Abstract

The steady-state load curve, defined as the steady-state relation between the voltage across the bolometer and the current through it, is obtained theoretically for a bolometer whose sensitive material is a semi-conductor. The derivation is based on two physical postulates: (1) The resistivity varies with the absolute temperature T according to the factor eτ/T, where τ is a constant which depends on the nature of the semi-conductor; (2) the bolometer has a steady-state temperature rise above the ambient temperature which is proportional to the power dissipated in the bolometer by the current passing through it. The results are expressed in terms of a parameter x = T0/τ, where T0 is the ambient temperature, and indicate that there is a maximum in the voltage versus current curve when the value of x is less than 14; this prediction is fully confirmed by experiment. Five sets of curves are presented which indicate the form of the relations among the voltage across, the current through, the resistance of, and the power dissipated in, the bolometer.

© 1946 Optical Society of America

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References

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  1. W. E. Forsythe, Measurement of Radiant Energy (McGraw-Hill Book Company, Inc., New York, 1937), pp. 207–210.
  2. C. H. Schlesman and F. G. Brockman, J. Opt. Soc. Am. 35, 755–760 (1945).
    [Crossref] [PubMed]
  3. F. G. Brockman, J. Opt. Soc. Am. 36, 32–35 (1946).
    [Crossref]
  4. B. H. Billings, W. L. Hyde, and E. E. Barr, J. Opt. Soc. Am. 36, 354A (1946).
  5. W. G. Langton, J. Opt. Soc. Am. 36, 355A (1946).
  6. John Strong, J. Opt. Soc. Am. 36, 355A (1946).
  7. W. H. Brattain and J. A. Becker, J. Opt. Soc. Am. 36, 354A (1946).
  8. A. H. Wilson, Semi-Conductors and Metals (Cambridge University Press, New York, 1939), pp. 44–57.
  9. Frederick Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940), pp. 186–194.
  10. R. Clark Jones, J. Opt. Soc. Am. 36, 355A (1946).

1946 (6)

F. G. Brockman, J. Opt. Soc. Am. 36, 32–35 (1946).
[Crossref]

B. H. Billings, W. L. Hyde, and E. E. Barr, J. Opt. Soc. Am. 36, 354A (1946).

W. G. Langton, J. Opt. Soc. Am. 36, 355A (1946).

John Strong, J. Opt. Soc. Am. 36, 355A (1946).

W. H. Brattain and J. A. Becker, J. Opt. Soc. Am. 36, 354A (1946).

R. Clark Jones, J. Opt. Soc. Am. 36, 355A (1946).

1945 (1)

Barr, E. E.

B. H. Billings, W. L. Hyde, and E. E. Barr, J. Opt. Soc. Am. 36, 354A (1946).

Becker, J. A.

W. H. Brattain and J. A. Becker, J. Opt. Soc. Am. 36, 354A (1946).

Billings, B. H.

B. H. Billings, W. L. Hyde, and E. E. Barr, J. Opt. Soc. Am. 36, 354A (1946).

Brattain, W. H.

W. H. Brattain and J. A. Becker, J. Opt. Soc. Am. 36, 354A (1946).

Brockman, F. G.

Clark Jones, R.

R. Clark Jones, J. Opt. Soc. Am. 36, 355A (1946).

Forsythe, W. E.

W. E. Forsythe, Measurement of Radiant Energy (McGraw-Hill Book Company, Inc., New York, 1937), pp. 207–210.

Hyde, W. L.

B. H. Billings, W. L. Hyde, and E. E. Barr, J. Opt. Soc. Am. 36, 354A (1946).

Langton, W. G.

W. G. Langton, J. Opt. Soc. Am. 36, 355A (1946).

Schlesman, C. H.

Seitz, Frederick

Frederick Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940), pp. 186–194.

Strong, John

John Strong, J. Opt. Soc. Am. 36, 355A (1946).

Wilson, A. H.

A. H. Wilson, Semi-Conductors and Metals (Cambridge University Press, New York, 1939), pp. 44–57.

J. Opt. Soc. Am. (7)

C. H. Schlesman and F. G. Brockman, J. Opt. Soc. Am. 35, 755–760 (1945).
[Crossref] [PubMed]

F. G. Brockman, J. Opt. Soc. Am. 36, 32–35 (1946).
[Crossref]

B. H. Billings, W. L. Hyde, and E. E. Barr, J. Opt. Soc. Am. 36, 354A (1946).

W. G. Langton, J. Opt. Soc. Am. 36, 355A (1946).

John Strong, J. Opt. Soc. Am. 36, 355A (1946).

