Abstract

This paper reports a novel recurrence theory that enables us to calculate the exact joint probability density function (pdf) of the random gain and the random avalanche buildup time in avalanche photodiodes (APDs) including the effect of dead space. Such calculations reveal a strong statistical correlation between the gain and the buildup time for all widths of the multiplication region. To facilitate the calculation of the photocurrent statistics in the presence of this correlation, the impulse-response function of the APD is approximately modeled by a function of time whose prespecified shape is appropriately parameterized by two random variables: the gain and the buildup time. The evaluation of the variance of the photocurrent under this model leads to the definition of the shot-noise-equivalent bandwidth of the APD, which captures the statistical correlation between the gain and the buildup time. It is shown that the shot-noise-equivalent bandwidth in GaAs APDs is greater, by approximately 30%, than the traditional buildup-time-limited 3-dB bandwidth, which is calculated from the mean of the impulse-response function. A thorough analysis of the performance of APD-based integrate-and-dump digital receivers reveals that the strong correlation between the gain and the buildup time accentuates intersymbol interference (ISI) noise, and thus, adversely affects receiver sensitivity at high transmission rates beyond previously known limits.

© 2006 IEEE

PDF Article

References

  • View by:
  • |

  1. R. J. McIntyre, "Multiplication noise in uniform avalanche photodiodes", IEEE Trans. Electron Devices, vol. ED-13, no. 1, pp. 164-168, Jan. 1966.
  2. P. Bhattacharya, Semiconductor Optoelectronic Devices, Upper Saddle River, NJ: Prentice-Hall, 1997.
  3. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, New York: Wiley, 1991.
  4. 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., vol. QE-22, no. 8, pp. 1184-1193, Aug. 1986.
  5. C. Hu, K. A. Anselm, B. G. Streetman and J. C. Campbell, "Noise characteristics of thin multiplication region GaAs avalanche photodiodes", Appl. Phys. Lett., vol. 69, no. 24, pp. 3734-3736, Dec. 1996.
  6. 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., vol. 71, no. 26, pp. 3883-3885, Dec. 1997.
  7. C. Lenox, P. Yuan, H. Nie, O. Baklenov, C. Hansing, J. C. Campbell, J. A. L. Holmes and B. G. Streetman, "Thin multiplication region InAlAs homojunction avalanche photodiodes", Appl. Phys. Lett., vol. 73, no. 6, pp. 783-784, Aug. 1998.
  8. 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+ -i -n+ diodes", IEEE Trans. Electron Devices, vol. 45, no. 10, pp. 2102-2107, Oct. 1998.
  9. K. F. Li, D. S. Ong, J. P. R. David, P. N. Robson, R. C. Tozer, G. J. Rees and R. Grey, "Low excess noise characteristics in thin avalanche region GaAs diodes", Electron. Lett., vol. 34, no. 1, pp. 125-126, Jan. 1998.
  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+ -i -n+ GaAs avalanche photodiodes", IEEE Trans. Electron Devices, vol. 45, no. 8, pp. 1804-1810, Aug. 1998.
  11. D. S. Ong, K. F. Li, G. J. Rees, J. P. R. David and P. N. Robson, "Monte Carlo estimation of multiplication noise in thin p+ -i -n+ GaAs diodes", Appl. Phys. Lett., vol. 72, no. 2, pp. 232-234, Jan. 1998.
  12. S. A. Plimmer, J. P. R. David, R. Grey and G. J. Rees, "Avalanche multiplication in AlxGa1-xAs (x = 0 to 0.60)", IEEE Trans. Electron Devices, vol. 47, no. 5, pp. 1089-1097, May 2000.
  13. K. F. Li, D. S. Ong, J. P. R. David, R. C. Tozer, G. J. Rees, S. A. Plimmer, K. Y. Chang and J. S. Roberts, "Avalanche noise characteristics of thin GaAs structures with distributed carrier generation", IEEE Trans. Electron Devices, vol. 47, no. 5, pp. 910-914, May 2000.
  14. C. H. Tan, J. C. Clark, J. R. P. David, G. J. Rees, S. A. Plimmer and R. C. Tozer, "Avalanche noise measurement in thin Si p+ -i -n+ diodes", Appl. Phys. Lett., vol. 76, no. 26, pp. 3926-3928, Jun. 2000.
  15. 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. Lightw. Technol., vol. 10, no. 10, pp. 1415-1425, Oct. 1992.
  16. M. M. Hayat, O. Kwon, Y. Pan, P. Sotirelis, J. C. Campbell, B. E. A. Saleh and M. C. Teich, "Gain-bandwidth characteristics of thin avalanche photodiodes", IEEE Trans. Electron Devices, vol. 49, no. 5, pp. 770-781, May 2002.
  17. 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 Devices, vol. 39, no. 3, pp. 546-552, Mar. 1992.
  18. X. Li, X. Zheng, S. Wang, F. Ma and J. C. Campbell, "Calculation of gain and noise with dead space for GaAs and AlxGa1-xAs avalanche photodiode", IEEE Trans. Electron Devices, vol. 49, no. 7, pp. 1112-1117, Jul. 2002.
  19. M. M. Hayat and G. Dong, "A new approach for computing the bandwidth statistics of avalanche photodiodes", IEEE Trans. Electron Devices, vol. 47, no. 6, pp. 1273-1279, Jun. 2000.
  20. M. M. Hayat, O. Kwon, S. Wang, J. C. Campbell, B. E. A. Saleh and M. C. Teich, "Boundary effects on multiplication noise in thin heterostructure avalanche photodiodes: Theory and experiment", IEEE Trans. Electron Devices, vol. 49, no. 12, pp. 2114-2123, Dec. 2002.
  21. N. R. Das and M. J. Deen, "A new model for avalanche build-up of carriers in a SAGCM avalanche photodiode", IEEE Trans. Electron Devices, vol. 49, no. 12, pp. 2362-2366, Dec. 2002.
  22. O.-H. Kwon, M. M. Hayat, J. C. Campbell, B. E. A. Saleh and M. C. Teich, "Effect of stochastic dead space on noise in avalanche photodiodes", IEEE Trans. Electron Devices, vol. 51, no. 5, pp. 693-700, May 2004.
  23. J. A. Gubner and M. M. Hayat, "A method to recover counting distributions from their characteristic functions", IEEE Signal Process. Lett., vol. 3, no. 6, pp. 184-186, Jun. 1996.
  24. 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 Devices, vol. 48, no. 12, pp. 2722-2731, Dec. 2001.
  25. S. Hava and M. Auslender, "Velocity-field relation in GaAlAs versus alloy composition", J. Appl. Phys., vol. 73, pp. 7431-7434, Jun. 1993.
  26. D. Snyder and M. Miller, Random Point Processes in Time and Space, New York: Springer-Verlag, 1991.
  27. M. M. Hayat, B. E. A. Saleh and J. A. Gubner, "Bit-error rates for optical receivers using avalanche photodiodes with dead space", IEEE Trans. Comm., vol. 43, no. 1, pp. 99-107, Jan. 1995.
  28. G. Kahraman, B. E. A. Saleh, W. L. Sargeant and M. C. Teich, "Time and frequency response of avalanche photodiodes with arbitrary structure", IEEE Trans. Electron Devices, vol. 39, no. 3, pp. 553-560, Mar. 1992.
  29. J. S. Ng, C. H. Tan, B. K. Ng, P. J. Hambleton, J. P. R. David, G. J. Rees, A. H. You and D. S. Ong, "Effect of dead space on avalanche speed", IEEE Trans. Electron Devices, vol. 49, no. 4, pp. 544-549, Apr. 2002.

