Abstract

Simple, approximate formulas are developed to calculate the mean gain and excess noise factor for avalanche photodiodes using the dead-space multiplication theory in the regime of small multiplication width and high applied electric field. The accuracy of the approximation is investigated by comparing it to the exact numerical method using recursive coupled integral equations and it is found that it works for dead spaces up to 15% of the multiplication width, which is substantial. The approximation is also tested for real materials such as GaAs, InP and Si for various multiplication widths, and the results found are accurate within ∼ 15% of the actual noise, which is a significant improvement over the local-theory noise formula. The results obtained for the mean gain also confirm the recently reported relationship between experimentally determined local ionization coefficients and the enabled non-local ionization coefficients.

© 2016 Optical Society of America

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Corrections

11 October 2016: A correction was made to the acknowledgments.


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References

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  1. N. Namekata, S. Adachi, and S. Inoue, “Ultra-low-noise sinusoidally gated avalanche photodiode for high-speed single-photon detection at telecommunication wavelengths,” IEEE Photon. Technol. Lett. 22(8), 529–531 (2010).
    [Crossref]
  2. A. Tosi, A. Della Frera, A. B. Shehata, and C. Scarcella, “Fully programmable single-photon detection module for InGaAs/InP single-photon avalanche diodes with clean and sub-nanosecond gating transitions,” Rev. Sci. Instrum. 83(1), 013104 (2012).
    [Crossref] [PubMed]
  3. M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Effect of dead space on gain and noise of double-carrier-multiplication avalanche photodiodes,” IEEE Trans. Electron. Dev. 39(3), 546–552 (1992).
    [Crossref]
  4. K. F. Li, D. S. Ong, J. P. R. David, G. J. Rees, R. C. Tozer, P. N. Robson, and R. Grey, “Avalanche multiplication noise characteristics in thin GaAs p+-in+ diodes,” IEEE Trans. Electron. Dev. 45(10), 2102–2107 (1998).
    [Crossref]
  5. V. Chandramouli, C. M. Maziar, and J. C. Campbell, “Design considerations for high performance avalanche photodiode multiplication layers,” IEEE Trans. Electron. Dev. 41(5), 648–654 (1994).
    [Crossref]
  6. R. J. McIntyre, “Multiplication noise in uniform avalanche diodes,” IEEE Trans. Electron. Dev. 13(1), 164–168 (1966).
    [Crossref]
  7. M. C. Teich, K. Matsuo, and B. E. A. Saleh, “Excess noise factors for conventional and superlattice avalanche photodiodes and photomultiplier tubes,” IEEE J. Quantum Electron. 22(8), 1184–1193 (1986).
    [Crossref]
  8. M. A. Saleh, M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Dead-space-based theory correctly predicts excess noise factor for thin GaAs and AlGaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 47(3), 625–633 (2000).
    [Crossref]
  9. M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, and M. C. Teich, “Impact-ionization and noise characteristics of thin III–V avalanche photodiodes,” IEEE Trans. Electron. Dev. 48(12), 2722–2731 (2001).
    [Crossref]
  10. D. S. Ong, K. F. Li, G. J. Rees, G. M. Dunn, J. P. R. David, and P. N. Robson, “A monte carlo investigation of multiplication noise in thin p+-in+ GaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 45(8), 1804–1810 (1998).
    [Crossref]
  11. G. P. Agrawal, Fiber-optic Communication Systems (John Wiley & Sons, 2012).
  12. A. Spinelli and A. L. Lacaita, “Mean gain of avalanche photodiodes in a dead space model,” IEEE Trans. Electron. Dev. 43(1), 23–30 (1996).
    [Crossref]
  13. M. M. Hayat, Z. Chen, and M. A. Karim, “An analytical approximation for the excess noise factor of avalanche photodiodes with dead space,” IEEE Electron. Dev. Lett. 20(7), 344–347 (1999).
    [Crossref]
  14. J. S. Cheong, M. M. Hayat, X. Zhou, and J. P. R. David, “Relating the experimental ionization coefficients in semiconductors to the nonlocal ionization coefficients,” IEEE Trans. Electron. Dev. 62(6), 1946–1952 (2015).
    [Crossref]
  15. K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
    [Crossref]
  16. M. M. Hossain, P. Zarkesh-Ha, J. P. R. David, and M. M. Hayat, “Low breakdown voltage CMOS compatible pn junction avalanche photodiode,” in Proceedings of IEEE Photonics Conference (IEEE, 2014), pp. 170–171.

