Abstract

Single-photon avalanche diodes (SPADs) are primary devices in photon counting systems used in quantum cryptography, time resolved spectroscopy and photon counting optical communication. SPADs convert each photo-generated electron hole pair to a measurable current via an avalanche of impact ionizations. In this paper, a stochastically self-regulating avalanche model for passively quenched SPADs is presented. The model predicts, in qualitative agreement with experiments, three important phenomena that traditional models are unable to predict. These are: (1) an oscillatory behavior of the persistent avalanche current; (2) an exponential (memoryless) decay of the probability density function of the stochastic quenching time of the persistent avalanche current; and (3) a fast collapse of the avalanche current, under strong feedback conditions, preventing the development of a persistent avalanche current. The model specifically captures the effect of the load’s feedback on the stochastic avalanche multiplication, an effect believed to be key in breaking today’s counting rate barrier in the 1.55–μm detection window.

© 2012 OSA

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2011 (1)

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

2010 (2)

M. M. Hayat, M. A. Itzler, D. A. Ramirez, and G. J. Rees, “Model for Passive Quenching of SPADs,” Proc. of SPIE 7608, 76082B–76082B–8 (2010).
[CrossRef]

M. A. Itzler, X. Jiang, B. M. Onat, and K. Slomkowski, “Progress in self-quenching InP-based single photon detectors,” Proc. of SPIE 7608, 760829 (2010).
[CrossRef]

2008 (2)

K. Zhao, S. You, J. Cheng, and Y. Lo, “Self-quenching and self-recovering InGaAs/InAlAs single photon avalanche detector,” Appl. Phys. Lett. 93, 153504 (2008).
[CrossRef]

L. J. J. Tan, J. S. Ng, C. H. Tan, and J. P. R. David, “Avalanche noise characteristics in submicron InP diodes,” IEEE J. Quantum Electron. 44, 378–382 (2008).
[CrossRef]

2007 (1)

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

2005 (1)

C. Groves, C. H. Tan, J. P. R. David, G. J. Rees, and M. M. Hayat, “Exponential time response in analogue and Geiger mode avalanche photodiodes,” IEEE Trans. Electron Devices 52, 1527–1534 (2005).
[CrossRef]

2002 (4)

J. S. Ng, C. H. Tan, J. P. R. David, and G. J. Rees, “A general method for estimating the duration of avalanche multiplication,” J. Lightwave Technol. 10, 1067–1071 (2002).

W. P. Risk and D. S. Bethune, “Quantum cryptography,” Opt. Photonics News 13, 26–32 (2002).
[CrossRef]

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

2000 (1)

M. M. Hayat and G. Dong, “A new approach for computing the bandwidth statistics of avalanche photodiodes,” IEEE Trans. Electron Devices 47, 1273–1279 (2000).
[CrossRef]

1996 (1)

1995 (1)

D. Shushakov and V. Shubin, “New solid state photomultiplier,” Proc. of SPIE 2397, 544–554 (1995).
[CrossRef]

1992 (1)

M. M. Hayat and B. E. A. Saleh, “Statistical properties of the impulse response function of double-carrier multiplication avalanche photodiodes including the effect of dead space,” J. Lightwave Technol. 10, 1415–1425 (1992).
[CrossRef]

1985 (1)

B. F. Levine, C. G. Bethea, and J. C. Campbell, “1.52 μm room temperature photon counting optical time domain reflectometer,” Electron. Lett. 21, 194–196 (1985).
[CrossRef]

1967 (1)

R. B. Emmons, “Avalanche-photodiode frequency response,” J. Appl. Phys. 38, 3705–3714 (1967).
[CrossRef]

1966 (1)

R. J. McIntyre, “Multiplication noise in uniform avalanche photodiodes,” IEEE Trans. Electron devices ED. 13, 164–168 (1966).
[CrossRef]

1964 (1)

R. H. Haitz, “Model for the electrical behavior of a microplasma,” J. Appl. Phys. 35, 1370–1376 (1964).
[CrossRef]

Acerbi, F.

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

Albota, M. A.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Athreya, K. B.

K. B. Athreya and P. Ney, Branching Processes (Berlin-Germany: Springer-Verlag, 1972).

Aull, B. A.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Aull, B. F.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

Ben-Michael, R.

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

Bethea, C. G.