Other (29)

R. J. McIntyre, "Multiplication noise in uniform avalanche photodiodes", IEEE Trans. Electron Devices, vol. ED-13, no. 1, pp. 164-168, Jan. 1966.

P. Bhattacharya, Semiconductor Optoelectronic Devices, Upper Saddle River, NJ: Prentice-Hall, 1997.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, New York: Wiley, 1991.

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., vol. QE-22, no. 8, pp. 1184-1193, Aug. 1986.

C. Hu, K. A. Anselm, B. G. Streetman and J. C. Campbell, "Noise characteristics of thin multiplication region GaAs avalanche photodiodes", Appl. Phys. Lett., vol. 69, no. 24, pp. 3734-3736, Dec. 1996.

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., vol. 71, no. 26, pp. 3883-3885, Dec. 1997.

C. Lenox, P. Yuan, H. Nie, O. Baklenov, C. Hansing, J. C. Campbell, J. A. L. Holmes and B. G. Streetman, "Thin multiplication region InAlAs homojunction avalanche photodiodes", Appl. Phys. Lett., vol. 73, no. 6, pp. 783-784, Aug. 1998.

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+ -i -n+ diodes", IEEE Trans. Electron Devices, vol. 45, no. 10, pp. 2102-2107, Oct. 1998.

K. F. Li, D. S. Ong, J. P. R. David, P. N. Robson, R. C. Tozer, G. J. Rees and R. Grey, "Low excess noise characteristics in thin avalanche region GaAs diodes", Electron. Lett., vol. 34, no. 1, pp. 125-126, Jan. 1998.

