[CrossRef]

J. A. Van Vechten, Phys. Rev. 182, 891 (1969).
[CrossRef]

1968 (1)

1966 (3)

F. Abelès and M. L. Thèye, Surface Sci. 5, 325 (1966).
[CrossRef]

A. H. Sommer and W. H. McCarroll, J. Appl. Phys. 37, 174 (1966).
[CrossRef]

M. Hagino and T. Takahashi, J. Appl. Phys. 37, 3741 (1966).
[CrossRef]

1965 (1)

H. Shiraki, Japan. J. Appl. Phys. 4, 238 (1965).
[CrossRef]

1959 (1)

E. A. Taft and H. R. Philipp, Phys. Rev. 115, 1583 (1959).
[CrossRef]

1958 (1)

W. E. Spicer, Phys. Rev. 112, 114 (1958).
[CrossRef]

1956 (1)

G. Wallis, Ann. Phys. (N. Y.) 6, 401 (1956).

1953 (1)

H. Miyazawa, J. Phys. Soc. Japan 8, 169 (1953).
[CrossRef]

Abelès, F.

F. Abelès and M. L. Thèye, Surface Sci. 5, 325 (1966).
[CrossRef]

DiDomenico, M.

S. H. Wemple and M. DiDomenico, Phys. Rev. B 3, 1338 (1971).
[CrossRef]

Hagino, M.

M. Hagino and T. Takahashi, J. Appl. Phys. 37, 3741 (1966).
[CrossRef]

Krolikowski, W. F.

See, for example, W. F. Krolikowski, Phys. Rev. 185, 882 (1969).
[CrossRef]

McCarroll, W. H.

A. H. Sommer and W. H. McCarroll, J. Appl. Phys. 37, 174 (1966).
[CrossRef]

Miyazawa, H.

H. Miyazawa, J. Phys. Soc. Japan 8, 169 (1953).
[CrossRef]

Moss, T. S.

T. S. Moss, Optical Properties of Semi-Conductors (Butterworths, London, 1959), p. 11.

Nilsson, P. O.

Philipp, H. R.

E. A. Taft and H. R. Philipp, Phys. Rev. 115, 1583 (1959).
[CrossRef]

Powell, R. J.

R. J. Powell and W. E. Spicer, Phys. Rev. B 2, 2182 (1970).
[CrossRef]

Shiraki, H.

H. Shiraki, Japan. J. Appl. Phys. 4, 238 (1965).
[CrossRef]

Sommer, A. H.

A. H. Sommer and W. H. McCarroll, J. Appl. Phys. 37, 174 (1966).
[CrossRef]

A. H. Sommer, Photoemissive Materials (Wiley, New York, 1968).

Spicer, W. E.

R. J. Powell and W. E. Spicer, Phys. Rev. B 2, 2182 (1970).
[CrossRef]

W. E. Spicer, Phys. Rev. 112, 114 (1958).
[CrossRef]

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), p. 511.

Taft, E. A.

E. A. Taft and H. R. Philipp, Phys. Rev. 115, 1583 (1959).
[CrossRef]

Takahashi, T.

M. Hagino and T. Takahashi, J. Appl. Phys. 37, 3741 (1966).
[CrossRef]

Thèye, M. L.

F. Abelès and M. L. Thèye, Surface Sci. 5, 325 (1966).
[CrossRef]

Van Vechten, J. A.

J. A. Van Vechten, Phys. Rev. 182, 891 (1969).
[CrossRef]

Wallis, G.

G. Wallis, Ann. Phys. (N. Y.) 6, 401 (1956).

Wemple, S. H.

S. H. Wemple and M. DiDomenico, Phys. Rev. B 3, 1338 (1971).
[CrossRef]

Ann. Phys. (N. Y.) (1)

G. Wallis, Ann. Phys. (N. Y.) 6, 401 (1956).

Appl. Opt. (1)

J. Appl. Phys. (2)

A. H. Sommer and W. H. McCarroll, J. Appl. Phys. 37, 174 (1966).
[CrossRef]

M. Hagino and T. Takahashi, J. Appl. Phys. 37, 3741 (1966).
[CrossRef]

J. Phys. Soc. Japan (1)

H. Miyazawa, J. Phys. Soc. Japan 8, 169 (1953).
[CrossRef]

Japan. J. Appl. Phys. (1)

H. Shiraki, Japan. J. Appl. Phys. 4, 238 (1965).
[CrossRef]

Phys. Rev. (4)

W. E. Spicer, Phys. Rev. 112, 114 (1958).
[CrossRef]

E. A. Taft and H. R. Philipp, Phys. Rev. 115, 1583 (1959).
[CrossRef]

See, for example, W. F. Krolikowski, Phys. Rev. 185, 882 (1969).
[CrossRef]

J. A. Van Vechten, Phys. Rev. 182, 891 (1969).
[CrossRef]

Phys. Rev. B (2)

S. H. Wemple and M. DiDomenico, Phys. Rev. B 3, 1338 (1971).
[CrossRef]

R. J. Powell and W. E. Spicer, Phys. Rev. B 2, 2182 (1970).
[CrossRef]

Surface Sci. (1)

F. Abelès and M. L. Thèye, Surface Sci. 5, 325 (1966).
[CrossRef]

Other (3)

J. A. Stratton, Electromagnetic Theory (McGraw–Hill, New York, 1941), p. 511.

T. S. Moss, Optical Properties of Semi-Conductors (Butterworths, London, 1959), p. 11.

A. H. Sommer, Photoemissive Materials (Wiley, New York, 1968).

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Figures (7)

Fig. 1
Fig. 1

Sample arrangement on a transparent substrate.

