Effect of dead space on mean gain, excess noise factor, and avalanche breakdown voltage for Si and GaAs avalanche photodiodes

We investigate 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. The dead space, which is a function of the electric field and position within the multiplication region, is the minimum distance that a newly generated carrier must travel to acquire sufficient energy to become capable of causing impact ionization. Recurrence relations in the form of coupled integral equations are derived to characterize the underlying avalanche multiplication process. Numerical solutions to the integral equations are obtained and the excess noise factor is plotted as function of the mean gain. We have found that, in each case, the presence of dead space results in a reduction of both the mean gain and the excess noise factor. The excess noise factor vs the mean gain curve is also lowered in comparison with the ideal case in which there is no dead space. Furthermore, dead space serves to increase the applied bias voltage at which avalanche breakdown occurs.