A new approach is described for calculating the current impulse response of an avalanche photodiode, allowing for an arbitrary model for carrier transport and also for an arbitrary distribution of ionization events in space and time, following carrier injection. The technique can evaluate both the mean current response and its variance. We find that while the effects of diffusion on mean current are small, the enhanced speed to early ionization can speed up the avalanche process significantly.
C. H. Tan, P. J. Hambleton, J. P. R. David, R. C. Tozer, and G. J. Rees, "Calculation of APD Impulse Response Using a Space-and Time-Dependent Ionization Probability Distribution Function," J. Lightwave Technol. 21, 155- (2003)