Response [px]
10 12 14 16 18 20 [%]ResponseRMS
0 5 10 15 20 25
I Fixed Voltage II Fixed Overvoltage III Response Equalisation
Response [px]
10 12 14 16 18 20 [%]ResponseRMS
0 5 10 15 20 25
I Fixed Voltage II Fixed Overvoltage III Response Equalisation
Response [px]
10 12 14 16 18 20 [%]ResponseRMS
0 5 10 15 20 25
I Fixed Voltage II Fixed Overvoltage III Response Equalisation
Figure 10.3: Spread of the response for different operational strategies for all three batches,1(left)2(middle) and3(right). The spread of the response including the spread of the set voltage from table 10.1.
Response [px]
10 12 14 16 18 20 [%]GainRMS
0 5 10 15 20 25
Response [px]
10 12 14 16 18 20 [%]GainRMS
0 5 10 15 20 25
Fixed OV Response equalisation Fixed Voltage
Response [px]
10 12 14 16 18 20 [%]GainRMS
0 5 10 15 20 25
Figure 10.4: Spread of the SiPM gain for different operational strategies for all three batches,1(left)2(middle) and3(right). The spread of the gain including the spread of the set voltage from table 10.1. The blue area depicts data sets with a gain too low to resolve single pixel spectra for over 90 % of the channels for operation with the Spiroc2b.
voltage (strategy I) for all SiPMs as can be seen in figure 10.4. The improvement does not justify the complex effort of measuring and setting the voltage for each SiPM individually.
Because of the large spread in gain, strategyIII demands the use of the single channel gain equalization with the internal amplification adjustment of the Spiroc2b. This leads to two additional parameters per channel that need to be set for operation. By comparing all three strategies that set the voltage for a given design response by setting all SiPM at the same voltages, strategyI is the most feasible option.
10.4 Optimization with fixed voltage (I)
Figure 10.5 shows the mean response of all three batches for strategyIwith one fixed voltage for all SiPMs of one batch. Apparent is the degradation after heating the SiPMs to prevent the popcorn effect from batch 2 to batch 3.
88 10. Operation Voltage Optimization
BiasVoltage [V]
29 30 31
MIP Response [px]
5 10 15 20
25
Batch 1Batch 2 Batch 3
Figure 10.5: Mean response in pixel per MIP for different voltages using operational strategyI (fixed volt-age / RegVal=0) for all three batches.
10.4.1 MIP efficiency
Detection efficiency is defined as the ratio of the total number of counts in the energy spectrum recorded by the detector by the number of MIP particles emitted by the detector. In this case the geometric efficiency is disregarded and only particles passing the detector count. As the trigger of the setup, see section 7.1.2 is independent of the signal in the TuT the efficiency of the trigger does not have to be taken into account. The particles that the setup triggered on are particles as simulated in figure 7.9. (Apart from noise hits from the setup that will be treated accordingly, see below). In this work, the MIP efficiency for a certain thresholdt is thus defined as the portion of all triggered hits F to the amount of hits Nt that the TuT itself would have triggered upon for a threshold t.,
M IP = Nt
F . (10.1)
A standard characterization measurement is seen in figure 10.6. The measurement has been rescaled to the MPV as 1 MIP. The data in blue would include the noise and zero counts as described in 7.1.2 and figure 7.12. Using the data to calculate the integrals would turn out a worse efficiency than the actual tile system provides. This method still underestimates the efficiency since the actual shape of a MIP signal, see figure 7.9 is narrower than the measurement. Using the Landau-Gaussian fit described in chapter 7.1.2 the efficiency is
10.4 Optimization with fixed voltage (I) 89
Deposited energy [MIP]
500 1000 1500 2000 2500 3000 3500
count
1 10 102
0 1 2 3 4 5
Figure 10.6: Sample measurement of tile 604. The efficiency is calculated as the ratio of signals below and above threshold, in this case 0.3 MIP. In blue the data. The green area depicts the signals over threshold while the yellow are is the part of the signal that is lost with this threshold setting. The measurement has been rescaled to the MPV as 1 MIP.
calculated. In figure 10.8 was extracted using M IP =
R∞
t F(f it)(x)dx R∞
0 F(f it)(x)dx. (10.2)
F(f it)(x) is the fit to the response function in section 7.1.2 expressed in MIP. The corresponding threshold t is also expressed in MIP. This excludes the zero and partial counts from the measurement and approximates the tail of a true Landau-Gaussian function as will be seen in a true MIP signal compared to the actual laboratory measurement. With an actual MIP distribution being narrower than the distribution from a90Sr source the efficiency is greatly underestimated in this measurement.
10.4.2 Noise over threshold
Following equation 7.5 the noise over threshold can be defined as DCRt=−ln(1−Ptn(tef fgate))
tef fgate (10.3)
for a gate lengthtef fgate. Ptnis the normalized fraction of events with pulse charges corresponding totor more pixel fired. Figure 10.7 is a time consuming high statistic pedestal with five million entries. Due to the low noise of the SiPMs investigated here the amount of entries over a few pixel threshold is not representing the true noise distribution anymore. Furthermore even in a measurement with more entries the noise over threshold will be in the same or smaller as
90 10. Operation Voltage Optimization
Entries 5000015 Mean 605.4 RMS 14.19
fired pixel
counts
1 10 102
103
104
105 Entries 5000015
Mean 605.4 RMS 14.19
0 2 4 6 8 10 12 14 16 18
Figure 10.7: Sample measurement of tile 604 with 5·106 entries. Even a time consuming measurement with million of data points does not yield more than a few entries over a threshold of several pixel. The higher energy signals are also dominated by cosmic Muons rather than SiPM noise.
cosmic muon signals (0.15 s−1, see [23], in a tile of 3×3×0.3cm3). To estimate the SiPM noise over threshold it is (wrongly) assumed that the correlated noise caused by any pixel is, following equation 7.6,
XTcorr = Pinf
k=2Pkn P1n =
Pinf k=tPkn
Pt−1n ∀t∈Nt >2 (10.4) This does not take into account the geometrical occupancy of the SiPM pixels since neighbor-ing pixels that are already fired do not contribute to the signal anymore. For a more detailed view on this topic see [77]. For a low occupancy of a few pixels in a SiPM this assumption is feasible. Following chapter 7.1.1
XTcorr = 1−(P0n+P1n)
P1n = 1−(P0n+P1n+Pt k=2Pkn)
Ptn ∀t∈Nt >2) (10.5) From here the probabilityPtn is
Ptn= 1−(P0n+P1n+Pt−1 k=2Pkn)
XTcorr+ 1 ) ∀t∈Nt >2 (10.6) . With equation 10.3 the noise over thresholdDCRtcan incrementally be calculated as
DCRt=−ln(1−1−(P0n+P1n+
Pt−1 k=2Pkn) XTcorr+1 )
tef fgate ∀t∈Nt >2) (10.7) . Figure 10.8 on the right shows the resulting approximated and overestimated noise for a single SiPM Tile system. The data used to extract XTcorr as mentioned in chapter 7.2,