Abstract

It has been demonstrated that it is possible to control the intensity of visible and infrared light being transmitted through cadmium sulfide by controlled variations in photoelectrically induced free charge carrier densities which absorb the transmitted light. The free carrier optical absorption coefficient is extended to fit the case of photoelectrically induced free carrier absorption in semiconductors. This results in a theoretical modulation parameter which predicts the extent to which light transmission can be controlled by induced free carrier absorption. An experimental technique is presented which demonstrates that photoelectrically induced variations in the density of free carriers in CdS can indeed bring about a consequential control of the light transmission. Complete control over the transmission, in addition to light amplification by stimulated absorption, is demonstrated in CdS for both infrared and visible light between 0.6 μ and 4.0 μ. Theoretically computed and experimentally observed values of modulation are in fair agreement, considering the limitation of the theory and the nature of the solid. The observed transmitted wavelength dependence in CdS is discussed on the basis of both the free carrier absorption theory and various photoconductivity mechanisms, and it is shown to be reasonably consistent with modern theory.

© 1966 Optical Society of America

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References

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  1. H. A. Lorentz, Theory of Electrons (Teubner, Leipzig, 1906).
  2. F. Seitz, Modern Theory of Solids (McGraw-Hill, New York, 1940), p. 633.
  3. R. M. Grant, “Photoelectrically Induced Free Carrier Modulation and Amplification of Light in Semiconductors”, Ph.D. dissertation, Technical University, Delft, The Netherlands, 1964.
  4. W. G. Spitzer, “Infrared Properties of Semiconductors”, Ph.D. dissertation, Purdue University, Lafayette, Ind., 1957.
  5. R. H. Bube, Photoconductivity of Solids (Wiley, New York, 1960).
  6. N. J. Harrick, Phys. Rev. 125, 1165 (1962).
    [CrossRef]
  7. T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959).
  8. M. Becker, Ph.D. dissertation Purdue University, Lafayette, Ind., 1953.
  9. R. J. Collins, Ph.D. dissertation, Purdue University, Lafayette, Ind., 1953.
  10. H. Y. Fan, W. Spitzer, R. J. Collins, Phys. Rev. 101, 566 (1956).
    [CrossRef]
  11. R. H. Bube, Photoconductivity of Solids (Wiley, New York, 1960), p. 64.
  12. A. C. Aten, Philips Research Laboratories, Waalre, The Netherlands, private communication.
  13. R. Fredrichs, Phys. Rev. 72, 594 (1947).
    [CrossRef]
  14. A. B. Francis, A. I. Carlson, J. Opt. Soc. Am. 50, 119 (1960).
    [CrossRef]
  15. D. Dutton, Tech. Rept. 14, Institute of Optics, University of Rochester, Rochester, N. Y., 1958.
  16. W. C. Dunlap, An Introduction to Semiconductors (Wiley, New York, 1960), p. 311.
  17. J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
    [CrossRef]
  18. J. J. Brophy, Phys. Rev. 122, 26 (1961).
    [CrossRef]
  19. F. I. Kreingoldd, Fiz. Tverd. Tela 4, 3415 (1962); Soviet Phys.—Solid State, 4, 2499 (1963).
  20. J. F. Hall, W. F. C. Ferguson, J. Opt. Soc. Am. 45, 714 (1955).
    [CrossRef]
  21. J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
    [CrossRef]
  22. G. W. S. Abbey, “Near Infrared Transmission of CdS”, Air Force Inst. of Tech. Rept No. G. E.-59-B-1 (1959).
  23. D. C. Reynolds, J. Opt. Soc. Am. 45, 136 (1955).
    [CrossRef]
  24. A. Halperin, G. F. J. Garlich, Proc. Phys. Soc. (London), B68, 758 (1956).
  25. T. S. Moss, Optical Properties of Semiconductors (Butterworths, London1959), p. 220.
  26. W. W. Piper, D. T. F. Marple, J. Appl. Phys. Suppl. 32, 2237 (1961).
    [CrossRef]
  27. T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959), p. 217.
  28. J. F. Hall, W. F. C. Ferguson, J. Opt. Soc. Am. 45, 714 (1955).
    [CrossRef]
  29. E. A. Taft, M. H. Hebb, J. Opt. Soc. Am. 42, 249 (1952).
    [CrossRef]
  30. B. A. Kulp, R. H. Kelley, J. Appl. Phys. 32, 1290 (1961).
    [CrossRef]

