Afterpulsing studies of low noise InGaAs/InP single-photon negative feedback avalanche diodes

We characterize the temporal evolution of the afterpulse probability in a free-running negative feedback avalanche diode (NFAD) over an extended range, from $\sim$300 ns to $\sim$1 ms. This is possible thanks to an extremely low dark count rate on the order of 1 cps at 10% efficiency, achieved by operating the NFAD at a temperatures as low as 143 K. Experimental results in a large range of operating temperatures (223-143 K) are compared with a legacy afterpulsing model based on multiple trap families at discrete energy levels, which is found to be lacking in physical completeness. Subsequently, we expand on a recent proposal which considers a continuous spectrum of traps by introducing well defined edges to the spectrum, which are experimentally observed.