Effect of dead space on the excess noise factor and time response of avalanche photodiodes

The effect of dead space on the statistics of the gain process in continuous-multiplication avalanche photodiodes (APDs) is determined using the theory of age-dependent branching processes. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to cause an impact ionization. Analytical expressions are derived for the mean gain, the excess noise factor, and the mean and standard deviation of the impulse response function, for the dead-space-modified avalanche photodiode (DAPD), under conditions of single carrier multiplication. The results differ considerably from the well-known formulas derived by R.J. McIntyre and S.D. Personick in the absence of dead space. Relatively simple asymptotic expressions for the mean gain and excess noise factor are obtained for devices with long multiplication regions. In terms of the signal-to-noise ratio (SNR) of an optical receiver in the presence of circuit noise, it is established that there is a salutory effect of using a properly designed DAPD in place of a conventional APD. The relative merits of using DAPD versus a multilayer (superlattice) avalanche photodiode (SAPD) are examined in the context of receiver SNR; the best choice turns out to depend on which device parameters are used for the comparison