Theory of noise for a general multiplication process

The classical concept of (carrier) multiplication underlying the design of low-noise avalanche photo diodes is one of a process which is random in magnitude but deterministic in time. Based on this concept, the theoretical limit on the noise performance is reached when the process is also made fully deterministic in magnitude, generating no noise. Then the signal-to-noise ratio after multiplication remains unaltered. Here, we examine a general multiplication process, one in which we allow randomness in both magnitude and time. In the deterministic limit we recover the classical results. In the random limit we observe an enhancement in the signal-to-noise ratio after amplification.