Afterpulsing model based on the quasi-continuous distribution of deep   levels in single-photon avalanche diodes
  We have performed a statistical characterization of the effect of afterpulsing in a free-running silicon single-photon detector by measuring the distribution of afterpulse waiting times in response to pulsed illumination and fitting it by a sum of exponentials. We show that a high degree of goodness of fit can be obtained for 5 exponentials, but the physical meaning of estimated characteristic times is dubious. We show that a continuous limit of the sum of exponentials with a uniform density between the limiting times gives excellent fitting results in the full range of the detector response function. This means that in certain detectors the afterpulsing is caused by a continuous band of deep levels in the active area of the photodetector. 
D. B. Horoshko, V. N. Chizhevsky, S. Ya. Kilin
quant-ph physics.ins-det physics.optics