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+ -i -n+ GaAs avalanche photodiodes", IEEE Trans. Electron Devices, vol. 45, no. 8, pp. 1804-1810, Aug. 1998.

D. S. Ong, K. F. Li, G. J. Rees, J. P. R. David and P. N. Robson, "Monte Carlo estimation of multiplication noise in thin p+ -i -n+ GaAs diodes", Appl. Phys. Lett., vol. 72, no. 2, pp. 232-234, Jan. 1998.

S. A. Plimmer, J. P. R. David, R. Grey and G. J. Rees, "Avalanche multiplication in AlxGa1-xAs (x = 0 to 0.60)", IEEE Trans. Electron Devices, vol. 47, no. 5, pp. 1089-1097, May 2000.

K. F. Li, D. S. Ong, J. P. R. David, R. C. Tozer, G. J. Rees, S. A. Plimmer, K. Y. Chang and J. S. Roberts, "Avalanche noise characteristics of thin GaAs structures with distributed carrier generation", IEEE Trans. Electron Devices, vol. 47, no. 5, pp. 910-914, May 2000.

C. H. Tan, J. C. Clark, J. R. P. David, G. J. Rees, S. A. Plimmer and R. C. Tozer, "Avalanche noise measurement in thin Si p+ -i -n+ diodes", Appl. Phys. Lett., vol. 76, no. 26, pp. 3926-3928, Jun. 2000.

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. Lightw. Technol., vol. 10, no. 10, pp. 1415-1425, Oct. 1992.

M. M. Hayat, O. Kwon, Y. Pan, P. Sotirelis, J. C. Campbell, B. E. A. Saleh and M. C. Teich, "Gain-bandwidth characteristics of thin avalanche photodiodes", IEEE Trans. Electron Devices, vol. 49, no. 5, pp. 770-781, May 2002.

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 Devices, vol. 39, no. 3, pp. 546-552, Mar. 1992.

X. Li, X. Zheng, S. Wang, F. Ma and J. C. Campbell, "Calculation of gain and noise with dead space for GaAs and AlxGa1-xAs avalanche photodiode", IEEE Trans. Electron Devices, vol. 49, no. 7, pp. 1112-1117, Jul. 2002.

M. M. Hayat and G. Dong, "A new approach for computing the bandwidth statistics of avalanche photodiodes", IEEE Trans. Electron Devices, vol. 47, no. 6, pp. 1273-1279, Jun. 2000.

M. M. Hayat, O. Kwon, S. Wang, J. C. Campbell, B. E. A. Saleh and M. C. Teich, "Boundary effects on multiplication noise in thin heterostructure avalanche photodiodes: Theory and experiment", IEEE Trans. Electron Devices, vol. 49, no. 12, pp. 2114-2123, Dec. 2002.

N. R. Das and M. J. Deen, "A new model for avalanche build-up of carriers in a SAGCM avalanche photodiode", IEEE Trans. Electron Devices, vol. 49, no. 12, pp. 2362-2366, Dec. 2002.

O.-H. Kwon, M. M. Hayat, J. C. Campbell, B. E. A. Saleh and M. C. Teich, "Effect of stochastic dead space on noise in avalanche photodiodes", IEEE Trans. Electron Devices, vol. 51, no. 5, pp. 693-700, May 2004.

J. A. Gubner and M. M. Hayat, "A method to recover counting distributions from their characteristic functions", IEEE Signal Process. Lett., vol. 3, no. 6, pp. 184-186, Jun. 1996.

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 Devices, vol. 48, no. 12, pp. 2722-2731, Dec. 2001.

S. Hava and M. Auslender, "Velocity-field relation in GaAlAs versus alloy composition", J. Appl. Phys., vol. 73, pp. 7431-7434, Jun. 1993.

D. Snyder and M. Miller, Random Point Processes in Time and Space, New York: Springer-Verlag, 1991.

M. M. Hayat, B. E. A. Saleh and J. A. Gubner, "Bit-error rates for optical receivers using avalanche photodiodes with dead space", IEEE Trans. Comm., vol. 43, no. 1, pp. 99-107, Jan. 1995.

G. Kahraman, B. E. A. Saleh, W. L. Sargeant and M. C. Teich, "Time and frequency response of avalanche photodiodes with arbitrary structure", IEEE Trans. Electron Devices, vol. 39, no. 3, pp. 553-560, Mar. 1992.

J. S. Ng, C. H. Tan, B. K. Ng, P. J. Hambleton, J. P. R. David, G. J. Rees, A. H. You and D. S. Ong, "Effect of dead space on avalanche speed", IEEE Trans. Electron Devices, vol. 49, no. 4, pp. 544-549, Apr. 2002.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.