Is the gain–voltage dependence of SiPMs linear?

The gain–voltage dependence for SiPMs from Ref.(V. Chmill et al., 2017) (V. Chmill et al., Study of the breakdown voltage of SiPMs) is reanalyzed and a non-linearity at the sub-percent level is observed. Simulations show that the non-linearity can be explained by the increase of the depletion depth of the avalanche region with over-voltage. A consequence of the non-linearity is that the voltage at which the discharge stops is systematically underestimated if a linear extrapolation is used. However, the shift is too small to explain the difference between the break-down voltage from the current–voltage dependence and the one obtained from the extrapolation of the gain–voltage dependence to gain one. The results are confirmed by measurement of a different MPPC produced by Hamamatsu which has a break-down voltage which is about a factor two higher.