Characterisation of highly radiation-damaged SiPMs using current measurements

The characterisation of radiation-damaged SiPMs is a major challenge, when the average time between dark counts approaches, or even exceeds, the signal decay time. In this note a collection of formulae is presented, which have been developed and used for the analysis of current measurements for SiPMs in the dark and illuminated by an LED, before and after hadron irradiation. It is shown, how parameters like the breakdown voltage, the quenching resistance, the dark-count rate, the reduction of the photo-detection efficiency due to dark counts and the Geiger discharge probability can be estimated from current-voltage measurements. The only additional SiPM parameters needed are the pixel capacitance, the number of pixels and the correlated noise. Central to the method is the concept of the pixel occupancy, the probability of a Geiger discharge in a single pixel during a given time interval, for which the decay time of the SiPM signal has been assumed. As an illustration the formulae are used to characterise a KETEK SiPM before and after irradiation by a fluence of 5E13 cm$^{-2}$ of reactor neutrons for temperatures of -30{\deg}C and +20{\deg}C, where dark-count rates exceeding 1E11 Hz are observed.