  Silicon Photo-Multipliers (SiPMs) are detectors sensitive to single photons
that are used to detect scintillation and Cherenkov light in a variety of
physics and medical-imaging applications. SiPMs measure single photons by
amplifying the photo-generated carriers (electrons or holes) via a Geiger-mode
avalanche. The Photon Detection Efficiency (PDE) is the combined probability
that a photon is absorbed in the active volume of the device with a
subsequently triggered avalanche. Absorption and avalanche triggering
probabilities are correlated since the latter probability depends on where the
photon is absorbed. In this paper, we introduce a physics motivated
parameterization of the avalanche triggering probability that describes the PDE
of a SiPM as a function of its reverse bias voltage, at different wavelengths.
This parameterization is based on the fact that in p-on-n SiPMs the induced
avalanches are electron-driven in the ultra-violet and near-ultra-violet
ranges, while they become increasingly hole-driven towards the near-infra-red
range. The model has been successfully applied to characterize two Hamamatsu
MPPCs and one FBK SiPM, and it can be extended to other SiPMs. Furthermore,
this model provides key insight on the electric field structure within SiPMs,
which can explain the limitation of existing devices and be used to optimize
the performance of future SiPMs.
