Abstract

Recent improvements in commercial silicon photodiodes and operational amplifiers permit electrical noise to be reduced to an equivalent of 0.1 fA of photocurrent when a measurement time of 400 s is used. This is equivalent to a photocurrent resulting from fewer than 800 photons/s, and it implies a dynamic range of 14 orders of magnitude for a detector circuit. We explain the circuit theory, paying particular attention to the measurement bandwidth, the causes of noise and drift, and the proper selection of circuit components. These optical radiation detectors complement the primary radiometric standards. These detectors may replace photomultiplier tubes that have been used traditionally and or that were too costly to be used.

© 1991 Optical Society of America

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References

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  1. G. Eppeldauer, “Measurement of very low light intensities by photovoltaic cells,” in Eleventh International Symposium on Photon Detectors, Weimar (GDR), 1984, Proc. 182 (IMEKO, Budapest, 1984).
  2. Data sheet of the HC210-3314 and HC212-3314, “Integrated silicon photodiode and amplifier for low light level detection,” (Hamamatsu Corp., 1988).
  3. W. Budde, “Multidecade linearity measurements on Si photodiodes,” Appl. Opt. 18, 1555–1558 (1979).
    [CrossRef] [PubMed]
  4. W. J. Borucki, “Photometric precision needed for planetary detection,” in Proceedings of the Workshop on Improvements to Photometry, San Diego, 1984, NASA Conf. Publ. CP-2350, 15–27 (1984); W. J. Borucki, A. L. Summers, “The photometric method of detecting other planetary systems,” Icarus 58, 121–134 (1984).
    [CrossRef]
  5. G. Eppeldauer, A. R. Schaefer, “Application of PN and avalanche silicon photodiodes to low-level optical radiation measurements,” in Second Workshop on Improvements to Photometry, Gaithersburg, 1987, NASA Conf. Publ. CP-10015, 111–151 (1988).
  6. E. F. Zalewskiand, J. Geist, “Silicon photodiode absolute spectral response self-calibration,” Appl. Opt. 19, 1214–1216(1980).
    [CrossRef]
  7. A. R. Schaefer, E. F. Zalewski, J. Geist, “Silicon detector nonlinearity and related effects,” Appl. Opt. 22, 1232–1236 (1983).
    [CrossRef] [PubMed]
  8. J. L. Gardner, F. J. Wilkinson, “Response time and linearity of inversion layer silicon photodiodes,” Appl. Opt. 24, 1531–1534 (1985).
    [CrossRef] [PubMed]
  9. E. F. Zalewski, C. R. Duda, “Silicon photodiode device with 100% external quantum efficiency,” Appl. Opt. 22, 2867–2873 (1983).
    [CrossRef] [PubMed]
  10. C. L. Wyatt, Radiometric System Design (Macmillan, New York, 1987), Chap. 18.
  11. A. Ambrózy, Electronic Noise (McGraw Hill, New York, 1982), p. 190.
  12. It is incorrect to say that the shunt resistance, defined as dV/dI at the operating point, is the effective resistance for thermal noise in the Johnson–Nyquist equation. However for the well-known exponential I–V relation of a junction diode, it is an appropriate approximation when the diode current is much less than its reverse saturation current. That is the case in this research, where Is ≈ 5 pA and I ≈ 0.05 pA owing to the op–amp input bias current. In general, the effective resistance (and hence the noise generated) will be less, approaching 1/2 dV/dI when I ≫ Is; see Eq. (19) in M. S. Gupta, “Thermal noise in nonlinear resistive devices and its circuit representation,” Proc. Inst. Electr. Eng. 70, 788–804 (1982).
  13. K. M. van Vliet, “Classification of noise phenomena,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 3–11 (1981).
  14. R. Müfller, “Generation–recombination noise,” in Noise in Physical Systems, Proceedings of the Fifth International Conference on Noise, Bad Nauheim (FRG), 1978 (Springer-Verlag, New York, 1978).
  15. S. M. Sze, The Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981), Chap. 2.
  16. See, e.g., D. A. Bell, “The role of mobility in 1/f noise” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 169–172 (1981); R. P. Jindal, A. Van der Ziel, “A model for 1/f mobility fluctuations in elemental semiconductors,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 173–177; B. K. Jones, “Excess conduction noise in silicon resistors,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 206–209.
  17. G. L. Pearson, H. C. Montgomery, W. L. Feldmann, “Noise in silicon p-n junction photocells,” J. Appl. Phys. 27, 91–92 (1956).
    [CrossRef]
  18. Linear Products Databook (Analog Devices, Inc., 1988), pp. 2–9.

