A new expression for the gain-noise relation of single-carrier avalanche photodiodes with arbitrary staircase multiplication regions

We propose a simple expression to relate the total excess noise factor of a single-carrier multiplication staircase avalanche photodiode (APD) to the excess noise factor and gain given by the individual conduction band discontinuities. The formula is valid when electron impact ionization dominates hole impact ionization; hence, it is especially suited for staircase APDs with In-rich multiplication regions, as opposed, for example, to GaAs/AlGaAs systems where hole ionization plays an important role. The formula has been verified by accurate means of numerical simulations based on a newly developed nonlocal history dependent impact ionization model.