  Single-photon detectors, like Avalanche Photo Diodes (APDs), have a great
importance in many fields like quantum key distribution, laser ranging,
florescence microscopy, etc. Afterpulsing is a typical non ideal behavior of
APDs, operated in Geiger mode, which adversely affects any application which
measures the number or timing of detection events. Several conflicting studies
have tried to model afterpulsing behavior and link it to fundamental
semiconductor physics. Here we describe experiments we performed on at least 2
different detectors from 3 manufacturers, all commonly used in quantum optics
setups. We report on the timing structure of the counts. By fitting different
models to these data, we found statistically significant differences between
the detectors used. Furthermore, we report on the presence of high order
afterpulses which are not accounted for in any of the standard models of
afterpulse behavior. This might have significant implication e.g. in quantum
key distribution systems, as the modeling of the devices in use will have to be
part of the security analysis for some systems. Significant differences between
manufacturers and even between seemingly identical detectors of the same make
and batch suggest that every individual detector needs to be calibrated. We
describe a reliable procedure to perform such a calibration and present our
findings on three different commercial products.
