A model to determine multiplication and noise in avalanche photodiodes with non-uniform electric field

A modification to the random path length technique (RPL) with a hard-threshold dead space (Eth) is demonstrated to be able to calculate the electron initiated avalanche multiplication (Me) and excess noise (Fe) in GaAs p+–i–n+ structures with n- and p-type background doping levels up to 1 × 1017 cm−3 in the multiplication region. This model’s Me, Fe, and position dependent ionization probabilities are compared with the results obtained from a multi-valley analytical band Monte Carlo model, enabling us to quantify how the ionization process is affected when the electric field changes rapidly. The RPL results for Me show excellent agreement with the Monte Carlo model, suggesting that the simple hard dead-space correction to the ionization probability distribution function works as well with a varying electric field up to 1400 kV/cm/μm as in a constant electric field and that the “history dependence” effects of a varying electric field are not very significant once the initial carrier dead space is allowed for. The modified RPL Fe also agrees well with the Monte Carlo model for p+–n−–n+ structures; however, it is underestimated for p+–p−–n+ structures. This is attributed to the hard dead space of the feedback carriers having a disproportionate effect on the variance in the multiplication.