Computation of output electron distributions in avalanche photodiodes

The cumulative probability distribution of the number of electrons counted during an interval (0, T) at the output of an avalanche photodiode is calculated from Personick's and McIntyre's model by numerical contour integration in the complex plane, a method that yields accurate results with a number of operations roughly independent of the numbers of electrons involved. The incident light is assumed for the sake of illustration to produce primary electrons with a Poisson distribution.