B. F. Levine, C. G. Bethea, and J. C. Campbell, “1.52 μm room temperature photon counting optical time domain reflectometer,” Electron. Lett. 21, 194–196 (1985).
[CrossRef]

Bethune, D. S.

W. P. Risk and D. S. Bethune, “Quantum cryptography,” Opt. Photonics News 13, 26–32 (2002).
[CrossRef]

Bondurant, R. S.

D. M. Boroson, R. S. Bondurant, and D. V. Murphy, “LDORA: A novel laser communications receiver array architecture,” Proc. of SPIE5338, 56–64 (2004).
[CrossRef]

Boroson, D. M.

D. M. Boroson, R. S. Bondurant, and D. V. Murphy, “LDORA: A novel laser communications receiver array architecture,” Proc. of SPIE5338, 56–64 (2004).
[CrossRef]

Campbell, J. C.

B. F. Levine, C. G. Bethea, and J. C. Campbell, “1.52 μm room temperature photon counting optical time domain reflectometer,” Electron. Lett. 21, 194–196 (1985).
[CrossRef]

Cheng, J.

K. Zhao, S. You, J. Cheng, and Y. Lo, “Self-quenching and self-recovering InGaAs/InAlAs single photon avalanche detector,” Appl. Phys. Lett. 93, 153504 (2008).
[CrossRef]

Cova, S.

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, “Avalanche photodiodes and quenching circuits for single-photon detection,” Appl. Opt. 35, 1956–1976 (1996).
[CrossRef] [PubMed]

Daniels, P. J.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

David, J. P. R.

L. J. J. Tan, J. S. Ng, C. H. Tan, and J. P. R. David, “Avalanche noise characteristics in submicron InP diodes,” IEEE J. Quantum Electron. 44, 378–382 (2008).
[CrossRef]

C. Groves, C. H. Tan, J. P. R. David, G. J. Rees, and M. M. Hayat, “Exponential time response in analogue and Geiger mode avalanche photodiodes,” IEEE Trans. Electron Devices 52, 1527–1534 (2005).
[CrossRef]

J. S. Ng, C. H. Tan, J. P. R. David, and G. J. Rees, “A general method for estimating the duration of avalanche multiplication,” J. Lightwave Technol. 10, 1067–1071 (2002).

Dong, G.

M. M. Hayat and G. Dong, “A new approach for computing the bandwidth statistics of avalanche photodiodes,” IEEE Trans. Electron Devices 47, 1273–1279 (2000).
[CrossRef]

Emmons, R. B.

R. B. Emmons, “Avalanche-photodiode frequency response,” J. Appl. Phys. 38, 3705–3714 (1967).
[CrossRef]

Entwistle, M.

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

Felton, B. J.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

Fouche, D. G.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Ghioni, M.

Groves, C.

C. Groves, C. H. Tan, J. P. R. David, G. J. Rees, and M. M. Hayat, “Exponential time response in analogue and Geiger mode avalanche photodiodes,” IEEE Trans. Electron Devices 52, 1527–1534 (2005).
[CrossRef]

Haitz, R. H.

R. H. Haitz, “Model for the electrical behavior of a microplasma,” J. Appl. Phys. 35, 1370–1376 (1964).
[CrossRef]

Hayat, M. M.

M. M. Hayat, M. A. Itzler, D. A. Ramirez, and G. J. Rees, “Model for Passive Quenching of SPADs,” Proc. of SPIE 7608, 76082B–76082B–8 (2010).
[CrossRef]

C. Groves, C. H. Tan, J. P. R. David, G. J. Rees, and M. M. Hayat, “Exponential time response in analogue and Geiger mode avalanche photodiodes,” IEEE Trans. Electron Devices 52, 1527–1534 (2005).
[CrossRef]

M. M. Hayat and G. Dong, “A new approach for computing the bandwidth statistics of avalanche photodiodes,” IEEE Trans. Electron Devices 47, 1273–1279 (2000).
[CrossRef]

M. M. Hayat and B. E. A. Saleh, “Statistical properties of the impulse response function of double-carrier multiplication avalanche photodiodes including the effect of dead space,” J. Lightwave Technol. 10, 1415–1425 (1992).
[CrossRef]

M. M. Hayat, G. J. Rees, D. A. Ramirez, and M. A. Itzler, “Statistics of self-quenching time in single photon avalanche diodes,” The 21st Annual Meeting of The IEEE Lasers and Electro-Optics Society pp. 203–231 (2008).