W. H. Brattain and J. A. Becker, J. Opt. Soc. Am. 36, 354A (1946).

R. Clark Jones, J. Opt. Soc. Am. 36, 355A (1946).

Other (3)

W. E. Forsythe, Measurement of Radiant Energy (McGraw-Hill Book Company, Inc., New York, 1937), pp. 207–210.

A. H. Wilson, Semi-Conductors and Metals (Cambridge University Press, New York, 1939), pp. 44–57.

Frederick Seitz, Modern Theory of Solids (McGraw-Hill Book Company, Inc., New York, 1940), pp. 186–194.

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Figures (5)

Fig. 1
Fig. 1

Showing the load curves (steady-state relations between the current through and the voltage across the bolometer element) of a semi-conductor bolometer according to the postulates represented by Eqs. (1) and (2). The four curves correspond to four different choices of the parameter x = T0/τ, where T0 is the absolute ambient temperature, and where τ is the constant in Eq. (1). The curves were plotted from Eqs. (8) and (9).

Fig. 2
Fig. 2

Another plot of the load curves of a semiconductor bolometer, for the ranges of voltage and current which include the practical operating ranges of a thermistor bolometer. The voltage is plotted as the abscissa, in accordance with established practice in drawing the load curves of electronic tubes. The curves were plotted from Eqs. (15) and (16), for two values of x. The solid curve is for x = 0, and the dashed curve for x = 0.085. The labels on the abscissa should be read as 0, 0.5, and 1.0.

Fig. 3
Fig. 3

Showing the relation between the steady-state conductivity of a semi-conductor bolometer and the voltage across it. The curves were plotted from Eqs. (15) and (17) for the two values of x used in Fig. 2. The labels on the abscissa should be read as 0, 0.5, and 1.0.

Fig. 4
Fig. 4

Showing the relation between the steady-state conductivity of a semi-conductor bolometer and the current through it. The curves were plotted from Eqs. (16) and (17).

Fig. 5
Fig. 5

Showing the relation between the power dissipated in a semi-conductor bolometer and the current through it. The curves were plotted from Eqs. (15) and (18). The labels on the abscissa should read as 0, 0.5, and 1.0.

Equations (31)

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R = R 0 exp [ ( τ / T ) ( τ / T 0 ) ] ,
T T 0 = k E I .
E = I R .
x T 0 / τ .
γ R 0 / R .
γ = R 0 I E = exp ( τ T T 0 T T 0 ) = [ e E n 2 E 2 + x γ ] log γ ,
E n ( R 0 T 0 2 / k e τ ) 1 2
E E n = [ e log γ γ ( 1 x log γ ) ] 1 2 ,
I E n / R 0 = [ γ e log γ 1 x log γ ] 1 2 ,
R / R 0 = 1 / γ ,
P E n 2 / R 0 = e log γ 1 x log γ ,
log γ m = 2 1 ± ( 1 4 x ) 1 2 ,
E m = E n [ e / γ m ] 1 2 log γ m ,
log γ m = 2 1 + ( 1 4 x ) 1 2 .
E = E E m = [ γ m log γ γ ( 1 x log γ ) log 2 γ m ] 1 2 ,
I = I E m / R 0 = [ γ γ m log γ ( 1 x log γ ) log 2 γ m ] 1 2 ,
R = R / R 0 = 1 / γ ,
P = P E m 2 / R 0 = γ m log γ ( 1 x log γ ) log 2 γ m .
R = R 0 exp [ ( T 0 T ) / τ ] .
γ = R 0 I E = exp ( T T 0 τ ) = e E m 2 E 2 log γ ,
E m ( τ R 0 k e ) 1 2
E = E E m = [ e log γ γ ] 1 2 ,
I = I E m / R 0 = [ γ e log γ ] 1 2 ,
R = R / R 0 = 1 / γ ,
P = P E m 2 / R 0 = e log γ .
P m = τ / ( k e ) ,
T m T 0 = τ ,
R m = R 0 / e .
P m = T 0 2 k τ log 2 γ m γ m ,
T m T 0 = 2 x T 0 1 2 x + ( 1 4 x ) 1 2 ,
R m = R 0 / γ m ,