Fig. 2
Fig. 2

Integration path for KK dispersion relation between amplitude transmittance and phase-shift angle.

Fig. 3
Fig. 3

Typical transmission spectrum of purple K3Sb; K3Sb No. 37, thickness 84 μm.

Fig. 4
Fig. 4

Calculated reflectivity of purple K3Sb using n and k for the case of the extrapolation in which high-energy optical density is reduced linearly with photon energy from the value at 6.2 eV to zero at 16.0 eV. A fit of the measured relative reflectivity to the calculated reflectivity at 3.6 eV gives the dashed curve. The dashed curve is compared with the calculated reflectivity spectrum.

Fig. 5
Fig. 5

Refractive index n and extinction coefficient k of purple K3Sb calculated by appling the KK relation to the transmittance data. Extrapolation of the high-energy optical density is the same as for Fig. 4.

Fig. 6
Fig. 6

Absorption coefficient of purple K3Sb from the extinction coefficient.

Fig. 7
Fig. 7

Square root of the effective dielectric constant eff ( E ) 1 2 of purple K3Sb calculated from the dispersion of the real part 1 and imaginary part 2 of the complex dielectric constant, by use of

Equations (15)

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E 0 + E 1 = E + 2 + E - 2 , E 0 - E 1 = Z 12 ( E + 2 - E - 2 ) , E + 2 exp ( i k 2 d ) + E - 2 exp ( - i k 2 d ) = E + 3 exp ( i k 3 d ) + E - 3 exp ( - i k 3 d ) , E + 2 exp ( i k 2 d ) - E - 2 exp ( - i k 2 d ) = Z 23 ( E + 3 exp ( i k 3 d ) - E - 3 exp ( - i k 3 d ) ) , E + 3 exp ( i k 3 ( d + D ) ) + E - 3 exp ( - i k 3 ( d + D ) ) = E 4 exp ( i k 4 ( d + D ) ) , E + 3 exp ( i k 3 ( d + D ) ) - E - 3 exp ( - i k 3 ( d + D ) ) = Z 34 E 4 exp ( i k 4 ( d + D ) ) ,
t = E 4 E 0 = 8 exp ( - i k 1 ( d + D ) + i k 2 d + i k 3 D ) ( 1 + Z 12 ) ( 1 + Z 23 ) ( 1 + Z 34 ) × 1 ( 1 + i Z i exp ( i θ i ) ) ,
r = E 1 E 0 = R 12 1 2 exp ( i δ 12 ) ( 1 + i Z i exp ( i θ i ) ) ( 1 + i Z i exp ( i θ i ) ) ,
Z 1 = ( R 12 R 23 ) 1 2 X ,             Z 2 = ( R 23 R 34 ) 1 2 ,             Z 3 = ( R 34 R 12 ) 1 2 X , θ 1 = 2 n d ω / c + δ 12 + δ 23 ,             θ 2 = 2 n s D ω / c + δ 23 , θ 3 = 2 n d ω / c + 2 n s D ω / c + δ 12 , X = exp ( - 2 k d ω / c ) , δ 12 = tan - 1 ( - 2 k / - ( n 2 + k 2 - 1 ) ) δ 23 = tan - 1 ( 2 n s k / ( n 2 + k 2 - n s 2 ) ) , Z 1 , 3 = Z 1 , 3 / R 12 ,             Z 2 = Z 2 ,             θ 1 , 3 = θ 1 , 3 - 2 δ 12 ,             θ 2 = θ 2 .
T ¯ = ( 1 - R 12 ) ( 1 - R 23 ) ( 1 - R 34 ) × ( 1 + k 2 / n 2 ) X / ( Y 1 - Y 2 ) ,
R ¯ = R 12 [ ( Y 1 + Y 2 ) - 2 ( Y 3 Y 3 + Y 4 Y 4 ) / Y 1 ] / × ( Y 1 - Y 2 ) .
2 ( Z 1 cos θ 1 - Z 2 Z 3 cos ( θ 1 - 2 δ 23 ) )
2 n d = m λ ( transmittance maxima ) , 2 n d = ( m + 1 2 ) λ ( transmittance minima ) ,
E + 3 / E 0 = t exp ( i φ ) ; E + 3 E 0 = 4 exp ( i ( k 2 - k 3 ) d ) ( 1 + Z 12 ) ( 1 + Z 23 ) 1 1 + i Z i exp ( i θ i ) = t exp ( i φ ) .
t ¯ = [ T ¯ / ( ( 1 - R 34 ) n s ) ( 1 - Y 2 / Y 1 ) ] 1 2 ,
φ ¯ = ( n - n s ) d ω / c - ( φ 1 + φ 2 + φ 3 ) ,
φ 1 = tan - 1 ( k / ( n + 1 ) ) ,             φ 2 = tan - 1 ( - k n s / ( n 2 + k 2 + n n s ) ) , φ 3 = tan - 1 ( Z 1 sin θ 1 / ( 1 + Z 1 cos θ 1 ) ) .
φ ¯ ( ω 0 ) = ( n ( ) - n s ( ) ) d ω 0 / c - 1 π 0 d ln t ¯ d ω ln | ω + ω 0 ω - ω 0 | d ω .
t ¯ = [ T / ( ( 1 - R 34 ) n s ) ] 1 2 .
eff ( E ) = 1 + 2 / π 0 E ( 2 ( E ) / E ) d E ,