A simple Monte Carlo model for prediction of avalanche multiplication process in Silicon

Abstract

A Simple Monte Carlo model has been developed to model the avalanche characteristics of Silicon. Good agreement with experimental results from Silicon p + -i-n + diodes with i-regions ranging from 0.082 to 0.26 µm, an n + -i-p + diode with an i-region of 0.82 µm and a p + n diode was obtained. Therefore our model can be used to model the avalanche process in diodes with varying electric field profiles. We also studied the competing effects of the ratio of electron to hole ionization coefficients and the dead space on excess noise factor, by varying these parameters in our simulations of ideal p + -i-n + diodes with avalanche regions width of 0.05 to 0.3 µm to cover the electric field range in the measured devices. As avalanche region width reduces from 0.3 to 0.05 µm, the electron to hole ionisation coefficient ratio decreases from 3.42 to 1.23 while the dead space to avalanche width ratio increases from 0.19 to 0.49 for electrons. The former increases the excess noise while the latter suppresses the avalanche noise such that on balance, a weak dependence of excess noise on the avalanche width for w < 0.3 µm was observed in these p + -i-n + diodes, consistent with the excess noise results reported in thin Silicon p + -i-n + diodes.

Avalanche Breakdown Timing Statistics for Silicon Single Photon Avalanche Diodes

“…This work is licensed under a Creative Commons Attribution 3.0 License. For more information, see http://creativecommons.org/licenses/by/3.0/ Since then, a Simple Monte Carlo (SMC) model [19] for simulating avalanche gain, M, and excess noise factor, F, as function of reverse bias, V, was developed for Si APDs [20]. A SMC model contains far less band structure details, and so requires far shorter computation-time, compared to standard Full Band Monte Carlo models.…”

“…Reported SMC models underwent extensive benchmarking with experimental data on impact ionization, covering a wide range of electric fields. For example, the Si SMC model in [20] was benchmarked against experimental V b , M(V), and F(M) of five Si diodes (with breakdown electric fields from 230 to 830 kV•cm −1 ), including a p-n diode with a highly non-uniform electric field profile.…”

“…Building on [20], in this work we report an SMC model for Si SPAD simulations. In addition to simulating V b , M(V), and F(M), as for the typical SMC models, our SMC model for Si SPADs provides breakdown probability, mean time to breakdown, and timing jitter as functions of reverse bias.…”

Simple Monte Carlo Simulator for Modelling Linear Mode and Geiger Mode Avalanche Photodiodes in C++

“…Simple Monte Carlo (SMC) modelling [5][6][7][8] offers an attractive combination of being sufficiently accurate while having reasonable computational demand. Compared to FBMC and ABMC models, SMC modelling uses a simplified band structure, reducing computational requirements.…”

“…The Simple Monte Carlo Simulator was developed to simulate silicon SPADs in [9] using a parameter set for Silicon from [5]. The simulator has been expanded to accept parameter sets for Gallium Arsenide [6] and Indium Gallium Phosphide [7].…”