Heinrichs, R. M.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Hsu, C. F.

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

Ispasoiu, R.

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

Itzler, M. A.

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

M. A. Itzler, X. Jiang, B. M. Onat, and K. Slomkowski, “Progress in self-quenching InP-based single photon detectors,” Proc. of SPIE 7608, 760829 (2010).
[CrossRef]

M. M. Hayat, M. A. Itzler, D. A. Ramirez, and G. J. Rees, “Model for Passive Quenching of SPADs,” Proc. of SPIE 7608, 76082B–76082B–8 (2010).
[CrossRef]

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

M. A. Itzler, X. Jiang, B. Nyman, and K. Slomkowski, “InP-based Negative Feedback Avalanche Diodes,” Proc. of SPIE7222, 72221K (2009).
[CrossRef]

M. M. Hayat, G. J. Rees, D. A. Ramirez, and M. A. Itzler, “Statistics of self-quenching time in single photon avalanche diodes,” The 21st Annual Meeting of The IEEE Lasers and Electro-Optics Society pp. 203–231 (2008).

Jiang, X.

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

M. A. Itzler, X. Jiang, B. M. Onat, and K. Slomkowski, “Progress in self-quenching InP-based single photon detectors,” Proc. of SPIE 7608, 760829 (2010).
[CrossRef]

M. A. Itzler, X. Jiang, B. Nyman, and K. Slomkowski, “InP-based Negative Feedback Avalanche Diodes,” Proc. of SPIE7222, 72221K (2009).
[CrossRef]

Kocher, D. G.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Lacaita, A.

Landers, D. J.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

Levine, B. F.

B. F. Levine, C. G. Bethea, and J. C. Campbell, “1.52 μm room temperature photon counting optical time domain reflectometer,” Electron. Lett. 21, 194–196 (1985).
[CrossRef]

Lo, Y.

K. Zhao, S. You, J. Cheng, and Y. Lo, “Self-quenching and self-recovering InGaAs/InAlAs single photon avalanche detector,” Appl. Phys. Lett. 93, 153504 (2008).
[CrossRef]

Loomis, A. H.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

Marino, R. M.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

McIntyre, R. J.

R. J. McIntyre, “Multiplication noise in uniform avalanche photodiodes,” IEEE Trans. Electron devices ED. 13, 164–168 (1966).
[CrossRef]

Mooney, J. G.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Murphy, D. V.

D. M. Boroson, R. S. Bondurant, and D. V. Murphy, “LDORA: A novel laser communications receiver array architecture,” Proc. of SPIE5338, 56–64 (2004).
[CrossRef]

Newbury, N. R.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Ney, P.

K. B. Athreya and P. Ney, Branching Processes (Berlin-Germany: Springer-Verlag, 1972).

Ng, J. S.

L. J. J. Tan, J. S. Ng, C. H. Tan, and J. P. R. David, “Avalanche noise characteristics in submicron InP diodes,” IEEE J. Quantum Electron. 44, 378–382 (2008).
[CrossRef]

J. S. Ng, C. H. Tan, J. P. R. David, and G. J. Rees, “A general method for estimating the duration of avalanche multiplication,” J. Lightwave Technol. 10, 1067–1071 (2002).

Nyman, B.

M. A. Itzler, X. Jiang, B. Nyman, and K. Slomkowski, “InP-based Negative Feedback Avalanche Diodes,” Proc. of SPIE7222, 72221K (2009).
[CrossRef]

OBrien, M. E.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Onat, B. M.

M. A. Itzler, X. Jiang, B. M. Onat, and K. Slomkowski, “Progress in self-quenching InP-based single photon detectors,” Proc. of SPIE 7608, 760829 (2010).
[CrossRef]

Player, B. E.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Ramirez, D. A.

M. M. Hayat, M. A. Itzler, D. A. Ramirez, and G. J. Rees, “Model for Passive Quenching of SPADs,” Proc. of SPIE 7608, 76082B–76082B–8 (2010).
[CrossRef]

M. M. Hayat, G. J. Rees, D. A. Ramirez, and M. A. Itzler, “Statistics of self-quenching time in single photon avalanche diodes,” The 21st Annual Meeting of The IEEE Lasers and Electro-Optics Society pp. 203–231 (2008).

Rees, G. J.

