A model for the jitter of avalanche photodiodes with separate absorption and multiplication regions

An improved version of the Random Path Length algorithm is used to simulate the time response of Separate Absorption and Multiplication Avalanche PhotoDiodes (SAM-APDs) in the linear regime. The model takes into account both the diffusion and the drift of carriers in the absorption region as well as impact ionization scattering events in the multiplication region. An extended formulation of Ramo's theorem is used to determine the current waveforms. The new algorithm has been used to extract the jitter of the time response of avalanche photodiodes to photons, which is a relevant figure of merit for time of flight applications of SAM-APDs. It is found that an electric field in the absorption region small enough to avoid unwanted carrier multiplication or band-to-band tunneling, is beneficial to reduce the jitter. Furthermore, we have found that, in APDs working in the linear regime, the stochastic duration of the current pulse makes difficult the use of circuit techniques, such as crossover timing, with constant delay lines aimed at detecting the individual pulses. The problem is partly mitigated when SAM-APDs are used for the detection of high energy photons, such as X-rays.