Abstract

This paper describes a method of obtaining the temporal and frequency response of avalanche photodiodes (APD) by performing simple noise measurements. From the measured noise spectrum and by using the Hilbert transformation technique, the complex transfer function of the detector is determined. The temporal response can then easily be calculated by means of fast Fourier transforming. The method has been applied on a high speed APD, with a bandwidth of ~2 GHz, and on a relatively slow APD, with a bandwidth of 0.2 GHz, to calculate the pulse response from a short optical pulse. The calculated pulse width for the fast APD was 215 psec, and the corresponding measured width was 210 psec, while for the slow APD the calculated and the measured widths both were 3.1 nsec. Also the shapes of the pulse responses showed excellent agreement. The method depends on the essentially identical frequency response of an APD and associated circuits for noise due to steady-state illumination and for a signal.

© 1980 Optical Society of America

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References

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  1. G. E. Stillman, C. M. Wolfe, Semiconductors and Semimetals, Vol. 12 (Willardson and Beer, New York, 1977).
  2. R. J. McIntyre, IEEE Trans. Electron Devices ED-13, 164 (1966).
    [CrossRef]
  3. P. P. Webb, R. J. McIntyre, J. Conradi, RCA Rev. 35, 235 (1974).
  4. T. Kaneda, H. Takaniashi, H. Matsumoto, T. Yamaoka, J. Appl. Phys. 47, 4960 (1976).
    [CrossRef]
  5. R. Kuvas, C. A. Lee, J. Appl. Phys. 41, 1743 (1970).
    [CrossRef]
  6. R. B. Emmons, J. Appl. Phys. 38, 3705 (1967).
    [CrossRef]
  7. B. J. Peyton, A. J. DiNardo, G. M. Kanischak, F. R. Arams, R. A. Lange, E. W. Sard, IEEE J. Quantum Electron. 8, 252 (1972).
    [CrossRef]
  8. B. J. Peyton, “Wideband Infrared Heterodyne Receiver Front End,” NASA CR-139172 (Aug.1974).
  9. J. M. Dumant, C. Y. Boisrobert, J. Debeau, Onde Electr. 56, 609 (1976).
  10. I. M. Naqvi, Solid-State Electron. 16, 19 (1972).
    [CrossRef]
  11. T. Kaneda, T. Takaniashi, Appl. Phys. Lett. 26, 642 (1975).
    [CrossRef]
  12. M. Yano, K. Seki, T. Kamiya, H. Yanai, Trans. IEEE J. E60, 508 (1977).
  13. L. K. Anderson, Proc. IEEE (1963).
  14. T. Andersson, S. Lundqvist, H. Eklund, “Frequency Response of Transit Time Limited Photodiodes from Signal and Shot-Noise Spectra,” Technical Report 8076, Department of Electrical Measurements, Chalmers U. Technology (Sweden, 1980).
  15. H. W. Ruegg, IEEE Trans. Electron Devices ED-14, 229 (1967).
  16. E. A. Guillemin, Theory of Linear Physical Systems (Wiley, New York1963).
  17. K. Berchtold, O. Krumpholz, J. Suri, Appl. Phys. Lett. 26, 585 (1975).
    [CrossRef]
  18. P. Torphammar, R. Tell, H. Eklund, A. R. Johnston, J. Quantum Electron. QE-15, 1271 (1979).
    [CrossRef]
  19. J. Johansson, T. Andersson, P. Torphammar, H. Eklund, S. T. Eng, “A computer system for analysis of high capacity components in optical-fiber links,” to be published in IEEE Trans. Instrum. Meas.

1979

P. Torphammar, R. Tell, H. Eklund, A. R. Johnston, J. Quantum Electron. QE-15, 1271 (1979).
[CrossRef]

1977

M. Yano, K. Seki, T. Kamiya, H. Yanai, Trans. IEEE J. E60, 508 (1977).

1976

T. Kaneda, H. Takaniashi, H. Matsumoto, T. Yamaoka, J. Appl. Phys. 47, 4960 (1976).
[CrossRef]

J. M. Dumant, C. Y. Boisrobert, J. Debeau, Onde Electr. 56, 609 (1976).

1975

T. Kaneda, T. Takaniashi, Appl. Phys. Lett. 26, 642 (1975).
[CrossRef]

K. Berchtold, O. Krumpholz, J. Suri, Appl. Phys. Lett. 26, 585 (1975).
[CrossRef]

1974

P. P. Webb, R. J. McIntyre, J. Conradi, RCA Rev. 35, 235 (1974).

1972

B. J. Peyton, A. J. DiNardo, G. M. Kanischak, F. R. Arams, R. A. Lange, E. W. Sard, IEEE J. Quantum Electron. 8, 252 (1972).
[CrossRef]

I. M. Naqvi, Solid-State Electron. 16, 19 (1972).
[CrossRef]

1970

R. Kuvas, C. A. Lee, J. Appl. Phys. 41, 1743 (1970).
[CrossRef]

1967

R. B. Emmons, J. Appl. Phys. 38, 3705 (1967).
[CrossRef]

H. W. Ruegg, IEEE Trans. Electron Devices ED-14, 229 (1967).

1966

R. J. McIntyre, IEEE Trans. Electron Devices ED-13, 164 (1966).
[CrossRef]

1963

L. K. Anderson, Proc. IEEE (1963).

Anderson, L. K.

