Simple Monte Carlo model with generalized carrier-trajectory tracking equations for prediction of avalanche multiplication statistics in avalanche photodiodes with arbitrary electric field gradient

摘要

A set of highly generalized electron-trajectory tracking equations are derived based on the fundamental of high field carrier transport and are employed in a Simple Monte Carlo model for gain and avalanche multiplication noise prediction in APDs with arbitrary electric field gradients. Using the model and assuming electron-only ionization, simulations are carried out on two one-sided abrupt np~+ and n~+p junctions with doping concentrations in the n and p regions set to 1.0×10~(18) cm~(-3) and the p~+ and n~+ regions set to infinity. Preliminary simulation results of gain, avalanche multiplication noise, and positions of electron ionizations obtained from the Simple Monte Carlo model employing the electron-trajectory tracking equations show excellent agreement with those obtained from the conventional Simple Monte Carlo model even though the one-sided abrupt np~+ and n~+p junctions are subjected to steep electric field gradient across the avalanche multiplication regions. These simulation results, and the positions of electron ionizations in particular, strongly imply that the electron-trajectory tracking equations employed in the Simple Monte Carlo model for avalanche photodiodes are able to track the trajectory of the electrons and valid, and the equations are highly generalized for APDs with arbitrary electric field gradients, ranging from uniform electric fields to steep electric field gradients.