M. M. Hayat, M. A. Itzler, D. A. Ramirez, and G. J. Rees, “Model for Passive Quenching of SPADs,” Proc. of SPIE 7608, 76082B–76082B–8 (2010).
[CrossRef]

C. Groves, C. H. Tan, J. P. R. David, G. J. Rees, and M. M. Hayat, “Exponential time response in analogue and Geiger mode avalanche photodiodes,” IEEE Trans. Electron Devices 52, 1527–1534 (2005).
[CrossRef]

J. S. Ng, C. H. Tan, J. P. R. David, and G. J. Rees, “A general method for estimating the duration of avalanche multiplication,” J. Lightwave Technol. 10, 1067–1071 (2002).

M. M. Hayat, G. J. Rees, D. A. Ramirez, and M. A. Itzler, “Statistics of self-quenching time in single photon avalanche diodes,” The 21st Annual Meeting of The IEEE Lasers and Electro-Optics Society pp. 203–231 (2008).

Risk, W. P.

W. P. Risk and D. S. Bethune, “Quantum cryptography,” Opt. Photonics News 13, 26–32 (2002).
[CrossRef]

Saleh, B. E. A.

M. M. Hayat and B. E. A. Saleh, “Statistical properties of the impulse response function of double-carrier multiplication avalanche photodiodes including the effect of dead space,” J. Lightwave Technol. 10, 1415–1425 (1992).
[CrossRef]

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Samori, C.

Shubin, V.

D. Shushakov and V. Shubin, “New solid state photomultiplier,” Proc. of SPIE 2397, 544–554 (1995).
[CrossRef]

D. Shushakov and V. Shubin, “New avalanche device with an ability of a few-photon light pulse detection in analog mode,” Proc. of SPIE2699, 173–183 (1996).
[CrossRef]

Shushakov, D.

D. Shushakov and V. Shubin, “New solid state photomultiplier,” Proc. of SPIE 2397, 544–554 (1995).
[CrossRef]

D. Shushakov and V. Shubin, “New avalanche device with an ability of a few-photon light pulse detection in analog mode,” Proc. of SPIE2699, 173–183 (1996).
[CrossRef]

Slomkowski, K.

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

M. A. Itzler, X. Jiang, B. M. Onat, and K. Slomkowski, “Progress in self-quenching InP-based single photon detectors,” Proc. of SPIE 7608, 760829 (2010).
[CrossRef]

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

M. A. Itzler, X. Jiang, B. Nyman, and K. Slomkowski, “InP-based Negative Feedback Avalanche Diodes,” Proc. of SPIE7222, 72221K (2009).
[CrossRef]

Tan, C. H.

L. J. J. Tan, J. S. Ng, C. H. Tan, and J. P. R. David, “Avalanche noise characteristics in submicron InP diodes,” IEEE J. Quantum Electron. 44, 378–382 (2008).
[CrossRef]

C. Groves, C. H. Tan, J. P. R. David, G. J. Rees, and M. M. Hayat, “Exponential time response in analogue and Geiger mode avalanche photodiodes,” IEEE Trans. Electron Devices 52, 1527–1534 (2005).
[CrossRef]

J. S. Ng, C. H. Tan, J. P. R. David, and G. J. Rees, “A general method for estimating the duration of avalanche multiplication,” J. Lightwave Technol. 10, 1067–1071 (2002).

Tan, L. J. J.

L. J. J. Tan, J. S. Ng, C. H. Tan, and J. P. R. David, “Avalanche noise characteristics in submicron InP diodes,” IEEE J. Quantum Electron. 44, 378–382 (2008).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

Tosi, A.

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

Watson, G. N.

E. T. Whittaker and G. N. Watson, A course on Modern Analysis (Cambridge Mathematical Library, 1996).

Whittaker, E. T.

E. T. Whittaker and G. N. Watson, A course on Modern Analysis (Cambridge Mathematical Library, 1996).

Willard, B. C.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

You, S.

K. Zhao, S. You, J. Cheng, and Y. Lo, “Self-quenching and self-recovering InGaAs/InAlAs single photon avalanche detector,” Appl. Phys. Lett. 93, 153504 (2008).
[CrossRef]

Young, D. J.

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

Zappa, F.

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, “Avalanche photodiodes and quenching circuits for single-photon detection,” Appl. Opt. 35, 1956–1976 (1996).
[CrossRef] [PubMed]

Zayhowski, J. J.