L. K. Anderson, Proc. IEEE (1963).

Andersson, T.

J. Johansson, T. Andersson, P. Torphammar, H. Eklund, S. T. Eng, “A computer system for analysis of high capacity components in optical-fiber links,” to be published in IEEE Trans. Instrum. Meas.

T. Andersson, S. Lundqvist, H. Eklund, “Frequency Response of Transit Time Limited Photodiodes from Signal and Shot-Noise Spectra,” Technical Report 8076, Department of Electrical Measurements, Chalmers U. Technology (Sweden, 1980).

Arams, F. R.

B. J. Peyton, A. J. DiNardo, G. M. Kanischak, F. R. Arams, R. A. Lange, E. W. Sard, IEEE J. Quantum Electron. 8, 252 (1972).
[CrossRef]

Berchtold, K.

K. Berchtold, O. Krumpholz, J. Suri, Appl. Phys. Lett. 26, 585 (1975).
[CrossRef]

Boisrobert, C. Y.

J. M. Dumant, C. Y. Boisrobert, J. Debeau, Onde Electr. 56, 609 (1976).

Conradi, J.

P. P. Webb, R. J. McIntyre, J. Conradi, RCA Rev. 35, 235 (1974).

Debeau, J.

J. M. Dumant, C. Y. Boisrobert, J. Debeau, Onde Electr. 56, 609 (1976).

DiNardo, A. J.

B. J. Peyton, A. J. DiNardo, G. M. Kanischak, F. R. Arams, R. A. Lange, E. W. Sard, IEEE J. Quantum Electron. 8, 252 (1972).
[CrossRef]

Dumant, J. M.

J. M. Dumant, C. Y. Boisrobert, J. Debeau, Onde Electr. 56, 609 (1976).

Eklund, H.

P. Torphammar, R. Tell, H. Eklund, A. R. Johnston, J. Quantum Electron. QE-15, 1271 (1979).
[CrossRef]

T. Andersson, S. Lundqvist, H. Eklund, “Frequency Response of Transit Time Limited Photodiodes from Signal and Shot-Noise Spectra,” Technical Report 8076, Department of Electrical Measurements, Chalmers U. Technology (Sweden, 1980).

J. Johansson, T. Andersson, P. Torphammar, H. Eklund, S. T. Eng, “A computer system for analysis of high capacity components in optical-fiber links,” to be published in IEEE Trans. Instrum. Meas.

Emmons, R. B.

R. B. Emmons, J. Appl. Phys. 38, 3705 (1967).
[CrossRef]

Eng, S. T.

J. Johansson, T. Andersson, P. Torphammar, H. Eklund, S. T. Eng, “A computer system for analysis of high capacity components in optical-fiber links,” to be published in IEEE Trans. Instrum. Meas.

Guillemin, E. A.

E. A. Guillemin, Theory of Linear Physical Systems (Wiley, New York1963).

Johansson, J.

J. Johansson, T. Andersson, P. Torphammar, H. Eklund, S. T. Eng, “A computer system for analysis of high capacity components in optical-fiber links,” to be published in IEEE Trans. Instrum. Meas.

Johnston, A. R.

P. Torphammar, R. Tell, H. Eklund, A. R. Johnston, J. Quantum Electron. QE-15, 1271 (1979).
[CrossRef]

Kamiya, T.

M. Yano, K. Seki, T. Kamiya, H. Yanai, Trans. IEEE J. E60, 508 (1977).

Kaneda, T.

T. Kaneda, H. Takaniashi, H. Matsumoto, T. Yamaoka, J. Appl. Phys. 47, 4960 (1976).
[CrossRef]

T. Kaneda, T. Takaniashi, Appl. Phys. Lett. 26, 642 (1975).
[CrossRef]

Kanischak, G. M.

B. J. Peyton, A. J. DiNardo, G. M. Kanischak, F. R. Arams, R. A. Lange, E. W. Sard, IEEE J. Quantum Electron. 8, 252 (1972).
[CrossRef]

Krumpholz, O.

