  Silicon Photomultipliers (SiPM), also so-called Solid State Photomultipliers
(SSPM), are based on Geiger mode avalanche breakdown limited by strong negative
feedback. SSPM can detect and resolve single photons due to high gain and
ultra-low excess noise of avalanche multiplication in this mode. Crosstalk and
afterpulsing processes associated with the high gain introduce specific excess
noise and deteriorate photon number resolution of the SSPM. Probabilistic
features of these processes are widely studied because of its high importance
for the SSPM design, characterization, optimization and application, but the
process modeling is mostly based on Monte Carlo simulations and numerical
methods. In this study, crosstalk is considered to be a branching Poisson
process, and analytical models of probability distribution and excess noise
factor (ENF) of SSPM signals based on the Borel distribution as an advance on
the geometric distribution models are presented and discussed. The models are
found to be in a good agreement with the experimental probability distributions
for dark counts and a few photon spectrums in a wide range of fired pixels
number as well as with observed super-linear behavior of crosstalk ENF.