1988 (1)

G. Eppeldauer, A. R. Schaefer, “Application of PN and avalanche silicon photodiodes to low-level optical radiation measurements,” in Second Workshop on Improvements to Photometry, Gaithersburg, 1987, NASA Conf. Publ. CP-10015, 111–151 (1988).

1985 (1)

J. L. Gardner, F. J. Wilkinson, “Response time and linearity of inversion layer silicon photodiodes,” Appl. Opt. 24, 1531–1534 (1985).
[CrossRef] [PubMed]

1984 (1)

W. J. Borucki, “Photometric precision needed for planetary detection,” in Proceedings of the Workshop on Improvements to Photometry, San Diego, 1984, NASA Conf. Publ. CP-2350, 15–27 (1984); W. J. Borucki, A. L. Summers, “The photometric method of detecting other planetary systems,” Icarus 58, 121–134 (1984).
[CrossRef]

1983 (2)

1982 (1)

It is incorrect to say that the shunt resistance, defined as dV/dI at the operating point, is the effective resistance for thermal noise in the Johnson–Nyquist equation. However for the well-known exponential I–V relation of a junction diode, it is an appropriate approximation when the diode current is much less than its reverse saturation current. That is the case in this research, where Is ≈ 5 pA and I ≈ 0.05 pA owing to the op–amp input bias current. In general, the effective resistance (and hence the noise generated) will be less, approaching 1/2 dV/dI when I ≫ Is; see Eq. (19) in M. S. Gupta, “Thermal noise in nonlinear resistive devices and its circuit representation,” Proc. Inst. Electr. Eng. 70, 788–804 (1982).

1981 (2)

K. M. van Vliet, “Classification of noise phenomena,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 3–11 (1981).

See, e.g., D. A. Bell, “The role of mobility in 1/f noise” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 169–172 (1981); R. P. Jindal, A. Van der Ziel, “A model for 1/f mobility fluctuations in elemental semiconductors,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 173–177; B. K. Jones, “Excess conduction noise in silicon resistors,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 206–209.

1980 (1)

E. F. Zalewskiand, J. Geist, “Silicon photodiode absolute spectral response self-calibration,” Appl. Opt. 19, 1214–1216(1980).
[CrossRef]

1979 (1)

1956 (1)

G. L. Pearson, H. C. Montgomery, W. L. Feldmann, “Noise in silicon p-n junction photocells,” J. Appl. Phys. 27, 91–92 (1956).
[CrossRef]

Ambrózy, A.

A. Ambrózy, Electronic Noise (McGraw Hill, New York, 1982), p. 190.

Bell, D. A.

See, e.g., D. A. Bell, “The role of mobility in 1/f noise” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 169–172 (1981); R. P. Jindal, A. Van der Ziel, “A model for 1/f mobility fluctuations in elemental semiconductors,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 173–177; B. K. Jones, “Excess conduction noise in silicon resistors,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 206–209.

Borucki, W. J.

W. J. Borucki, “Photometric precision needed for planetary detection,” in Proceedings of the Workshop on Improvements to Photometry, San Diego, 1984, NASA Conf. Publ. CP-2350, 15–27 (1984); W. J. Borucki, A. L. Summers, “The photometric method of detecting other planetary systems,” Icarus 58, 121–134 (1984).
[CrossRef]

Budde, W.

Duda, C. R.

Eppeldauer, G.

G. Eppeldauer, A. R. Schaefer, “Application of PN and avalanche silicon photodiodes to low-level optical radiation measurements,” in Second Workshop on Improvements to Photometry, Gaithersburg, 1987, NASA Conf. Publ. CP-10015, 111–151 (1988).

G. Eppeldauer, “Measurement of very low light intensities by photovoltaic cells,” in Eleventh International Symposium on Photon Detectors, Weimar (GDR), 1984, Proc. 182 (IMEKO, Budapest, 1984).

Feldmann, W. L.

G. L. Pearson, H. C. Montgomery, W. L. Feldmann, “Noise in silicon p-n junction photocells,” J. Appl. Phys. 27, 91–92 (1956).
[CrossRef]

Gardner, J. L.

J. L. Gardner, F. J. Wilkinson, “Response time and linearity of inversion layer silicon photodiodes,” Appl. Opt. 24, 1531–1534 (1985).
[CrossRef] [PubMed]

Geist, J.

A. R. Schaefer, E. F. Zalewski, J. Geist, “Silicon detector nonlinearity and related effects,” Appl. Opt. 22, 1232–1236 (1983).
[CrossRef] [PubMed]

E. F. Zalewskiand, J. Geist, “Silicon photodiode absolute spectral response self-calibration,” Appl. Opt. 19, 1214–1216(1980).
[CrossRef]

Gupta, M. S.