K. Berchtold, O. Krumpholz, J. Suri, Appl. Phys. Lett. 26, 585 (1975).
[CrossRef]

Kuvas, R.

R. Kuvas, C. A. Lee, J. Appl. Phys. 41, 1743 (1970).
[CrossRef]

Lange, R. A.

B. J. Peyton, A. J. DiNardo, G. M. Kanischak, F. R. Arams, R. A. Lange, E. W. Sard, IEEE J. Quantum Electron. 8, 252 (1972).
[CrossRef]

Lee, C. A.

R. Kuvas, C. A. Lee, J. Appl. Phys. 41, 1743 (1970).
[CrossRef]

Lundqvist, S.

T. Andersson, S. Lundqvist, H. Eklund, “Frequency Response of Transit Time Limited Photodiodes from Signal and Shot-Noise Spectra,” Technical Report 8076, Department of Electrical Measurements, Chalmers U. Technology (Sweden, 1980).

Matsumoto, H.

T. Kaneda, H. Takaniashi, H. Matsumoto, T. Yamaoka, J. Appl. Phys. 47, 4960 (1976).
[CrossRef]

McIntyre, R. J.

P. P. Webb, R. J. McIntyre, J. Conradi, RCA Rev. 35, 235 (1974).

R. J. McIntyre, IEEE Trans. Electron Devices ED-13, 164 (1966).
[CrossRef]

Naqvi, I. M.

I. M. Naqvi, Solid-State Electron. 16, 19 (1972).
[CrossRef]

Peyton, B. J.

B. J. Peyton, A. J. DiNardo, G. M. Kanischak, F. R. Arams, R. A. Lange, E. W. Sard, IEEE J. Quantum Electron. 8, 252 (1972).
[CrossRef]

B. J. Peyton, “Wideband Infrared Heterodyne Receiver Front End,” NASA CR-139172 (Aug.1974).

Ruegg, H. W.

H. W. Ruegg, IEEE Trans. Electron Devices ED-14, 229 (1967).

Sard, E. W.

B. J. Peyton, A. J. DiNardo, G. M. Kanischak, F. R. Arams, R. A. Lange, E. W. Sard, IEEE J. Quantum Electron. 8, 252 (1972).
[CrossRef]

Seki, K.

M. Yano, K. Seki, T. Kamiya, H. Yanai, Trans. IEEE J. E60, 508 (1977).

Stillman, G. E.

G. E. Stillman, C. M. Wolfe, Semiconductors and Semimetals, Vol. 12 (Willardson and Beer, New York, 1977).

Suri, J.

K. Berchtold, O. Krumpholz, J. Suri, Appl. Phys. Lett. 26, 585 (1975).
[CrossRef]

Takaniashi, H.

T. Kaneda, H. Takaniashi, H. Matsumoto, T. Yamaoka, J. Appl. Phys. 47, 4960 (1976).
[CrossRef]

Takaniashi, T.

T. Kaneda, T. Takaniashi, Appl. Phys. Lett. 26, 642 (1975).
[CrossRef]

Tell, R.

P. Torphammar, R. Tell, H. Eklund, A. R. Johnston, J. Quantum Electron. QE-15, 1271 (1979).
[CrossRef]

Torphammar, P.

P. Torphammar, R. Tell, H. Eklund, A. R. Johnston, J. Quantum Electron. QE-15, 1271 (1979).
[CrossRef]

J. Johansson, T. Andersson, P. Torphammar, H. Eklund, S. T. Eng, “A computer system for analysis of high capacity components in optical-fiber links,” to be published in IEEE Trans. Instrum. Meas.

Webb, P. P.

P. P. Webb, R. J. McIntyre, J. Conradi, RCA Rev. 35, 235 (1974).

Wolfe, C. M.

G. E. Stillman, C. M. Wolfe, Semiconductors and Semimetals, Vol. 12 (Willardson and Beer, New York, 1977).

Yamaoka, T.

T. Kaneda, H. Takaniashi, H. Matsumoto, T. Yamaoka, J. Appl. Phys. 47, 4960 (1976).
[CrossRef]

Yanai, H.

M. Yano, K. Seki, T. Kamiya, H. Yanai, Trans. IEEE J. E60, 508 (1977).

Yano, M.

M. Yano, K. Seki, T. Kamiya, H. Yanai, Trans. IEEE J. E60, 508 (1977).

Appl. Phys. Lett.

T. Kaneda, T. Takaniashi, Appl. Phys. Lett. 26, 642 (1975).
[CrossRef]

K. Berchtold, O. Krumpholz, J. Suri, Appl. Phys. Lett. 26, 585 (1975).
[CrossRef]

IEEE J. Quantum Electron.