2015 (1)

J. S. Cheong, M. M. Hayat, X. Zhou, and J. P. R. David, “Relating the experimental ionization coefficients in semiconductors to the nonlocal ionization coefficients,” IEEE Trans. Electron. Dev. 62(6), 1946–1952 (2015).
[Crossref]

2012 (1)

A. Tosi, A. Della Frera, A. B. Shehata, and C. Scarcella, “Fully programmable single-photon detection module for InGaAs/InP single-photon avalanche diodes with clean and sub-nanosecond gating transitions,” Rev. Sci. Instrum. 83(1), 013104 (2012).
[Crossref] [PubMed]

2010 (1)

N. Namekata, S. Adachi, and S. Inoue, “Ultra-low-noise sinusoidally gated avalanche photodiode for high-speed single-photon detection at telecommunication wavelengths,” IEEE Photon. Technol. Lett. 22(8), 529–531 (2010).
[Crossref]

2001 (1)

M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, and M. C. Teich, “Impact-ionization and noise characteristics of thin III–V avalanche photodiodes,” IEEE Trans. Electron. Dev. 48(12), 2722–2731 (2001).
[Crossref]

2000 (1)

M. A. Saleh, M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Dead-space-based theory correctly predicts excess noise factor for thin GaAs and AlGaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 47(3), 625–633 (2000).
[Crossref]

1999 (1)

M. M. Hayat, Z. Chen, and M. A. Karim, “An analytical approximation for the excess noise factor of avalanche photodiodes with dead space,” IEEE Electron. Dev. Lett. 20(7), 344–347 (1999).
[Crossref]

1998 (2)

D. S. Ong, K. F. Li, G. J. Rees, G. M. Dunn, J. P. R. David, and P. N. Robson, “A monte carlo investigation of multiplication noise in thin p+-in+ GaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 45(8), 1804–1810 (1998).
[Crossref]

K. F. Li, D. S. Ong, J. P. R. David, G. J. Rees, R. C. Tozer, P. N. Robson, and R. Grey, “Avalanche multiplication noise characteristics in thin GaAs p+-in+ diodes,” IEEE Trans. Electron. Dev. 45(10), 2102–2107 (1998).
[Crossref]

1997 (1)

K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
[Crossref]

1996 (1)

A. Spinelli and A. L. Lacaita, “Mean gain of avalanche photodiodes in a dead space model,” IEEE Trans. Electron. Dev. 43(1), 23–30 (1996).
[Crossref]

1994 (1)

V. Chandramouli, C. M. Maziar, and J. C. Campbell, “Design considerations for high performance avalanche photodiode multiplication layers,” IEEE Trans. Electron. Dev. 41(5), 648–654 (1994).
[Crossref]

1992 (1)

M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Effect of dead space on gain and noise of double-carrier-multiplication avalanche photodiodes,” IEEE Trans. Electron. Dev. 39(3), 546–552 (1992).
[Crossref]

1986 (1)

M. C. Teich, K. Matsuo, and B. E. A. Saleh, “Excess noise factors for conventional and superlattice avalanche photodiodes and photomultiplier tubes,” IEEE J. Quantum Electron. 22(8), 1184–1193 (1986).
[Crossref]

1966 (1)

R. J. McIntyre, “Multiplication noise in uniform avalanche diodes,” IEEE Trans. Electron. Dev. 13(1), 164–168 (1966).
[Crossref]

Adachi, S.

N. Namekata, S. Adachi, and S. Inoue, “Ultra-low-noise sinusoidally gated avalanche photodiode for high-speed single-photon detection at telecommunication wavelengths,” IEEE Photon. Technol. Lett. 22(8), 529–531 (2010).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, Fiber-optic Communication Systems (John Wiley & Sons, 2012).

Anselm, K. A.

K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
[Crossref]

Campbell, J. C.

M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, and M. C. Teich, “Impact-ionization and noise characteristics of thin III–V avalanche photodiodes,” IEEE Trans. Electron. Dev. 48(12), 2722–2731 (2001).
[Crossref]

K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
[Crossref]

V. Chandramouli, C. M. Maziar, and J. C. Campbell, “Design considerations for high performance avalanche photodiode multiplication layers,” IEEE Trans. Electron. Dev. 41(5), 648–654 (1994).
[Crossref]

Chandramouli, V.

