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 (E_th) is demonstrated to be able to calculate the electron initiated avalanche multiplication (M_e) and excess noise (F_e) in GaAs p⁺–i–n⁺ structures with n- and p-type background doping levels up to 1 × 10¹⁷cm⁻³ in the multiplication region. This model’s M_e, F_e, 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 M_e 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 F_e 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.