Modeling of Hot-Carrier Degradation driven by silicon-hydrogen bond dissociation in SPADs

Abstract: A novel approach for modeling Dark Count Rate (DCR) drift in Single-Photon Avalanche Diodes (SPADs) is proposed based on Hot-Carrier Degradation (HCD) inducing silicon-hydrogen bond dissociation at the Si/SiO2 interface. The energy and the quantity of hot-carriers are modeled by the interplay of carrier energy distribution and current density. The carrier energy distribution, achieved by a Full-Band Monte-Carlo simulation considering the band structure and the scattering mechanisms, establishes a crucial link to the degradation of the top SPAD interface, primarily influenced by hot electrons due to their broader energy spread. The current density is determined by analyzing the generation rates of carriers under dark and photo conditions, along with the multiplication rate, through a combination of experimental data and modeling techniques. Subsequently,these hot carriers are correlated with the distribution of bond dissociation energy, which is modeled by the disorder-induced local variations among the Si-H bond energy at the Si/SiO2 interface. The impact-ionization probability between hot carriers and Si-H bonds is then calculated by differentiating their energies, thereby determining the degradation kinetics. This enables the capture of the rise in dark current density with stress duration by the increasing number of defects, which in turn affects the modeling of degradation rate. For the first time, a direct correlation between the dark current and DCR, along with their drift over stress time, has been established, relying on the carrier generation rate originating from these defects together with the position-dependent breakdown probability Pt.This physic-based model allows to predict DCR for unprecedented long-term stress measurement time up to 10e6s, covering a whole set of characterization and stress conditions for SPAD devices.