Is the gain-voltage dependence of SiPMs linear?

TL;DR

This paper investigates the gain-voltage relationship in SiPMs, revealing a subtle non-linearity caused by increasing depletion depth, which affects breakdown voltage estimations but does not fully account for observed discrepancies.

Contribution

It demonstrates the non-linearity in gain-voltage dependence of SiPMs and explains its origin through simulations, providing insights for more accurate breakdown voltage measurements.

Findings

Non-linearity at sub-percent level in gain-voltage dependence.

Simulation shows non-linearity due to increasing depletion depth.

Systematic underestimation of breakdown voltage when assuming linearity.

Abstract

The gain-voltage dependence for SiPMs from 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 he 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.