Abstract

The random multiplication process in avalanche photodiodes (APDs) is complicated by the existence of an inherent dead space D within which a newly created carrier cannot initiate a new ionization. A threshold energy must be built up before the carrier can reionize. We provide an analysis of noise in single-carrier-initiation single-carrier-multiplication APDs, including the effect of dead space. The carrier counting process is cast as an age-dependent branching process, whose statistics are well known. Expressions for the mean gain and excess noise factor are determined. Dead space reduces the excess noise factor F; however, this is accompanied by a reduction in the mean gain G. For APDs with ionization coefficient α = 2 × 10³ cm^-1, D = 0.5 µm, and a 10-µm multiplication region, reductions in F and G are 14% and 33%, respectively. Expressions for the mean and variance of the impulse response function arising from a single photon absorption are determined as functions of time. Asymptotic expressions for the mean gain and the excess noise factor, describing devices in which the length of the multiplication region is much larger than the dead space, are derived in terms of the Malthusian parameter of the branching process. In this case F is time independent.

© 1989 Optical Society of America