V. Chandramouli, C. M. Maziar, and J. C. Campbell, “Design considerations for high performance avalanche photodiode multiplication layers,” IEEE Trans. Electron. Dev. 41(5), 648–654 (1994).
[Crossref]

Chen, Z.

M. M. Hayat, Z. Chen, and M. A. Karim, “An analytical approximation for the excess noise factor of avalanche photodiodes with dead space,” IEEE Electron. Dev. Lett. 20(7), 344–347 (1999).
[Crossref]

Cheong, J. S.

J. S. Cheong, M. M. Hayat, X. Zhou, and J. P. R. David, “Relating the experimental ionization coefficients in semiconductors to the nonlocal ionization coefficients,” IEEE Trans. Electron. Dev. 62(6), 1946–1952 (2015).
[Crossref]

David, J. P. R.

J. S. Cheong, M. M. Hayat, X. Zhou, and J. P. R. David, “Relating the experimental ionization coefficients in semiconductors to the nonlocal ionization coefficients,” IEEE Trans. Electron. Dev. 62(6), 1946–1952 (2015).
[Crossref]

D. S. Ong, K. F. Li, G. J. Rees, G. M. Dunn, J. P. R. David, and P. N. Robson, “A monte carlo investigation of multiplication noise in thin p+-in+ GaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 45(8), 1804–1810 (1998).
[Crossref]

K. F. Li, D. S. Ong, J. P. R. David, G. J. Rees, R. C. Tozer, P. N. Robson, and R. Grey, “Avalanche multiplication noise characteristics in thin GaAs p+-in+ diodes,” IEEE Trans. Electron. Dev. 45(10), 2102–2107 (1998).
[Crossref]

M. M. Hossain, P. Zarkesh-Ha, J. P. R. David, and M. M. Hayat, “Low breakdown voltage CMOS compatible pn junction avalanche photodiode,” in Proceedings of IEEE Photonics Conference (IEEE, 2014), pp. 170–171.

Della Frera, A.

A. Tosi, A. Della Frera, A. B. Shehata, and C. Scarcella, “Fully programmable single-photon detection module for InGaAs/InP single-photon avalanche diodes with clean and sub-nanosecond gating transitions,” Rev. Sci. Instrum. 83(1), 013104 (2012).
[Crossref] [PubMed]

Dunn, G. M.

D. S. Ong, K. F. Li, G. J. Rees, G. M. Dunn, J. P. R. David, and P. N. Robson, “A monte carlo investigation of multiplication noise in thin p+-in+ GaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 45(8), 1804–1810 (1998).
[Crossref]

Grey, R.

K. F. Li, D. S. Ong, J. P. R. David, G. J. Rees, R. C. Tozer, P. N. Robson, and R. Grey, “Avalanche multiplication noise characteristics in thin GaAs p+-in+ diodes,” IEEE Trans. Electron. Dev. 45(10), 2102–2107 (1998).
[Crossref]

Hayat, M. M.

J. S. Cheong, M. M. Hayat, X. Zhou, and J. P. R. David, “Relating the experimental ionization coefficients in semiconductors to the nonlocal ionization coefficients,” IEEE Trans. Electron. Dev. 62(6), 1946–1952 (2015).
[Crossref]

M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, and M. C. Teich, “Impact-ionization and noise characteristics of thin III–V avalanche photodiodes,” IEEE Trans. Electron. Dev. 48(12), 2722–2731 (2001).
[Crossref]

M. A. Saleh, M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Dead-space-based theory correctly predicts excess noise factor for thin GaAs and AlGaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 47(3), 625–633 (2000).
[Crossref]

M. M. Hayat, Z. Chen, and M. A. Karim, “An analytical approximation for the excess noise factor of avalanche photodiodes with dead space,” IEEE Electron. Dev. Lett. 20(7), 344–347 (1999).
[Crossref]

M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Effect of dead space on gain and noise of double-carrier-multiplication avalanche photodiodes,” IEEE Trans. Electron. Dev. 39(3), 546–552 (1992).
[Crossref]

M. M. Hossain, P. Zarkesh-Ha, J. P. R. David, and M. M. Hayat, “Low breakdown voltage CMOS compatible pn junction avalanche photodiode,” in Proceedings of IEEE Photonics Conference (IEEE, 2014), pp. 170–171.