1962

N. J. Harrick, Phys. Rev. 125, 1165 (1962).
[CrossRef]

F. I. Kreingoldd, Fiz. Tverd. Tela 4, 3415 (1962); Soviet Phys.—Solid State, 4, 2499 (1963).

1961

W. W. Piper, D. T. F. Marple, J. Appl. Phys. Suppl. 32, 2237 (1961).
[CrossRef]

B. A. Kulp, R. H. Kelley, J. Appl. Phys. 32, 1290 (1961).
[CrossRef]

J. J. Brophy, Phys. Rev. 122, 26 (1961).
[CrossRef]

1960

J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
[CrossRef]

A. B. Francis, A. I. Carlson, J. Opt. Soc. Am. 50, 119 (1960).
[CrossRef]

J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
[CrossRef]

1956

H. Y. Fan, W. Spitzer, R. J. Collins, Phys. Rev. 101, 566 (1956).
[CrossRef]

A. Halperin, G. F. J. Garlich, Proc. Phys. Soc. (London), B68, 758 (1956).

1955

1952

1947

R. Fredrichs, Phys. Rev. 72, 594 (1947).
[CrossRef]

Abbey, G. W. S.

G. W. S. Abbey, “Near Infrared Transmission of CdS”, Air Force Inst. of Tech. Rept No. G. E.-59-B-1 (1959).

Aten, A. C.

A. C. Aten, Philips Research Laboratories, Waalre, The Netherlands, private communication.

Becker, M.

M. Becker, Ph.D. dissertation Purdue University, Lafayette, Ind., 1953.

Brophy, J. J.

J. J. Brophy, Phys. Rev. 122, 26 (1961).
[CrossRef]

J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
[CrossRef]

J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
[CrossRef]

Bube, R. H.

R. H. Bube, Photoconductivity of Solids (Wiley, New York, 1960), p. 64.

R. H. Bube, Photoconductivity of Solids (Wiley, New York, 1960).

Carlson, A. I.

A. B. Francis, A. I. Carlson, J. Opt. Soc. Am. 50, 119 (1960).
[CrossRef]

Collins, R. J.

H. Y. Fan, W. Spitzer, R. J. Collins, Phys. Rev. 101, 566 (1956).
[CrossRef]

R. J. Collins, Ph.D. dissertation, Purdue University, Lafayette, Ind., 1953.

Dunlap, W. C.

W. C. Dunlap, An Introduction to Semiconductors (Wiley, New York, 1960), p. 311.

Dutton, D.

D. Dutton, Tech. Rept. 14, Institute of Optics, University of Rochester, Rochester, N. Y., 1958.

Fan, H. Y.

H. Y. Fan, W. Spitzer, R. J. Collins, Phys. Rev. 101, 566 (1956).
[CrossRef]

Ferguson, W. F. C.

Francis, A. B.

A. B. Francis, A. I. Carlson, J. Opt. Soc. Am. 50, 119 (1960).
[CrossRef]

Fredrichs, R.

R. Fredrichs, Phys. Rev. 72, 594 (1947).
[CrossRef]

Garlich, G. F. J.

A. Halperin, G. F. J. Garlich, Proc. Phys. Soc. (London), B68, 758 (1956).

Grant, R. M.

R. M. Grant, “Photoelectrically Induced Free Carrier Modulation and Amplification of Light in Semiconductors”, Ph.D. dissertation, Technical University, Delft, The Netherlands, 1964.

Hall, J. F.

Halperin, A.

A. Halperin, G. F. J. Garlich, Proc. Phys. Soc. (London), B68, 758 (1956).

Harrick, N. J.

N. J. Harrick, Phys. Rev. 125, 1165 (1962).
[CrossRef]

Hebb, M. H.

Kelley, R. H.

B. A. Kulp, R. H. Kelley, J. Appl. Phys. 32, 1290 (1961).
[CrossRef]

Kreingoldd, F. I.

