An improved nonlocal history-dependent model for gain and noise in avalanche photodiodes based on energy balance equation

We present a nonlocal history-dependent model for impact ionization gain and noise in avalanche photodiodes (APDs) especially suited for staircase APDs. The model uses a simple energy balance equation to define effective electric fields valid also in the presence of band discontinuities which are then used to express the ionization coefficients. The model parameters have been calibrated against literature data for gain and noise in GaAs and AlxGa1-xAs (x = 0.2, 0.6, 0.8) p-i-n diodes. Application to the experimental data for gain and noise in heterojunction and staircase separate absorption and multiplication APDs is reported to demonstrate the ability of the model in describing complex APD structures. It is found that, in spite of conduction band discontinuities being much larger than valence band ones, hole impact ionization contributes a significant degradation of the noise metrics in GaAs/AlGaAs staircase APDs. These nontrivial insights demonstrate the usefulness of the model to steer device design and optimization.