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G. Lutz and R. Klanner
the amplification region and cause delayed cross-talk. The result of prompt crosstalk is that the number of entries in the peaks does not follow a Poisson distribution,
even if the number of photons causing initial Geiger discharges does. As shown
in [51] the result of cross-talk is that the number of entries in the peaks follows
a Generalised-Poisson instead of a Poisson distribution. We note that the solid
curve shown in Figs. 5.57 and 5.58 is the result of a model fit which includes both
after-pulsing and prompt cross-talk simulated by a Generalised Poisson distribution.
The model provides a fair description of the measurements and gives a precise
determination of the SiPM parameters [50]. As both, after-pulses and cross-talk
are related to the number of charge carriers in the Geiger discharge and thus to the
Gain, the corresponding probabilities are expected to be approximately proportional
to V bias – V off , which is also observed. Typical values at V bias – V off = 5 V for afterpulsing as well as prompt cross-talk are 5 % resulting in an excess noise factor,
the ratio of the square of the relative resolution to the Poisson expectation, ENF
= [(σ meas /mean meas )/(σ Poisson /mean Poisson )] 2 of ≈ 1.08. As the photon detection
efficiency increases with voltage and finally saturates, whereas Gain and ENF
continue to increase, there is a voltage at which the photon number measurement
is optimal.
Dark counts are another limitation of SiPMs. Typical dark count rates (DCR) for
SiPMs before irradiation are between 10 and 100 kHz/mm 2 at room temperature.
Cooling reduces the DCR by about a factor 2 for an 8 ◦ C reduction in temperature.
Ionizing radiation, which mainly causes damage to the SiO 2 , hardly affects the
DCR. However non-ionizing radiation, like neutrons or high energy (> 5 MeV)
particles, significantly affect the performance. At sufficiently high fluences ()
the DCR is so high that most pixels are in a state of Geiger discharge, the
photon-detection efficiency decreases and finally the SiPM stops working as a
photo-detector. Whereas V bd and the electrical SiPM parameters hardly change up
to = 5 × 10 13 cm –2 , DCR increases by many orders of magnitude: For a KETEK
SiPM with 15 μm pitch at –30 ◦ C and (V bias – V off ) = 5 V, DCR increases from
≈ 10 kHz/mm 2 before irradiation to ≈ 200 GHz/mm 2 after irradiation by reactor
neutrons to = 5 × 10 13 cm –2 [52, 53]. It is found that the increase in DCR
is approximately proportional to . It is also observed that after irradiation the
increase of DCR with excess voltage is significantly steeper and the decrease with
temperature slower after than before irradiation. As a result of the increased DCR,
the signal baseline shows large fluctuations and single photon detection becomes
impossible. Finally the occupancy of the pixels by dark counts is so high that the
probability of a photon hitting a pixel which is already busy increases and the
photon detection efficiency degrades. For the KETEK SiPM with 15 μm pitch at –
30 ◦ C the photon detection efficiency due to dark counts is reduced by a factor
2 for = 5 × 10 13 cm –2 at (V bias – V off ) ≈ 2.5 V, and essentially zero for
= 5 × 10 14 cm –2 [53]. At these high fluences the dark currents exceed several
tens of mA and thermal run-away has to be avoided.
After irradiation a significant reduction of DCR by annealing occurs. Annealing
is a strong function of temperature: The typical reduction of DCR is a factor 2–3
after several days at room temperature, and a factor 10–50 at 175 ◦ C. A systematic
G. Lutz and R. Klanner
the amplification region and cause delayed cross-talk. The result of prompt crosstalk is that the number of entries in the peaks does not follow a Poisson distribution,
even if the number of photons causing initial Geiger discharges does. As shown
in [51] the result of cross-talk is that the number of entries in the peaks follows
a Generalised-Poisson instead of a Poisson distribution. We note that the solid
curve shown in Figs. 5.57 and 5.58 is the result of a model fit which includes both
after-pulsing and prompt cross-talk simulated by a Generalised Poisson distribution.
The model provides a fair description of the measurements and gives a precise
determination of the SiPM parameters [50]. As both, after-pulses and cross-talk
are related to the number of charge carriers in the Geiger discharge and thus to the
Gain, the corresponding probabilities are expected to be approximately proportional
to V bias – V off , which is also observed. Typical values at V bias – V off = 5 V for afterpulsing as well as prompt cross-talk are 5 % resulting in an excess noise factor,
the ratio of the square of the relative resolution to the Poisson expectation, ENF
= [(σ meas /mean meas )/(σ Poisson /mean Poisson )] 2 of ≈ 1.08. As the photon detection
efficiency increases with voltage and finally saturates, whereas Gain and ENF
continue to increase, there is a voltage at which the photon number measurement
is optimal.
Dark counts are another limitation of SiPMs. Typical dark count rates (DCR) for
SiPMs before irradiation are between 10 and 100 kHz/mm 2 at room temperature.
Cooling reduces the DCR by about a factor 2 for an 8 ◦ C reduction in temperature.
Ionizing radiation, which mainly causes damage to the SiO 2 , hardly affects the
DCR. However non-ionizing radiation, like neutrons or high energy (> 5 MeV)
particles, significantly affect the performance. At sufficiently high fluences ()
the DCR is so high that most pixels are in a state of Geiger discharge, the
photon-detection efficiency decreases and finally the SiPM stops working as a
photo-detector. Whereas V bd and the electrical SiPM parameters hardly change up
to = 5 × 10 13 cm –2 , DCR increases by many orders of magnitude: For a KETEK
SiPM with 15 μm pitch at –30 ◦ C and (V bias – V off ) = 5 V, DCR increases from
≈ 10 kHz/mm 2 before irradiation to ≈ 200 GHz/mm 2 after irradiation by reactor
neutrons to = 5 × 10 13 cm –2 [52, 53]. It is found that the increase in DCR
is approximately proportional to . It is also observed that after irradiation the
increase of DCR with excess voltage is significantly steeper and the decrease with
temperature slower after than before irradiation. As a result of the increased DCR,
the signal baseline shows large fluctuations and single photon detection becomes
impossible. Finally the occupancy of the pixels by dark counts is so high that the
probability of a photon hitting a pixel which is already busy increases and the
photon detection efficiency degrades. For the KETEK SiPM with 15 μm pitch at –
30 ◦ C the photon detection efficiency due to dark counts is reduced by a factor
2 for = 5 × 10 13 cm –2 at (V bias – V off ) ≈ 2.5 V, and essentially zero for
= 5 × 10 14 cm –2 [53]. At these high fluences the dark currents exceed several
tens of mA and thermal run-away has to be avoided.
After irradiation a significant reduction of DCR by annealing occurs. Annealing
is a strong function of temperature: The typical reduction of DCR is a factor 2–3
after several days at room temperature, and a factor 10–50 at 175 ◦ C. A systematic