Weibull-Fréchet random path length model for avalanche gain and noise in photodiodes

<jats:title>Abstract</jats:title>
<jats:p>A four-parameter Weibull-Fréchet (WF) distribution function has been introduced in the random path length (RPL) model for nonlocal modelling of soft-threshold ionisation in semiconductors. The WF function has been demonstrated to be capable of reproducing the realistic probability distribution function (PDF) of electron and hole ionisation path lengths extracted from full band Monte Carlo (FBMC) transport simulations of bulk GaAs. The electron-initiated multiplication in GaAs avalanche photodiodes (APDs) calculated by the WF-RPL model is in excellent agreement with the results from FBMC. The predicted excess noise factor is closer to that of FBMC as compared to the hard threshold RPL model. The advantage of this improved RPL model as a tool for predicting the PDF of electron and hole ionisation path lengths in AlAs<jats:sub>0.56</jats:sub>Sb<jats:sub>0.44</jats:sub> from the experimentally measured avalanche gain and noise has been analysed. The electron ionisation path length PDF of AlAs<jats:sub>0.56</jats:sub>Sb<jats:sub>0.44</jats:sub> has a unique feature of two decay rates with a narrow full width at half maximum and a long tail. The extremely low hole ionisation coefficient in AlAs<jats:sub>0.56</jats:sub>Sb<jats:sub>0.44</jats:sub> is found with a PDF of ionisation path length spanning over 50 <jats:italic>µ</jats:italic>m at an electric field of 600 kVcm<jats:sup>−1</jats:sup>, supporting the very low hole feedback ionisation in AlAs<jats:sub>0.56</jats:sub>Sb<jats:sub>0.44</jats:sub> APDs. The combination of the detailed and peaked electron’s ionisation path length PDF and of the broad hole’s ionisation path length PDF is responsible for the extremely low avalanche noise in the 1.55 <jats:italic>µ</jats:italic>m thick AlAs<jats:sub>0.56</jats:sub>Sb<jats:sub>0.44</jats:sub> APDs.</jats:p>