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Stochastic Quenching Mechanisms and a Scaling Law for Single Photon Avalanche Diodes

A comprehensive scaling law for single photon avalanche diodes (SPADs) is presented through stochastic analyses of quenching mechanisms using a Monte Carlo method. By simulating random impact ionization events for individual carriers, two distinct quenching mechanisms are identified: successful quen...

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Bibliographic Details
Published in:IEEE transactions on electron devices 2024-01, Vol.71 (1), p.904-910
Main Author: Inoue, Akito
Format: Article
Language:English
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Summary:A comprehensive scaling law for single photon avalanche diodes (SPADs) is presented through stochastic analyses of quenching mechanisms using a Monte Carlo method. By simulating random impact ionization events for individual carriers, two distinct quenching mechanisms are identified: successful quenching (SQ) and unsuccessful quenching (UQ). SQ occurs when quenching is achieved after the initial pulse of avalanche multiplication (AM), mainly attributed to the minimum average carrier number within a multiplication region (MR). In contrast, UQ involves prolonged and repetitive pulses, caused by stochastic fluctuations around the equilibrium carrier number. This study has derived an analytical expression for the probability of quenching failure (1- {P}_{\text {Q}} ) as functions of the quenching resistance and the capacitance of the MR. This analytical expression exhibits a good agreement with the simulation results. Moreover, analytical formulas for the threshold quenching resistance and the dead time have been derived as a function of the desired {P}_{\text {Q}} value. Notably, the tradeoff relationship between the dead time and the standard deviation of the voltage swing is elucidated, leading to the scaling limitation. Additionally, avalanche triggering probability (ATP), breakdown voltage, and the average voltage swing are revealed to be scale-invariant. Based on these aforementioned observations, the comprehensive scaling law is established.
ISSN:0018-9383
1557-9646
DOI:10.1109/TED.2023.3338596