We present a procedure to extract the nonlocal impact ionization coefficients in Avalanche Photodiodes (APDs) operating in the linear regime from Full Band Monte Carlo simulations. The Monte Carlo calculations have been calibrated on existing experimental data for GaAs p-i-n APDs with different thickness of the intrinsic region. Inspection of impact ionization generation rate in p-i-n and staircase GaAs APDs led us to identify the limitations of existing nonlocal-history dependent impact ionization models. The introduction of an energy dependent relaxation length for the computation of the effective fields significantly improves the model accuracy in predicting the gain and noise associated to conduction and valence band steps in staircase APDs without additional computational burden. This improved nonlocal-history dependent model is thus a powerful tool to design and optimize APDs with different architectures.
