Abstract

The electrical and photoconductive properties of chemically deposited PbS detectors are presented for a wide range of frequency, detector temperature, and background conditions. Emphasis is placed on those parameters (and interrelations among parameters) which may affect the system engineer’s decisions in writing a detector specification. Interactions which frequently give rise to misunderstanding as to the best utilization of detectors are discussed. Physical configurations, sizes, and mechanical tolerances achievable are presented.

© 1965 Optical Society of America

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References

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  1. R. A. Smith, Semiconductors (Cambridge Univ. Press, Cambridge, 1961), Chap. 7.
  2. Reference 1, Chap. 11.
  3. J. N. Humphrey, R. L. Petritz, Phys. Rev. 105, 1192 (1957).
    [Crossref]
  4. R. C. Jones, D. Goodwin, G. Pullan, “Standard Procedure for Testing Infrared Detectors and for Describing Their Performance”, Office of Director of Defense Research and Engineering, Washington 25, D.C. (Sept.1960).
  5. L. G. Mundie, D. D. Kirk, Natl. Bur. Std. Rept. 30-E-109 (15Aug.1952).
  6. R. L. Petritz, Phys. Rev. 104, 1508 (1956).
    [Crossref]
  7. J. F. Woods, Phys. Rev. 106, 235 (1957).
    [Crossref]
  8. F. L. Lummis, R. L. Petritz, Phys. Rev. 105, 502 (1957).
    [Crossref]
  9. R. C. Jones, Nature 170, 937 (1952); J. Opt. Soc. Am. 42, 286 (1952). Proc. IRIS 2, 9 (1957). Proc. Inst. Radio Engrs. 47, 1495 (1959).
    [Crossref]
  10. R. L. Petritz, Proc. Inst. Radio Engrs. 47, 1461 (1959).

1959 (1)

R. L. Petritz, Proc. Inst. Radio Engrs. 47, 1461 (1959).

1957 (3)

J. N. Humphrey, R. L. Petritz, Phys. Rev. 105, 1192 (1957).
[Crossref]

J. F. Woods, Phys. Rev. 106, 235 (1957).
[Crossref]

F. L. Lummis, R. L. Petritz, Phys. Rev. 105, 502 (1957).
[Crossref]

1956 (1)

R. L. Petritz, Phys. Rev. 104, 1508 (1956).
[Crossref]

1952 (1)

R. C. Jones, Nature 170, 937 (1952); J. Opt. Soc. Am. 42, 286 (1952). Proc. IRIS 2, 9 (1957). Proc. Inst. Radio Engrs. 47, 1495 (1959).
[Crossref]

Goodwin, D.

R. C. Jones, D. Goodwin, G. Pullan, “Standard Procedure for Testing Infrared Detectors and for Describing Their Performance”, Office of Director of Defense Research and Engineering, Washington 25, D.C. (Sept.1960).

Humphrey, J. N.

J. N. Humphrey, R. L. Petritz, Phys. Rev. 105, 1192 (1957).
[Crossref]

Jones, R. C.

R. C. Jones, Nature 170, 937 (1952); J. Opt. Soc. Am. 42, 286 (1952). Proc. IRIS 2, 9 (1957). Proc. Inst. Radio Engrs. 47, 1495 (1959).
[Crossref]

R. C. Jones, D. Goodwin, G. Pullan, “Standard Procedure for Testing Infrared Detectors and for Describing Their Performance”, Office of Director of Defense Research and Engineering, Washington 25, D.C. (Sept.1960).

Kirk, D. D.

L. G. Mundie, D. D. Kirk, Natl. Bur. Std. Rept. 30-E-109 (15Aug.1952).

Lummis, F. L.

F. L. Lummis, R. L. Petritz, Phys. Rev. 105, 502 (1957).
[Crossref]

Mundie, L. G.

L. G. Mundie, D. D. Kirk, Natl. Bur. Std. Rept. 30-E-109 (15Aug.1952).

Petritz, R. L.