B. J. Peyton, A. J. DiNardo, G. M. Kanischak, F. R. Arams, R. A. Lange, E. W. Sard, IEEE J. Quantum Electron. 8, 252 (1972).
[CrossRef]

IEEE Trans. Electron Devices

R. J. McIntyre, IEEE Trans. Electron Devices ED-13, 164 (1966).
[CrossRef]

H. W. Ruegg, IEEE Trans. Electron Devices ED-14, 229 (1967).

J. Appl. Phys.

T. Kaneda, H. Takaniashi, H. Matsumoto, T. Yamaoka, J. Appl. Phys. 47, 4960 (1976).
[CrossRef]

R. Kuvas, C. A. Lee, J. Appl. Phys. 41, 1743 (1970).
[CrossRef]

R. B. Emmons, J. Appl. Phys. 38, 3705 (1967).
[CrossRef]

J. Quantum Electron.

P. Torphammar, R. Tell, H. Eklund, A. R. Johnston, J. Quantum Electron. QE-15, 1271 (1979).
[CrossRef]

Onde Electr.

J. M. Dumant, C. Y. Boisrobert, J. Debeau, Onde Electr. 56, 609 (1976).

Proc. IEEE

L. K. Anderson, Proc. IEEE (1963).

RCA Rev.

P. P. Webb, R. J. McIntyre, J. Conradi, RCA Rev. 35, 235 (1974).

Solid-State Electron.

I. M. Naqvi, Solid-State Electron. 16, 19 (1972).
[CrossRef]

Trans. IEEE J.

M. Yano, K. Seki, T. Kamiya, H. Yanai, Trans. IEEE J. E60, 508 (1977).

Other

T. Andersson, S. Lundqvist, H. Eklund, “Frequency Response of Transit Time Limited Photodiodes from Signal and Shot-Noise Spectra,” Technical Report 8076, Department of Electrical Measurements, Chalmers U. Technology (Sweden, 1980).

J. Johansson, T. Andersson, P. Torphammar, H. Eklund, S. T. Eng, “A computer system for analysis of high capacity components in optical-fiber links,” to be published in IEEE Trans. Instrum. Meas.

E. A. Guillemin, Theory of Linear Physical Systems (Wiley, New York1963).

B. J. Peyton, “Wideband Infrared Heterodyne Receiver Front End,” NASA CR-139172 (Aug.1974).

G. E. Stillman, C. M. Wolfe, Semiconductors and Semimetals, Vol. 12 (Willardson and Beer, New York, 1977).

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Figures (6)

Fig. 1
Fig. 1

Assumed equivalent circuit of the APD, where is and in are the signal and noise currents, Rp and C are the parallel resistance and capacitance, Rs is the series resistance, L is the lead inductance, and R0 is the load resistance (50 Ω).

Fig. 2
Fig. 2

Measured shot-noise spectra V n 2 for different gain factors. Curves are normalized to the noise level corresponding to M = 100 for low frequencies. Low and high frequency slopes are assumed to be 0 and 24 dB/oct, respectively.

Fig. 3
Fig. 3

Frequency characteristics of the fast APD for a gain factor of 100: (a) magnitude obtained from the noise spectrum and TDR measurements; (b) phase calculated using the Hilbert transform.

Fig. 4
Fig. 4

Measured shot-noise spectrum for the slow APD.

Fig. 5
Fig. 5

Temporal response of the fast APD: (a) calculated detector signal for a 65-psec wide laser pulse; (b) measured detector signal.

Fig. 6
Fig. 6

Temporal response of the slow APD for a 1.4-nsec wide laser pulse: (a) calculated detector signal; (b) measured detector signal.

Equations (8)

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G ( j ω ) = [ V s ( j ω ) ] / [ P s ( j ω ) ] ,
I s = R M ( j ω ) D ( j ω ) P s ( j ω ) ,
G ( j ω ) = R M ( j ω ) D ( j ω ) Z ( j ω ) ,
V n 2 ( ω ) = 2 e | M ( j ω ) | 2 F P 0 R B | D ( j ω ) | 2 | Z ( j ω ) | 2 ,
M ( j ω ) = M 0 / ( 1 + j ω τ 1 M 0 ) .
D ( j ω ) = 1 exp ( j ω τ p ) j ω τ p γ [ 1 exp ( γ ) ] ( γ 2 + ω 2 τ n 2 ) × { γ [ cos ω τ n exp ( γ ) ] + ω τ n sin ω τ n + j [ ω τ n [ cos ω τ n exp ( γ ) ] γ sin ω τ n ] } ,
G ( j ω ) = | G ( j ω ) | exp [ j ϕ ( ω ) ] .
| G ( j ω ) | ~ | sin ω τ p 2 | / ω 4 ,

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