Effect of dead space on gain and noise in Si and GaAs avalanche photodiodes

The effect of dead space on the mean gain, the excess noise factor, and the avalanche breakdown voltage for Si and GaAs avalanche photodiodes (APDs) with nonuniform carrier ionization coefficients are examined. The dead space, which is a function of the electric field and position within the multiplication region of the APD, is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing impact ionization. Recurrence relations in the form of coupled linear integral equations are derived to characterize the underlying avalanche multiplication process. Numerical solutions to the integral equations are obtained and the mean gain and the excess noise factor are computed