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Zhao, K.

K. Zhao, S. You, J. Cheng, and Y. Lo, “Self-quenching and self-recovering InGaAs/InAlAs single photon avalanche detector,” Appl. Phys. Lett. 93, 153504 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

K. Zhao, S. You, J. Cheng, and Y. Lo, “Self-quenching and self-recovering InGaAs/InAlAs single photon avalanche detector,” Appl. Phys. Lett. 93, 153504 (2008).
[CrossRef]

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B. F. Levine, C. G. Bethea, and J. C. Campbell, “1.52 μm room temperature photon counting optical time domain reflectometer,” Electron. Lett. 21, 194–196 (1985).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. J. J. Tan, J. S. Ng, C. H. Tan, and J. P. R. David, “Avalanche noise characteristics in submicron InP diodes,” IEEE J. Quantum Electron. 44, 378–382 (2008).
[CrossRef]

IEEE Trans. Electron Devices (2)

C. Groves, C. H. Tan, J. P. R. David, G. J. Rees, and M. M. Hayat, “Exponential time response in analogue and Geiger mode avalanche photodiodes,” IEEE Trans. Electron Devices 52, 1527–1534 (2005).
[CrossRef]

M. M. Hayat and G. Dong, “A new approach for computing the bandwidth statistics of avalanche photodiodes,” IEEE Trans. Electron Devices 47, 1273–1279 (2000).
[CrossRef]

R. J. McIntyre, “Multiplication noise in uniform avalanche photodiodes,” IEEE Trans. Electron devices ED. 13, 164–168 (1966).
[CrossRef]

J. Appl. Phys. (2)

R. H. Haitz, “Model for the electrical behavior of a microplasma,” J. Appl. Phys. 35, 1370–1376 (1964).
[CrossRef]

R. B. Emmons, “Avalanche-photodiode frequency response,” J. Appl. Phys. 38, 3705–3714 (1967).
[CrossRef]

J. Lightwave Technol. (2)

J. S. Ng, C. H. Tan, J. P. R. David, and G. J. Rees, “A general method for estimating the duration of avalanche multiplication,” J. Lightwave Technol. 10, 1067–1071 (2002).

M. M. Hayat and B. E. A. Saleh, “Statistical properties of the impulse response function of double-carrier multiplication avalanche photodiodes including the effect of dead space,” J. Lightwave Technol. 10, 1415–1425 (1992).
[CrossRef]

J. Mod. Opt. (2)

M. A. Itzler, X. Jiang, M. Entwistle, K. Slomkowski, A. Tosi, F. Acerbi, F. Zappa, and S. Cova, “Advances in InGaAsP-based avalanche diode single photon detectors,” J. Mod. Opt. 58, 174–200 (2011).
[CrossRef]

M. A. Itzler, R. Ben-Michael, C. F. Hsu, K. Slomkowski, A. Tosi, S. Cova, F. Zappa, and R. Ispasoiu, “Single photon avalanche diodes (SPADs) for 1.5 μm photon counting applications,” J. Mod. Opt. 54, 283–304 (2007).
[CrossRef]

Lincoln Lab. J. (2)

B. F. Aull, A. H. Loomis, D. J. Young, R. M. Heinrichs, B. J. Felton, P. J. Daniels, and D. J. Landers, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

M. A. Albota, B. A. Aull, D. G. Fouche, R. M. Heinrichs, D. G. Kocher, R. M. Marino, J. G. Mooney, N. R. Newbury, M. E. OBrien, B. E. Player, B. C. Willard, and J. J. Zayhowski, “Three-dimensional imaging laser radars with Geiger-mode avalanche photodiode arrays,” Lincoln Lab. J. 13, 351–367 (2002).

Opt. Photonics News (1)

W. P. Risk and D. S. Bethune, “Quantum cryptography,” Opt. Photonics News 13, 26–32 (2002).
[CrossRef]

Proc. of SPIE (3)

M. M. Hayat, M. A. Itzler, D. A. Ramirez, and G. J. Rees, “Model for Passive Quenching of SPADs,” Proc. of SPIE 7608, 76082B–76082B–8 (2010).
[CrossRef]

M. A. Itzler, X. Jiang, B. M. Onat, and K. Slomkowski, “Progress in self-quenching InP-based single photon detectors,” Proc. of SPIE 7608, 760829 (2010).
[CrossRef]