Holmes, A. L.

M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, and M. C. Teich, “Impact-ionization and noise characteristics of thin III–V avalanche photodiodes,” IEEE Trans. Electron. Dev. 48(12), 2722–2731 (2001).
[Crossref]

Hossain, M. M.

M. M. Hossain, P. Zarkesh-Ha, J. P. R. David, and M. M. Hayat, “Low breakdown voltage CMOS compatible pn junction avalanche photodiode,” in Proceedings of IEEE Photonics Conference (IEEE, 2014), pp. 170–171.

Hu, C.

K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
[Crossref]

Inoue, S.

N. Namekata, S. Adachi, and S. Inoue, “Ultra-low-noise sinusoidally gated avalanche photodiode for high-speed single-photon detection at telecommunication wavelengths,” IEEE Photon. Technol. Lett. 22(8), 529–531 (2010).
[Crossref]

Karim, M. A.

M. M. Hayat, Z. Chen, and M. A. Karim, “An analytical approximation for the excess noise factor of avalanche photodiodes with dead space,” IEEE Electron. Dev. Lett. 20(7), 344–347 (1999).
[Crossref]

Kinsey, G.

K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
[Crossref]

Lacaita, A. L.

A. Spinelli and A. L. Lacaita, “Mean gain of avalanche photodiodes in a dead space model,” IEEE Trans. Electron. Dev. 43(1), 23–30 (1996).
[Crossref]

Lenox, C.

K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
[Crossref]

Li, K. F.

K. F. Li, D. S. Ong, J. P. R. David, G. J. Rees, R. C. Tozer, P. N. Robson, and R. Grey, “Avalanche multiplication noise characteristics in thin GaAs p+-in+ diodes,” IEEE Trans. Electron. Dev. 45(10), 2102–2107 (1998).
[Crossref]

D. S. Ong, K. F. Li, G. J. Rees, G. M. Dunn, J. P. R. David, and P. N. Robson, “A monte carlo investigation of multiplication noise in thin p+-in+ GaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 45(8), 1804–1810 (1998).
[Crossref]

Matsuo, K.

M. C. Teich, K. Matsuo, and B. E. A. Saleh, “Excess noise factors for conventional and superlattice avalanche photodiodes and photomultiplier tubes,” IEEE J. Quantum Electron. 22(8), 1184–1193 (1986).
[Crossref]

Maziar, C. M.

V. Chandramouli, C. M. Maziar, and J. C. Campbell, “Design considerations for high performance avalanche photodiode multiplication layers,” IEEE Trans. Electron. Dev. 41(5), 648–654 (1994).
[Crossref]

McIntyre, R. J.

R. J. McIntyre, “Multiplication noise in uniform avalanche diodes,” IEEE Trans. Electron. Dev. 13(1), 164–168 (1966).
[Crossref]

Namekata, N.

N. Namekata, S. Adachi, and S. Inoue, “Ultra-low-noise sinusoidally gated avalanche photodiode for high-speed single-photon detection at telecommunication wavelengths,” IEEE Photon. Technol. Lett. 22(8), 529–531 (2010).
[Crossref]

Nie, H.

K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
[Crossref]

Ong, D. S.

K. F. Li, D. S. Ong, J. P. R. David, G. J. Rees, R. C. Tozer, P. N. Robson, and R. Grey, “Avalanche multiplication noise characteristics in thin GaAs p+-in+ diodes,” IEEE Trans. Electron. Dev. 45(10), 2102–2107 (1998).
[Crossref]

D. S. Ong, K. F. Li, G. J. Rees, G. M. Dunn, J. P. R. David, and P. N. Robson, “A monte carlo investigation of multiplication noise in thin p+-in+ GaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 45(8), 1804–1810 (1998).
[Crossref]

Rees, G. J.

D. S. Ong, K. F. Li, G. J. Rees, G. M. Dunn, J. P. R. David, and P. N. Robson, “A monte carlo investigation of multiplication noise in thin p+-in+ GaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 45(8), 1804–1810 (1998).
[Crossref]

K. F. Li, D. S. Ong, J. P. R. David, G. J. Rees, R. C. Tozer, P. N. Robson, and R. Grey, “Avalanche multiplication noise characteristics in thin GaAs p+-in+ diodes,” IEEE Trans. Electron. Dev. 45(10), 2102–2107 (1998).
[Crossref]

Robson, P. N.