F. I. Kreingoldd, Fiz. Tverd. Tela 4, 3415 (1962); Soviet Phys.—Solid State, 4, 2499 (1963).

Kulp, B. A.

B. A. Kulp, R. H. Kelley, J. Appl. Phys. 32, 1290 (1961).
[CrossRef]

Lorentz, H. A.

H. A. Lorentz, Theory of Electrons (Teubner, Leipzig, 1906).

Marple, D. T. F.

W. W. Piper, D. T. F. Marple, J. Appl. Phys. Suppl. 32, 2237 (1961).
[CrossRef]

Moss, T. S.

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London1959), p. 220.

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959).

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959), p. 217.

Piper, W. W.

W. W. Piper, D. T. F. Marple, J. Appl. Phys. Suppl. 32, 2237 (1961).
[CrossRef]

Reynolds, D. C.

Robinson, R. J.

J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
[CrossRef]

J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
[CrossRef]

Seitz, F.

F. Seitz, Modern Theory of Solids (McGraw-Hill, New York, 1940), p. 633.

Spitzer, W.

H. Y. Fan, W. Spitzer, R. J. Collins, Phys. Rev. 101, 566 (1956).
[CrossRef]

Spitzer, W. G.

W. G. Spitzer, “Infrared Properties of Semiconductors”, Ph.D. dissertation, Purdue University, Lafayette, Ind., 1957.

Taft, E. A.

Fiz. Tverd. Tela

F. I. Kreingoldd, Fiz. Tverd. Tela 4, 3415 (1962); Soviet Phys.—Solid State, 4, 2499 (1963).

J. Appl. Phys.

B. A. Kulp, R. H. Kelley, J. Appl. Phys. 32, 1290 (1961).
[CrossRef]

J. Appl. Phys. Suppl.

W. W. Piper, D. T. F. Marple, J. Appl. Phys. Suppl. 32, 2237 (1961).
[CrossRef]

J. Opt. Soc. Am.

Phys. Rev.

H. Y. Fan, W. Spitzer, R. J. Collins, Phys. Rev. 101, 566 (1956).
[CrossRef]

J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
[CrossRef]

J. J. Brophy, Phys. Rev. 122, 26 (1961).
[CrossRef]

N. J. Harrick, Phys. Rev. 125, 1165 (1962).
[CrossRef]

J. J. Brophy, R. J. Robinson, Phys. Rev. 118, 959 (1960).
[CrossRef]

R. Fredrichs, Phys. Rev. 72, 594 (1947).
[CrossRef]

Proc. Phys. Soc. (London)

A. Halperin, G. F. J. Garlich, Proc. Phys. Soc. (London), B68, 758 (1956).

Other

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London1959), p. 220.

R. H. Bube, Photoconductivity of Solids (Wiley, New York, 1960), p. 64.

A. C. Aten, Philips Research Laboratories, Waalre, The Netherlands, private communication.

D. Dutton, Tech. Rept. 14, Institute of Optics, University of Rochester, Rochester, N. Y., 1958.

W. C. Dunlap, An Introduction to Semiconductors (Wiley, New York, 1960), p. 311.

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959).

M. Becker, Ph.D. dissertation Purdue University, Lafayette, Ind., 1953.

R. J. Collins, Ph.D. dissertation, Purdue University, Lafayette, Ind., 1953.

H. A. Lorentz, Theory of Electrons (Teubner, Leipzig, 1906).

F. Seitz, Modern Theory of Solids (McGraw-Hill, New York, 1940), p. 633.

R. M. Grant, “Photoelectrically Induced Free Carrier Modulation and Amplification of Light in Semiconductors”, Ph.D. dissertation, Technical University, Delft, The Netherlands, 1964.

W. G. Spitzer, “Infrared Properties of Semiconductors”, Ph.D. dissertation, Purdue University, Lafayette, Ind., 1957.

R. H. Bube, Photoconductivity of Solids (Wiley, New York, 1960).

G. W. S. Abbey, “Near Infrared Transmission of CdS”, Air Force Inst. of Tech. Rept No. G. E.-59-B-1 (1959).

T. S. Moss, Optical Properties of Semiconductors (Butterworths, London, 1959), p. 217.

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Figures (9)

Fig. 1
Fig. 1

Absorption coefficient vs thickness diagram for a semiconductor free carrier modulator.