D. Shushakov and V. Shubin, “New solid state photomultiplier,” Proc. of SPIE 2397, 544–554 (1995).
[CrossRef]

Other (7)

D. Shushakov and V. Shubin, “New avalanche device with an ability of a few-photon light pulse detection in analog mode,” Proc. of SPIE2699, 173–183 (1996).
[CrossRef]

E. T. Whittaker and G. N. Watson, A course on Modern Analysis (Cambridge Mathematical Library, 1996).

K. B. Athreya and P. Ney, Branching Processes (Berlin-Germany: Springer-Verlag, 1972).

M. M. Hayat, G. J. Rees, D. A. Ramirez, and M. A. Itzler, “Statistics of self-quenching time in single photon avalanche diodes,” The 21st Annual Meeting of The IEEE Lasers and Electro-Optics Society pp. 203–231 (2008).

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[CrossRef]

D. M. Boroson, R. S. Bondurant, and D. V. Murphy, “LDORA: A novel laser communications receiver array architecture,” Proc. of SPIE5338, 56–64 (2004).
[CrossRef]

M. A. Itzler, X. Jiang, B. Nyman, and K. Slomkowski, “InP-based Negative Feedback Avalanche Diodes,” Proc. of SPIE7222, 72221K (2009).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Models for passively quenched SPADs. (a) Traditional model for a passively quenching SPAD circuit. id represents the self sustaining current through the multiplication region of the SPAD; Rd is its equivalent dynamic resistance; Cd is its junction capacitance; RL is the load resistor and CL is its parasitic capacitance. The traditional model neglects the effect of feedback on the impact ionization process; it assumes that after the trigger of an avalanche, the electric field remains constant at the breakdown threshold, so that the core of the device is represented by a voltage generator, Vb. (b) Stochastically self-regulating avalanche model for passively quenched SPADs. The circuit represents a series combination of a SPAD and a negative feedback load. The load is described as a parallel combination of a resistance, RL and a capacitance, CL. The SPAD is modeled as two parallel branches; one branch consists of the diode depletion capacitance, Cd, the other includes the Monte Carlo simulator, which is represented by the stochastic voltage controlled current source (VCCS) id. The resistor Rd, in series with the VCCS, accounts for the resistance of the bulk regions.

Fig. 2
Fig. 2

Experimental results. (a) Measured pdf of the quenching time [13]. The exponential decay of the pdf implies that the quenching time is memoryless. (b) Measured voltage across the SPAD for an excess bias of Vex ≈ 1.7 V [13]. The current shows oscillatory behavior about the steady state before it quenches spontaneously. The complete structure of the device can be found elsewhere [14].

Fig. 3
Fig. 3

Monte-Carlo simulator for id. The expanded section on the left describes the simulator represented in the circuit on the right by the stochastic VCCS id. In the example a hole is injected at the start of the multiplication region, x = 0, at time t = 0. At time 2Δt the first impact ionization occurs and as a result one hole and one electron are created in the multiplication region. For simplicity we have assumed that electrons and holes have the same drift velocity, v, i.e., v = ve = vh.

Fig. 4
Fig. 4

Calculated current-voltage evolution of SPAD after an avalanche trigger. (a) Calculated avalanche current, ia = id + iCd, (b) voltage across the feedback resistor, RL, and (c) voltage across the SPAD, VCd as a function of time for an excess bias voltage Vex ≈ 0.39 V and a feedback resistor RL = 22 kΩ. It can be seen that the oscillations are centered around their steady state values; thus, the avalanche current oscillates around Iss ≈ 18 μA, the feedback voltage oscillations are centered around VRL = Vex ≈ 0.39 V and the voltage across the SPAD fluctuates around the breakdown voltage Vf = Vb ≈ 64.61 V. Note that quenching occurs at about 2340 transit times. In the simulations it is assumed that the electric field in the multiplication region is spatially uniform, which corresponds to a multiplication region without doping.

Fig. 5
Fig. 5

Timing relationship between the voltage across the junction capacitance and the number of carriers in the multiplication region. The red curve shows the voltage across the junction capacitor VCd and the blue curve shows the current id calculated by the Monte-Carlo simulator. For clarity, the current id was truncated and its first peak is not shown. The stages of the current-voltage evolution identified are: (1) onset of the avalanche, (2) discharge of the junction capacitor, (3) recharge of the junction capacitor and (4) spontaneous quenching.

