Dark-current multiplication noises in avalanche photodiodes and optimum gains

Theoretical probabilities for a number of hole-electron pairs are derived for the dark-current and signal multiplication noises in avalanche photodiodes (APD). The excess noise factors for the dark-current multiplication noises are given in forms similar to the signal multiplication noise. The error probabilities influenced by the multiplication noises are calculated, and it is pointed out that the error probabilities basically have no dependency on the ratio of the ionization coefficients when APD has no dark-current source. The optimum gain characteristics are analyzed for the detection systems which include the multiplication noises, the thermal noise of load resistance, and the following amplifier\´s noise.