Fig. 2
Fig. 2

Schematic diagram of free carrier absorption experiment.

Fig. 3
Fig. 3

Cadmium sulfide transmission and absorption characteristics.

Fig. 4
Fig. 4

Measured free carrier modulation as a function of irradiance for alternating and direct excitation light.

Fig. 5
Fig. 5

Percentage free carrier modulation in cadmium sulfide as a function of λ1 obtained for various values of irradiance, Ψ2.

Fig. 6
Fig. 6

Experimental and theoretical comparison of −ln(1 − M) vs λ12.

Fig. 7
Fig. 7

The family of M1) curves for the values of irradiance indicated in Fig. 6.

Fig. 8
Fig. 8

M12) for irradiance levels of 165 mW/cm2 (upper curve) and 117 mW/cm2 (lower curve). ΔM = 0.26; ΔΨ2 = 48.

Fig. 9
Fig. 9

Free carrier modulation excitation irradiance characteristic curves (not to scale).

Equations (36)

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α ( ω ) = σ 0 c 0 N 1 1 + [ ω 2 / ( e 2 / m 2 μ d 2 ) ] ,
α ( λ 1 ) = e 2 4 π 2 c 3 m * 2 μ d 2 0 N σ 0 λ 1 2
α ( λ 1 ) = β n λ 1 2 ,
β = e 3 / 4 π 2 c 3 m * μ d 0 N ,
J 1 0 ( λ 1 ) = J 1 ( λ 1 ) e - α 0 l , = J 1 ( λ 1 ) e β σ 0 λ 1 2 l ,
α ( x ) = α ( x ) + α 0 ,
α ( x ) = β n ( x ) λ 1 2
n ( x ) = n ( o ) e - H 2 x ,
Δ J 1 = - α ( x ) J 1 Δ x ,
J 1 = J 1 e - 0 l α ( x ) d x
T = e - 0 l α ( x ) d x e - α 0 1 ,
e - 0 l α ( x ) d x
α ( x ) = β n ( o ) e - H 2 x λ 1 2 ,
T = e - β n ( o ) λ 1 2 0 l e - H 2 x d x e - α 0 l
T = e - β n ( o ) H 2 ( 1 - e - H 2 l ) λ 1 2 e - α 0 l .
N * = g τ = N ν τ ¯ ,
N * = 0 l n ( x ) d x ,
N * = n ( 0 ) H 2 ( 1 - e - H 2 l ) .
n ( 0 ) = H 2 1 - e - H 2 1 N ν τ ¯ .
Ψ 2 = N h c λ 2
N = Ψ 2 λ 2 h c .
n ( 0 ) = ( H 2 1 - e - H 2 l ) Ψ 2 λ 2 ν τ ¯ h c .
T 1 = e - β Ψ 2 λ 2 ν τ ¯ λ 1 2 / h c e - α 0 l
T 1 0 = e - α 0 l ,
M * = T 1 0 - T 1 T 1 0 ,
M * = 1 - e - β Ψ 2 λ 2 ν τ ¯ / h c λ 1 2
= 1 - e - β n λ 1 2 ,
n = Ψ 2 λ 2 ν τ ¯ h c
M * = 1 - e - ν τ ¯ Ψ 2 λ 2 e 3 λ 1 2 4 π 2 h c 4 m * 2 μ d 0 N
M * = 1 - e - ξ λ 1 2 ,
ξ ν τ ¯ Ψ 2 λ 2 e 3 4 π 2 h c 4 m * 2 μ d 0 N .
M theor = 2 ( 2 ) ½ M * theor .
μ = [ Δ Ψ 1 Δ Ψ 2 ] λ 1 = [ Ψ 1 Ψ 2 ] λ 1 ,
Δ Ψ 2 = ( Ψ 2 ) P 4 - ( Ψ 2 ) P 3 = 165 - 152 = 13 mW / cm 2
( M P 4 - M P 3 ) λ 1 = 2 μ = 0.20.
μ = ( Δ Ψ 1 Δ Ψ 2 ) λ 1 = 2 μ = 100.

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