Fig. 6
Fig. 6

Quenching characteristics of the simulated passively quenched SPAD. (a) Quenching behavior of the simulated passively quenched SPAD for different values of the current Iss. As the current Iss decreases the avalanche current spontaneously quenches sooner, on average. (b) Calculated probability density function of quenching time, Tq.

Equations (22)

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F I ( t ) P { T q t } exp ( T / t ) ,
X e ( t j + 1 , x k ) = X e ( t j , x k + 1 ) + b ( X e ( t j , x k + 1 ) , α ( E C d ( t ) ) Δ w ) + b ( X h ( t j , x k 1 ) , β ( E C d ( t ) ) Δ w )
X h ( t j + 1 , x k ) = X h ( t j , x k 1 ) + b ( X h ( t j , x k 1 ) , β ( E C d ( t ) ) Δ w ) + b ( X e ( t j , x k + 1 ) , α ( E C d ( t ) ) Δ w ) .
i d ( t j ) = q v w k = 1 L ( X e ( t j , k ) + X h ( t j , k ) ) .
M = 1 k exp ( ( 1 k ) α w ) k .
F e ( z , t ) = R e ( z , t ) Q e ( z , t ) + 0 w z 0 t h e ( ζ , τ ) F e 2 ( z + ζ , t τ ) F h ( z + ζ , t τ ) d τ d ζ
F h ( z , t ) = R h ( z , t ) Q h ( z , t ) + 0 z 0 t h h ( ζ , τ ) F h 2 ( z ζ , t τ ) F e ( z ζ , t τ ) d τ d ζ .
f e ( z , t ) = R e ( z , t ) ( 1 Q e ( z , t ) ) + 0 w z 0 t h e ( ζ , τ ) ( 2 f e + f h f e 2 2 f e f h + f e 2 f h ) d τ d ζ
f h ( z , t ) = R h ( z , t ) ( 1 Q h ( z , t ) ) + 0 z 0 t h h ( ζ , τ ) ( 2 f h + f e f h 2 2 f h f e + f h 2 f e ) d τ d ζ .
f e , h ( z , t ) = n = 1 f e , h ; n ( z ) × ( t ) n .
h e ( ζ , τ ) = α exp ( α ζ ) δ ( τ ζ / v e ) and h h ( ζ , τ ) = β exp ( β ζ ) δ ( τ ζ / v h ) .
φ e ( s , r ) = exp ( a ( s 1 ) ) θ ( 1 s r / ρ e ) + a 0 1 s exp ( a p ) ( 2 φ e + φ h φ e 2 2 φ e φ h + φ e 2 φ h ) d p
φ h ( s , r ) = exp ( b ( s 1 ) ) θ ( 1 s r / ρ b ) + b 0 1 s exp ( b p ) ( 2 φ h + φ e φ h 2 2 φ h φ e + φ h 2 φ e ) d p .
φ e ( s ) = a 0 1 s exp ( a p ) ( 2 φ e ( s + p ) + φ h ( s + p ) ) d p
φ h ( s ) = b 0 s exp ( b p ) ( 2 φ h ( s p ) + φ h ( s p ) ) d p .
exp ( a s ) φ e ( s ) = a 0 1 exp ( a u ) ( 2 φ e ( u ) + φ h ( u ) ) d u
exp ( b s ) φ h ( s ) = b 0 s exp ( b u ) ( 2 φ h ( u ) + φ e ( u ) ) d u .
φ e ( s ) = C d ( exp ( d ( 1 s ) ) 1 ) and φ h ( s ) = C d ( 1 exp ( d s ) ) .
f e ; 1 ( z ) = C τ 0 δ w ( exp ( δ ( w z ) ) 1 ) and f h ; 1 ( z ) = C τ 0 δ w ( 1 exp ( δ z ) ) .
n ( z ) = I ( 1 exp ( δ z ) ) q v e ( exp ( δ z ) 1 ) and p ( z ) = I ( exp ( δ z ) exp ( δ w ) ) q v h ( exp ( δ w ) 1 ) ,
ln ( F I ( t ) ) = i ln ( 1 f e , h ( z i ) / t ) 1 t i f e , h ( z i ) .
ln ( F I ( t ) ) 1 t ( 0 w n ( z ) f e ; 1 ( z ) d z + 0 w f h ; 1 p ( z ) d z ) .

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