R. L. Petritz, Proc. Inst. Radio Engrs. 47, 1461 (1959).

F. L. Lummis, R. L. Petritz, Phys. Rev. 105, 502 (1957).
[Crossref]

J. N. Humphrey, R. L. Petritz, Phys. Rev. 105, 1192 (1957).
[Crossref]

R. L. Petritz, Phys. Rev. 104, 1508 (1956).
[Crossref]

Pullan, G.

R. C. Jones, D. Goodwin, G. Pullan, “Standard Procedure for Testing Infrared Detectors and for Describing Their Performance”, Office of Director of Defense Research and Engineering, Washington 25, D.C. (Sept.1960).

Smith, R. A.

R. A. Smith, Semiconductors (Cambridge Univ. Press, Cambridge, 1961), Chap. 7.

Woods, J. F.

J. F. Woods, Phys. Rev. 106, 235 (1957).
[Crossref]

Nature (1)

R. C. Jones, Nature 170, 937 (1952); J. Opt. Soc. Am. 42, 286 (1952). Proc. IRIS 2, 9 (1957). Proc. Inst. Radio Engrs. 47, 1495 (1959).
[Crossref]

Phys. Rev. (4)

R. L. Petritz, Phys. Rev. 104, 1508 (1956).
[Crossref]

J. F. Woods, Phys. Rev. 106, 235 (1957).
[Crossref]

F. L. Lummis, R. L. Petritz, Phys. Rev. 105, 502 (1957).
[Crossref]

J. N. Humphrey, R. L. Petritz, Phys. Rev. 105, 1192 (1957).
[Crossref]

Proc. Inst. Radio Engrs. (1)

R. L. Petritz, Proc. Inst. Radio Engrs. 47, 1461 (1959).

Other (4)

R. C. Jones, D. Goodwin, G. Pullan, “Standard Procedure for Testing Infrared Detectors and for Describing Their Performance”, Office of Director of Defense Research and Engineering, Washington 25, D.C. (Sept.1960).

L. G. Mundie, D. D. Kirk, Natl. Bur. Std. Rept. 30-E-109 (15Aug.1952).

R. A. Smith, Semiconductors (Cambridge Univ. Press, Cambridge, 1961), Chap. 7.

Reference 1, Chap. 11.

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Figures (19)

Fig. 1
Fig. 1

Relative spectral response of PbS detectors at 25°C with normal and with heavy oxide doping.

Fig. 2
Fig. 2

Dimensions of a PbS detector.

Fig. 3
Fig. 3

Variation of time constant with surface resistivity of PbS at 25°C.

Fig. 4
Fig. 4

Variation of specific responsivity with surface resistivity of PbS at 25°C. Levels of oxide doping are the levels shown in Fig. 3.

Fig. 5
Fig. 5

Frequency dependence of responsivity in PbS at 25°C. Vertical marks indicate the frequency fc = 1/2πτ.

Fig. 6
Fig. 6

Theoretical curves for determining the ratio of 1/f to GR noise. Value of quantity X is determined at angular frequency ω = 1/τ (after Lummis and Petritz).

Fig. 7
Fig. 7

Frequency dependence of detectivity for various relative amounts of 1/f to G–R noise (X values), showing effect of 1/f noise on detectivity at all frequencies. All curves for X ≥ 4 reduce to the curve shown for X = 4.

Fig. 8
Fig. 8

Dependence of detectivity on detector time constant, τ, at a specified frequency ω0. Curves assume a constant value of p ¯d independent of τ. Figure 3 indicates how this variation of τ without varying p ¯d can be obtained.

Fig. 9
Fig. 9

Relative spectral response of normally doped PbS at various temperatures. (Curves are arbitrarily normalized to unity at 2.25 μ.)

Fig. 10
Fig. 10

Range of resistivities available in high-performance PbS detectors as a function of element temperature and background condition.

Fig. 11
Fig. 11

Range of time constants available in high-performance PbS detectors, as a function of element temperature and background condition.

Fig. 12
Fig. 12

Frequency dependence of responsivity of a typical PbS detector over the temperature range +25°C to −80°C (cold-background conditions).

