Operating principles of Solid State Photomultipliers are based on Geiger mode avalanche breakdown limited by strong negative feedback. This operating mode provides both high gain and ultra-low excess noise of avalanche multiplication resulting in ability to detect single photons. On the other hand high gain is accompanied with cross-talk and afterpulsing processes changing the probability distribution function of output signals and arising specific excess noise. There are many reports regarding its influence on signal distribution and noise, and we suggest that some analytical expressions would be useful. We therefore are presenting a simple model of probability distribution of output signals in the presence of cross-talk and afterpulsing (namely compound Poisson distribution). The model results allow us to calculate excess noise factor of cross-talk and afterpulsing as well as to find simple way to measure its probabilities.

Solid State Photomultipliers (SSPM) are widely recognized as a new generation of photodetectors competitive with APD and PMT in various applications. SSPM advantages are high gain, ultra-low excess noise factor of internal amplification, good photon detection efficiency, and fast timing. SSPM drawbacks are high dark count rate, considerable probability of cross-talk and afterpulsing, and low dynamic range. Detection of scintillation light pulses in nuclear science and medical imaging is one of the most attractive and thoroughly studied SSPM applications. The key parameter of the detection is energy resolution, which is used in respect to the photodetector itself by output pulse height resolution. Resolution of SSPM is considerably affected by non-linearity of the photoresponse due to the limited number of pixels and finite reset time of the pixel. Thus, output signal resolution calibrated in photon scale or Photon Number Resolution (PNR) should be used to reflect the non-linearity. The purpose of this study is to express PNR of SSPM in an analytical form taking into account excess noise factor of cross-talk and afterpulsing, and non-linearity. The normalization of PNR relative to an ideal detector characterizes the efficiency of SSPM in terms of the total excess noise factor of photodetection or, inversely, in terms of the detective quantum efficiency. The presented PNR model is suitable for performance optimization as well as for evaluation of SSPM applicability and competitiveness.