Investigating the Statistics of the Random Gain in Avalanche Photodiodes Using a Soft Dead Space Model

A modified model for calculating mean gain and excess noise factor of p⁺-i-n⁺ avalanche photodiodes (APD´s) is presented. The proposed model accounts for the effect of dead space by considering a soft ionization rate of enabled carriers. The application of the soft dead space model is intended to be mainly beneficial in the analysis of thin APD´s. Based on the proposed model, renewal arguments governing multiplication gain and noise of APD´s have been modified and solved using numerical methods.