Analysis of the response of silicon photomultipliers to optical light fields

Silicon Photo-Multipliers (SiPMs) consist of a high density array of p-n junctions with a common output (∼ 103 cells per mm2), operated beyond the breakdown voltage in a Geiger-Müller regime. With a typical gain of the order of 106, time resolution at the 100 ps level, a dead time per diode limited to 100 ns, enhanced blue sensitivity, photon detection efficiency in excess of 30% and, notably, a photon number resolving capability up to a few tens of photons even at room temperatures, their performances are comparable with the common use Photo-Multiplier Tubes, with the advantage of operability in magnetic fields. However, SiPMs present a significant Dark Count Rate (DCR), ranging from a few 100 kHZ to the MHz level at room temperature, and a relevant optical cross-talk between the cells, with values depending on the detector design and the biasing condition, so that their use is far from being trivial. The performance of SiPMs have been tested in the context of the characterization of the photon number distribution in a light field. Infact, while the Geiger-Müller avalanche triggering by impinging photons can be modelized as a pure bernoullian process that preserves the photon number distribution of measured light field, relevant values of DCR and cross-talk can cause sizeable deviations from this statistics. Taking into account the DCR and cross-talk effects in the Geiger-Müller avalanche distribution, we demonstrate that photon number distributions in a poissonian and thermal-like light field can be properly reconstructed.