K. F. Li, D. S. Ong, J. P. R. David, G. J. Rees, R. C. Tozer, P. N. Robson, and R. Grey, “Avalanche multiplication noise characteristics in thin GaAs p+-in+ diodes,” IEEE Trans. Electron. Dev. 45(10), 2102–2107 (1998).
[Crossref]

D. S. Ong, K. F. Li, G. J. Rees, G. M. Dunn, J. P. R. David, and P. N. Robson, “A monte carlo investigation of multiplication noise in thin p+-in+ GaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 45(8), 1804–1810 (1998).
[Crossref]

Saleh, B. E. A.

M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, and M. C. Teich, “Impact-ionization and noise characteristics of thin III–V avalanche photodiodes,” IEEE Trans. Electron. Dev. 48(12), 2722–2731 (2001).
[Crossref]

M. A. Saleh, M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Dead-space-based theory correctly predicts excess noise factor for thin GaAs and AlGaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 47(3), 625–633 (2000).
[Crossref]

M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Effect of dead space on gain and noise of double-carrier-multiplication avalanche photodiodes,” IEEE Trans. Electron. Dev. 39(3), 546–552 (1992).
[Crossref]

M. C. Teich, K. Matsuo, and B. E. A. Saleh, “Excess noise factors for conventional and superlattice avalanche photodiodes and photomultiplier tubes,” IEEE J. Quantum Electron. 22(8), 1184–1193 (1986).
[Crossref]

Saleh, M. A.

M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, and M. C. Teich, “Impact-ionization and noise characteristics of thin III–V avalanche photodiodes,” IEEE Trans. Electron. Dev. 48(12), 2722–2731 (2001).
[Crossref]

M. A. Saleh, M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Dead-space-based theory correctly predicts excess noise factor for thin GaAs and AlGaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 47(3), 625–633 (2000).
[Crossref]

Scarcella, C.

A. Tosi, A. Della Frera, A. B. Shehata, and C. Scarcella, “Fully programmable single-photon detection module for InGaAs/InP single-photon avalanche diodes with clean and sub-nanosecond gating transitions,” Rev. Sci. Instrum. 83(1), 013104 (2012).
[Crossref] [PubMed]

Shehata, A. B.

A. Tosi, A. Della Frera, A. B. Shehata, and C. Scarcella, “Fully programmable single-photon detection module for InGaAs/InP single-photon avalanche diodes with clean and sub-nanosecond gating transitions,” Rev. Sci. Instrum. 83(1), 013104 (2012).
[Crossref] [PubMed]

Sotirelis, P. P.

M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, and M. C. Teich, “Impact-ionization and noise characteristics of thin III–V avalanche photodiodes,” IEEE Trans. Electron. Dev. 48(12), 2722–2731 (2001).
[Crossref]

Spinelli, A.

A. Spinelli and A. L. Lacaita, “Mean gain of avalanche photodiodes in a dead space model,” IEEE Trans. Electron. Dev. 43(1), 23–30 (1996).
[Crossref]

Streetman, B. G.

K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
[Crossref]

Teich, M. C.

M. A. Saleh, M. M. Hayat, P. P. Sotirelis, A. L. Holmes, J. C. Campbell, B. E. A. Saleh, and M. C. Teich, “Impact-ionization and noise characteristics of thin III–V avalanche photodiodes,” IEEE Trans. Electron. Dev. 48(12), 2722–2731 (2001).
[Crossref]

M. A. Saleh, M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Dead-space-based theory correctly predicts excess noise factor for thin GaAs and AlGaAs avalanche photodiodes,” IEEE Trans. Electron. Dev. 47(3), 625–633 (2000).
[Crossref]

M. M. Hayat, B. E. A. Saleh, and M. C. Teich, “Effect of dead space on gain and noise of double-carrier-multiplication avalanche photodiodes,” IEEE Trans. Electron. Dev. 39(3), 546–552 (1992).
[Crossref]

M. C. Teich, K. Matsuo, and B. E. A. Saleh, “Excess noise factors for conventional and superlattice avalanche photodiodes and photomultiplier tubes,” IEEE J. Quantum Electron. 22(8), 1184–1193 (1986).
[Crossref]

Tosi, A.

