Random path length analysis of gain and noise in e-APDs for electron ionisation characterisation

Accurate modelling of electron-initiated avalanche photodiodes (e-APDs) requires a precise understanding of electron impact ionisation in semiconductors. This study examines the limitations of the conventional hard-threshold random path length (RPL) model and introduces a field-dependent RPL model, which uses a Weibull-Fréchet distribution to represent the spatial characteristics of ionisation. By fitting the measured gain and excess noise characteristics, this model enables direct extraction of the electron ionisation coefficient as a function of electric field, along with the spatial probability distribution of ionisation events. The model accurately reproduces experimental results for InAs and Hg 07 Cd 03 Te e-APDs, capturing soft-threshold ionisation behaviour and realistic dead space effects. The extracted ionisation coefficients differ significantly from those derived using traditional local models, highlighting the need to re-examine standard extraction methods. This framework offers a physically consistent approach for characterising impact ionisation in low-noise avalanche photodiodes and provides a valuable tool for designing advanced photodetectors.