Effect of dead space on gain and noise double-carrier-multiplication avalanche photodiodes

Abstract

The effect of dead space on the mean gain and the excess noise factor of double-carrier multiplication avalanche photodiodes has been studied using recurrence relations in the form of coupled integral equations. The dead space is the minimum distance that a newly generated carrier must travel to acquire sufficient energy to become capable of causing an impact ionization. These equations are solved numerically to produce the mean gain and the excess noise factor. We have found that dead space reduces the mean gain since it results in fewer ionizations. The reduction is relatively greater as the hole-to-electron ionization ratio k approaches unity since the growth rate of the branching process is reduced by the inhibiting effect of dead space. We also show that dead space causes a lower excess noise factor since it introduces some orderliness in the random ionization process. In certain conditions the dead space has a beneficial effect on the performance of the optical detector when used in optical receivers with circuit noise. It may therefore be advantageous to select materials for which the dead space is enhanced, without jeopardizing other parameters such as large electron ionization coefficient and small k.