Temporal dependence of transient dark counts in an avalanche photodiode: A solution for power-law behavior of afterpulsing

This paper offers a theoretical explanation of the temperature and temporal dependencies of transient dark count rates (DCRs) measured for a linear-mode silicon avalanche photodiode (APD) and the dependencies of afterpulsing that were measured in Geiger-mode Si and InGaAs/InP APDs. The temporal dependencies exhibit power-law behavior, at least to some extent. For the transient DCR, the value of the DCR for a given time period increases with decreases in temperature, while the power-law behavior remains unchanged. The transient DCR is attributed to electron emissions from traps in the multiplication layer of the APD with a high electric field, and its temporal dependence is explained by a continuous change in the electron emission rate as a function of the electric field strength. The electron emission rate is calculated using a quantum model for phonon-assisted tunnel emission. We applied the theory to the temporal dependence of afterpulsing that was measured for Si and InGaAs/InP APDs. The power-law temp...