A. Tosi, A. Della Frera, A. B. Shehata, and C. Scarcella, “Fully programmable single-photon detection module for InGaAs/InP single-photon avalanche diodes with clean and sub-nanosecond gating transitions,” Rev. Sci. Instrum. 83(1), 013104 (2012).
[Crossref] [PubMed]

Tozer, R. C.

K. F. Li, D. S. Ong, J. P. R. David, G. J. Rees, R. C. Tozer, P. N. Robson, and R. Grey, “Avalanche multiplication noise characteristics in thin GaAs p+-in+ diodes,” IEEE Trans. Electron. Dev. 45(10), 2102–2107 (1998).
[Crossref]

Yuan, P.

K. A. Anselm, P. Yuan, C. Hu, C. Lenox, H. Nie, G. Kinsey, J. C. Campbell, and B. G. Streetman, “Characteristics of GaAs and AlGaAs homojunction avalanche photodiodes with thin multiplication regions,” Appl. Phys. Lett. 20(26), 3883–3885 (1997).
[Crossref]

Zarkesh-Ha, P.

M. M. Hossain, P. Zarkesh-Ha, J. P. R. David, and M. M. Hayat, “Low breakdown voltage CMOS compatible pn junction avalanche photodiode,” in Proceedings of IEEE Photonics Conference (IEEE, 2014), pp. 170–171.

Zhou, X.

J. S. Cheong, M. M. Hayat, X. Zhou, and J. P. R. David, “Relating the experimental ionization coefficients in semiconductors to the nonlocal ionization coefficients,” IEEE Trans. Electron. Dev. 62(6), 1946–1952 (2015).
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A. Tosi, A. Della Frera, A. B. Shehata, and C. Scarcella, “Fully programmable single-photon detection module for InGaAs/InP single-photon avalanche diodes with clean and sub-nanosecond gating transitions,” Rev. Sci. Instrum. 83(1), 013104 (2012).
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Other (2)

M. M. Hossain, P. Zarkesh-Ha, J. P. R. David, and M. M. Hayat, “Low breakdown voltage CMOS compatible pn junction avalanche photodiode,” in Proceedings of IEEE Photonics Conference (IEEE, 2014), pp. 170–171.

G. P. Agrawal, Fiber-optic Communication Systems (John Wiley & Sons, 2012).

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Figures (7)

Fig. 1
Fig. 1 The enabled ionization parameters, α* and β*, as a function of the inverse applied electric field for Si, InP and GaAs [14]. The encircled area highlights the ionization coefficients and electric field across the APD devices where the assumption k ≈ 1 is valid. As an example, for a GaAs APD with the multiplication width = 0.05 − 0.1μm [4], which has k = 0.86 and mean gain = 8, the assumption of k ≈ 1 may be used to get an estimation of the mean gain and the excess noise.
Fig. 2
Fig. 2 Mean gain, found from ENM and CM techniques, is shown as a function of the ionization parameter, α*w, for d′ = d/w = 0, 0.1 and 0.15. These results hold for any avalanche region for which the assumption, k = 1 is justified. The mean gain found from Spinelli analytical formulation is also shown for the case of d′ = 0.1 for comparison.
Fig. 3
Fig. 3 The excess noise factor, F, as a function of the mean gain, 〈G〉, is shown for both the ENM and CM techniques. The normalized dead spaces of d′ = d/w = 0, 0.1 and 0.15 are considered for comparison and the effective McIntyre ionization coefficient, keff is noted for each case and stated in the legend.
Fig. 4
Fig. 4 The excess noise factor as a function of the mean gain is shown for the ENM and traditional CM [13] method for k = 0.9 and compared to the modified CM (k = 1). The normalized dead space, d′ = d/w, is taken to be 0.15. It can be seen that the modified CM gives a better approximation than the traditional method.
Fig. 5
Fig. 5 The excess noise factor, F, shown as a function of the mean gain for various multiplication widths of GaAs. The CM technique predicts the excess noise far better than McIntyre’s local-theory (LT) model with equal ionization coefficients assumption. Data is also shown for experimental GaAs APDs of widths 500 and 800 nm, respectively, as reference [15].
Fig. 6
Fig. 6 Relative errors between the excess noise factors, found by comparing the ENM to McIntyre’s local-theory model (with k ≠ 1) and the CM technique, are shown. The errors are plotted as a function of various multiplication widths of GaAs, InP and Si APD devices for a mean gain of 22. We use these values to determine the multiplication widths for which the CM approximation may be used practically.
Fig. 7
Fig. 7 Relative errors in the excess noise calculated from McIntyre’s local-theory (LT) model (k ≠ 1) and the CM technique, as compared to ENM technique for three different widths of (a) GaAs, (b) InP and (c) Si [14]. As the gain increases, the relative error associated with the CM technique approaches a constant value.

