An analytical approximation for the excess noise factor of avalanche photodiodes with dead space

Approximate analytical expressions are derived for the mean gain and the ex cess noise factor of avalanche photodiodes including the effect of dead spa ce. The analysis is based on undertaking a characteristic-equation approach to obtain an approximate analytical solution to the existing system of rec urrence equations which characterize the statistics of the random multiplic ation gain. The analytical expressions for the excess noise factor and the mean gain are shown to be in good agreement with the exact results obtained from numerical solutions of the recurrence equations for values of the dea d space reaching up to 20% of the width of the multiplication region.