Effect of dead space on gain and noise of double-carrier-multiplication avalanche photodiodes

The effect of dead space on the statistics of the gain in a double-carrier-multiplication avalanche photodiode (APD) is determined using a recurrence method. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing an impact ionization. Recurrence equations are derived for the first moment, the second moment, and the probability distribution function of two random variables that are related, in a deterministic way, to the random gain of the APD. These equations are solved numerically to produce the mean gain and the excess noise factor. The presence of dead space reduces both the mean gain and the excess noise factor of the device. This may have a beneficial effect on the performance of the detector when used in optical receivers with photon noise and circuit noise