Afterpulsing in APDs
Afterpulse probability, trap dynamics, and dead time trade-offs in avalanche photodiodes.
Afterpulse Probability
0.410%
per recorded avalanche
Afterpulse Rate
3.909e+3 cps
recorded rate × P_ap
Recorded Rate
0.9524 Mcps
non-paralyzable dead time
Trap 1 Released in 50 ns
91.8%
1 − e^(−t_d/τ₁), harmless
P_ap = Σ η_k · exp(−t_d / τ_k) [Cova 1991; Ziarkash 2018]
R_ap = m · P_ap, m = R / (1 + R·t_d)
A carrier trapped during an avalanche and released after the dead time retriggers the diode. A longer dead time lets more traps empty harmlessly, at the cost of a lower maximum count rate.
Rate vs Dead Time
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Each trap level empties exponentially, so the afterpulse probability is Σ η·e^(−t_d/τ) over up to two levels, with the recorded rate from a non-paralyzable dead time. η and τ are device fits (the defaults give 0.41 %, the order of a Si SPCM at 50 ns), and the afterpulse rate is first order in P_ap (no afterpulse cascades) and in R·τ (no trap saturation).
- Cova S., Lacaita A., Ripamonti G. (1991). Trapping phenomena in avalanche photodiodes on nanosecond scale. IEEE Electron Device Lett. 12, 685–687. Afterpulsing from trap release, η·e^(−t/τ). doi:10.1109/55.116955
- Ziarkash A. W., Joshi S. K., Stipčević M., Ursin R. (2018). Comparative study of afterpulsing behavior and models in single photon counting avalanche photo diode detectors. Sci. Rep. 8, 5076. Multiple-exponential model; measured P_ap 0.01–8.5 % at 22–53 ns dead time (SPCM-AQ4C 0.16–0.29 % at 50 ns). doi:10.1038/s41598-018-23398-z