It is incorrect to say that the shunt resistance, defined as dV/dI at the operating point, is the effective resistance for thermal noise in the Johnson–Nyquist equation. However for the well-known exponential I–V relation of a junction diode, it is an appropriate approximation when the diode current is much less than its reverse saturation current. That is the case in this research, where Is ≈ 5 pA and I ≈ 0.05 pA owing to the op–amp input bias current. In general, the effective resistance (and hence the noise generated) will be less, approaching 1/2 dV/dI when I ≫ Is; see Eq. (19) in M. S. Gupta, “Thermal noise in nonlinear resistive devices and its circuit representation,” Proc. Inst. Electr. Eng. 70, 788–804 (1982).

Montgomery, H. C.

G. L. Pearson, H. C. Montgomery, W. L. Feldmann, “Noise in silicon p-n junction photocells,” J. Appl. Phys. 27, 91–92 (1956).
[CrossRef]

Müfller, R.

R. Müfller, “Generation–recombination noise,” in Noise in Physical Systems, Proceedings of the Fifth International Conference on Noise, Bad Nauheim (FRG), 1978 (Springer-Verlag, New York, 1978).

Pearson, G. L.

G. L. Pearson, H. C. Montgomery, W. L. Feldmann, “Noise in silicon p-n junction photocells,” J. Appl. Phys. 27, 91–92 (1956).
[CrossRef]

Schaefer, A. R.

G. Eppeldauer, A. R. Schaefer, “Application of PN and avalanche silicon photodiodes to low-level optical radiation measurements,” in Second Workshop on Improvements to Photometry, Gaithersburg, 1987, NASA Conf. Publ. CP-10015, 111–151 (1988).

A. R. Schaefer, E. F. Zalewski, J. Geist, “Silicon detector nonlinearity and related effects,” Appl. Opt. 22, 1232–1236 (1983).
[CrossRef] [PubMed]

Sze, S. M.

S. M. Sze, The Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981), Chap. 2.

van Vliet, K. M.

K. M. van Vliet, “Classification of noise phenomena,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 3–11 (1981).

Wilkinson, F. J.

J. L. Gardner, F. J. Wilkinson, “Response time and linearity of inversion layer silicon photodiodes,” Appl. Opt. 24, 1531–1534 (1985).
[CrossRef] [PubMed]

Wyatt, C. L.

C. L. Wyatt, Radiometric System Design (Macmillan, New York, 1987), Chap. 18.

Zalewski, E. F.

Zalewskiand, E. F.

E. F. Zalewskiand, J. Geist, “Silicon photodiode absolute spectral response self-calibration,” Appl. Opt. 19, 1214–1216(1980).
[CrossRef]

Appl. Opt. (2)

E. F. Zalewskiand, J. Geist, “Silicon photodiode absolute spectral response self-calibration,” Appl. Opt. 19, 1214–1216(1980).
[CrossRef]

J. L. Gardner, F. J. Wilkinson, “Response time and linearity of inversion layer silicon photodiodes,” Appl. Opt. 24, 1531–1534 (1985).
[CrossRef] [PubMed]

Appl. Opt. (3)

J. Appl. Phys. (1)

G. L. Pearson, H. C. Montgomery, W. L. Feldmann, “Noise in silicon p-n junction photocells,” J. Appl. Phys. 27, 91–92 (1956).
[CrossRef]

Proc. Inst. Electr. Eng. (1)

It is incorrect to say that the shunt resistance, defined as dV/dI at the operating point, is the effective resistance for thermal noise in the Johnson–Nyquist equation. However for the well-known exponential I–V relation of a junction diode, it is an appropriate approximation when the diode current is much less than its reverse saturation current. That is the case in this research, where Is ≈ 5 pA and I ≈ 0.05 pA owing to the op–amp input bias current. In general, the effective resistance (and hence the noise generated) will be less, approaching 1/2 dV/dI when I ≫ Is; see Eq. (19) in M. S. Gupta, “Thermal noise in nonlinear resistive devices and its circuit representation,” Proc. Inst. Electr. Eng. 70, 788–804 (1982).

Proceedings of the Workshop on Improvements to Photometry, San Diego, 1984 (1)

W. J. Borucki, “Photometric precision needed for planetary detection,” in Proceedings of the Workshop on Improvements to Photometry, San Diego, 1984, NASA Conf. Publ. CP-2350, 15–27 (1984); W. J. Borucki, A. L. Summers, “The photometric method of detecting other planetary systems,” Icarus 58, 121–134 (1984).
[CrossRef]

Second Workshop on Improvements to Photometry, Gaithersburg, 1987 (1)

G. Eppeldauer, A. R. Schaefer, “Application of PN and avalanche silicon photodiodes to low-level optical radiation measurements,” in Second Workshop on Improvements to Photometry, Gaithersburg, 1987, NASA Conf. Publ. CP-10015, 111–151 (1988).

Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981 (1)

See, e.g., D. A. Bell, “The role of mobility in 1/f noise” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 169–172 (1981); R. P. Jindal, A. Van der Ziel, “A model for 1/f mobility fluctuations in elemental semiconductors,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 173–177; B. K. Jones, “Excess conduction noise in silicon resistors,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 206–209.

Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981 (1)

K. M. van Vliet, “Classification of noise phenomena,” in Sixth International Conference on Noise in Physical Systems, Gaithersburg, 1981, Natl. Bur. Stand. (U.S.) Tech. Note 614, 3–11 (1981).

Other (7)

R. Müfller, “Generation–recombination noise,” in Noise in Physical Systems, Proceedings of the Fifth International Conference on Noise, Bad Nauheim (FRG), 1978 (Springer-Verlag, New York, 1978).

S. M. Sze, The Physics of Semiconductor Devices, 2nd ed. (Wiley, New York, 1981), Chap. 2.

G. Eppeldauer, “Measurement of very low light intensities by photovoltaic cells,” in Eleventh International Symposium on Photon Detectors, Weimar (GDR), 1984, Proc. 182 (IMEKO, Budapest, 1984).

Data sheet of the HC210-3314 and HC212-3314, “Integrated silicon photodiode and amplifier for low light level detection,” (Hamamatsu Corp., 1988).

Linear Products Databook (Analog Devices, Inc., 1988), pp. 2–9.

C. L. Wyatt, Radiometric System Design (Macmillan, New York, 1987), Chap. 18.

A. Ambrózy, Electronic Noise (McGraw Hill, New York, 1982), p. 190.

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Figures (4)

Fig. 1
Fig. 1

Model circuit (a) components and (b) noise sources.

Fig. 2
Fig. 2

Circuit details.

Fig. 3
Fig. 3

Balancing noise and drift. The noise (solid curves) and thermal drift (dotted curves) are expressed in terms of the photocurrent that would cause an equal change in amplifier output. The two figures at the left show the expected performance of the OPA111BM amplifier; those on the right show the performance of the OPA128LM amplifier. The two top figures show easy specifications for integration time and temperature stability; the bottom two show tight specifications.

Fig. 4
Fig. 4

Noise measurements of OPA128LM amplifiers with different source resistances. The hatched areas at the left show the range of the characteristic input voltage noises of the amplifier types reported in Table I. The dashed line guides the eye toward the voltage noise level of these particular amplifiers. This level of minimum noise cannot be much reduced by longer integration. The solid lines are the Johnson noise of the source resistances for our two integration times (300 mHz in open symbols and 1.25 mHz in filled symbols).

Tables (2)

Tables Icon

Table I Statistics of Amplifier Output Measurements Showing the Mean (the Offset Voltage) and the Standard Deviation (the Voltage Noise)a

Tables Icon

Table II Noise and Drift of Complete Detector–Amplifier Packages Cast In Terms of the Photocurrent that Would Cause the Same Change In Output

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

V IN 2 = V VN 2 + 4 e I Bias R so 2 Δ f + 4 k T R so Δ f + ( I Bias R XN ) 2 .
V Offset = - A V ( V O + I Bias R so ) .
I Offset = V O / R so + I Bias
Δ I Offset = ( V D / R so + V O R SD / R so + I D I Bias ) Δ T .
I Noise = V ON / R f = V IN / R so .
f ( t ) = 1 τ t - τ t f ( t ) d t             ( Case I ) ,
f ( t ) = 1 τ - t exp [ - ( t - t ) τ ] f ( t ) d t             ( Case II ) .
f ( t ) = ( e i ω τ - 1 i ω τ ) e - i ω t             ( Case I ) ,
f ( t ) = ( 1 1 - i ω τ ) e - i ω t .             ( Case II ) .
Δ ω = 0 2 [ 1 - cos ( ω τ ) ] ( ω τ ) 2 d ω = π τ             ( Case I ) ,
Δ ω = 0 1 1 + ( ω τ ) 2 d ω = π 2 τ             ( Case II ) ,
Δ ω = 0 { 2 [ 1 - cos ( ω τ ) ] ( ω τ ) 2 } { [ 1 - cos ( N ω T ) ] N 2 [ 1 - cos ( ω T ) ] } d ω .

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