This work presents a physical model describing the IV curves of SiPM detectors allowing to easily determine important device parameters like breakdown voltage VBD and the shape of Geiger triggering probability PGeiger. We measured IV curves and tested our IV model in a temperature range −35°C<T<+35°C on various SiPMs from two vendors (Hamamatsu devices of 3×3mm2 total area and 50×50μm2 μcell size, 2011 and 2015 year production runs and KETEK devices of 0.5×0.5mm2 total area and 50×50μm2 μcell size, 2015 production run). The shape of IV curve can be described in terms of Geiger probability and afterpulsing in a very large current range of 10−12A<Ipost−BD<10−5A over the full working range of all tested devices. It has also been found that VBD from IV curves is slightly higher (few hundred mV) than the “breakdown voltage” determined from the usual method of linear fit of gain as a function of bias voltage, this discrepancy reflecting the fundamental difference in the physical significance of the “breakdown voltage” determined by these two methods. The recent generation of SiPMs have very wide working range and there is an evidence phenomena beyond afterpulsing like heating or non-quenched pulses contributing to the fast increase of the current at high bias voltages.