Tables (1)

Tables Icon

Table 1 Material widths for which the CM techniques predicts noise within 15% of the ENM. The upper limit of d′ corresponds to the lower limit of the multiplication width and vice versa. From [14], the second set of ionization parameters are used for GaAs and Si whereas the third set is used for InP.

Equations (24)

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M ( x ) = exp ( x w [ β ( x ) α ( x ) ] d x ) 1 0 w [ β ( x ) exp ( x w [ β ( x ) α ( x ) ] d x ) ] d x .
G = 1 1 α w .
F = k G + ( 1 k ) ( 2 1 G ) ,
G = 0.5 ( z ( 0 ) + 1 )
F = G 2 G 2 = ( z 0 ( 0 ) + 4 G 1 ) 4 G 2 .
z ( x ) α * [ z ( x ) 2 z ( x + d e ) y ( x + d e ) ] = 0
y ( x ) + β * [ y ( x ) 2 y ( x d h ) z ( x d h ) ] = 0 ,
z ( x ) α * [ z ( x ) 2 z ( x + d ) y ( x + d ) ] = 0
y ( x ) + α * [ y ( x ) 2 y ( x d ) z ( x d ) ] = 0 .
( r α * + 2 α * e r d ) ( r + α * 2 α * e r d ) + α * 2 = 0 .
G = 1 + 2 α * d 1 + 3 α * d α * w ,
G = 1 + 2 α ˜ * d 1 + 3 α ˜ * d α ˜ * ,
G = 1 1 + 2 α ˜ * d α ˜ * ,
G = 1 1 α ˜ * + α ˜ * d ( 1 + 2 α ˜ ) ( α ˜ * 1 ) ( 3 α ˜ * d α ˜ * + 1 ) .
G = 1 1 α * w .
z 2 ( x ) α * [ z 2 ( x ) 2 z 2 ( x + d ) y 2 ( x + d ) ] = 2 α * z ( x + d ) ( 2 y ( x + d ) + z ( x + d ) )
y 2 ( x ) + α * [ y 2 ( x ) 2 y 2 ( x d ) z 2 ( x d ) ] = 2 α * y ( x d ) ( 2 z ( x d ) + y ( x d ) ) .
z 2 ( 0 ) = 3 α * 3 d 3 + 5 α * 3 d 2 w + α * 3 d w 2 α * 3 w 3 + 7 α * 2 d 2 + 6 α * 2 d w α * 2 w 2 + α * d + 5 α * w + 1 ( 3 α * d α * w + 1 ) 3
F = 12 α * 3 d 3 4 w α * 3 d 2 + 16 α * 2 d 2 4 w α * 2 d + 6 α * d + 1 ( 2 α * d + 1 ) 2 ( 3 α * d α * w + 1 ) ,
F = 12 α ˜ * 3 d 3 4 α ˜ * 3 d 2 + 16 α ˜ * 2 d 2 4 α ˜ * 2 d + 6 α ˜ * d + 1 ( 2 α ˜ * d + 1 ) 2 ( 3 α ˜ * d α ˜ * + 1 ) .
F = 1 1 α ˜ * + f ( d ) ,
12 α ˜ * 4 d 3 + 4 α ˜ * 4 d 2 16 α ˜ * 3 d 2 + 4 α ˜ * 3 d 6 α ˜ * 2 d α ˜ * d d 3 ( 12 α ˜ * 4 + 12 α ˜ * 3 ) + d 2 ( 4 α ˜ * 4 20 α ˜ * 3 + 16 α ˜ * 2 ) + d ( 4 α ˜ * 3 11 α ˜ * 2 + 7 α ˜ * ) + 1 2 α ˜ * + α ˜ * 2 .
G = 1 1 α w .
α = 1 ( d / w ) ( α * ) 1 + 2 d .

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