Fig. 13
Fig. 13

Range of specific responsivity available in high-performance PbS detectors, as a function of element temperature and background condition.

Fig. 14
Fig. 14

Frequency dependence of specific noise of the PbS detector of Fig. 12, over the temperature range +25°C to −80°C (cold-background conditions). For clarity, data points at 0°C and −40°C for frequencies above 100 cps are not shown.

Fig. 15
Fig. 15

Range of specific noise available in high-performance PbS detectors, as a function of element temperature and background condition.

Fig. 16
Fig. 16

Frequency dependence of detectivity of the PbS detector of Fig. 12, over the temperature range +25°C to −80°C(cold-background conditions).

Fig. 17
Fig. 17

Maximum detectivities available in PbS detectors, as a function of element temperature and background condition, compared to the theoretical limits of detectivity under the same conditions.

Fig. 18
Fig. 18

Approximate relationship among detectivity, resistivity, and time constant for PbS under cold-background conditions.

Fig. 19
Fig. 19

Portion of a multielement array having minimum element dimensions and closest tolerances.

Equations (25)

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λ c = 1.24 / E g ,
ρ = 1 / σ = 1 / p ¯ e μ h ,
R C = ρ L / W d ,
R / = ρ / d = 1 p ¯ e μ h d .
τ = 1 / ( 2 π f c ) .
V ( f ) = V 0 / [ 1 + ( 2 π f τ ) 2 ] ½ .
V S = H V B S 1 [ 4 R L R C / ( R L + R C ) 2 ] ,
S 1 = V S H V B Δ R 4 R C Δ σ 4 σ
V S = S 1 V B W A 4 R C R L ( R C + R L ) 2 ,
R = 4 S 1 I opt R C / A .
Δ σ σ = ( Δ σ Δ p ) μ h Δ p σ = e μ h Δ p p ¯ e μ h = Δ p p ¯ ,
Δ p = H γ τ / d [ 1 + ( ω τ ) 2 ] ½ ,
S 1 = γ τ / 4 p ¯ d [ 1 + ( ω τ ) 2 ] ½ .
G [ I 2 ( total ) ] = G [ I 2 ( Johnson ) ] + G [ I 2 ( G - R ) ] + G [ I 2 ( 1 f ) ] = [ 4 k T R + 4 τ I d c 2 A p ¯ d [ 1 + ( ω τ ) 2 ] + C I d c 2 A f d ] ,
V N = N 1 V B ( Δ f A ) ½ 4 R C R L ( R C + R L ) 2 ,
N 1 = ( G [ I 2 ] A ) ½ / 4 I d c .
N 1 ( G - R + 1 f ) = [ τ 4 p ¯ d [ 1 + ( ω τ ) 2 ] + C 16 f d ] ½ .
X = N 1 ( 1 / f ) N 1 ( G - R ) | ω τ = 1 = { C / 16 f d τ / 4 p ¯ d [ 1 + ω τ ) 2 ] } ½ | ω τ = 1 = ( π p ¯ C ) ½ .
N 1 ( G - R + 1 f ) = ( τ 4 p ¯ d ) ½ [ 1 1 + ( ω τ ) 2 + X 2 2 ω τ ] ½ .
NEP = W / ( V S / V N ) .
D * = ( A Δ f ) ½ NEP = V S / V N W ( A Δ f ) ½ = V S / F N H ( Δ f A ) ½ .
D * = S 1 / N 1 = γ τ / 4 p ¯ d [ 1 + ( ω τ ) 2 ] ½ [ A k T 4 I 2 R + τ 4 p ¯ d ( 1 1 + ( ω τ ) 2 + X 2 2 ω T ) ] ½ .
D * = γ ( τ / 4 p ¯ d ) ½ .
D * ( ω , X ) D * ( ω 0 , X ) = ( [ 1 + ( ω τ ) 2 ] - 1 [ 1 + ( ω τ ) 2 ] - 1 + X 2 / 2 ω τ · ( 1 + X 2 ) ) ½ .
D * 1.4 × 10 11 ( R / ) ¼ τ ½ ,

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