8.5 Comparison with Data
8.5.2 Quantitative Comparison
Fig. 8.25shows the A/E distributions for the 90Sr measurement and MC simulation with different recombination rates. The two ROIs of 650− 1000 keV and 1000 − 1450 keV are distinguished in the left and right plots. The interesting region around the SSB is enlarged in the bottom plots. Also shown is the spectrum of a 63.9 h background measurement
17Note that this reference contains a typo: The ”+l” in the denominator of the last term in formula (1)
which was scaled to the 90Sr measurement live-time of 1.3 h. It is used to subtract the background influence in the quantitative analysis. Both spectra are then normalized to the background corrected number of 90Sr events in the respective energy region of the A/E spectrum. The same normalization is done for each MC spectrum individually18. The vertical dashed lines are the A/E cut values at 0.98 and 1.07, separating the spectrum into three regions: low A/E, SSB and high A/E region. The cuts are chosen to separate the three regions as best as possible in the data and MC alike.
(a) 650− 1000 keV (b) 1000− 1450 keV
(c) 650− 1000 keV zoom (d) 1000− 1450 keV zoom
Figure 8.25 Comparison of90Sr A/E values between measurement (solid gray) and various recombi-
nation models (colored lines).
It can be seen that the overall shape of the A/E spectrum can be reproduced by the MC with the recombination probability of 0.002 per ns (green histogram) which was identified as the best model. The extreme cases of full recombination and the zero combination do not reproduce the shape. This is a strong indication that a finite charge recombination rate is realized in the outer layers of the n+ electrode and that this kind of analysis is sensitive to its value. Even a measurement of the recombination rate can be envisioned with more investigations on the systematic influence of the other model parameters.
The high A/E region is the same for all MC spectra since the recombination models only affect slow pulses. A larger high A/E tail can be seen in the MC compared to the data similar to the observation with the DEP in208Tl. However, the generally strong reduction
18Note that the total number of events in the various MC spectra differ and that each MC spectrum has
8.5 Comparison with Data 157
of events in the valley just above the SSB is reproduced and can be used to strongly sep- arate p+ electrode events from the rest. The minimum and maximum value of high A/E events in the data is larger and lower respectively, which, however, does not affect this analysis. The fraction of background corrected high A/E events compared to all events is shown in Tab. 8.2. In the ROI 1 spectrum it is 29.5± 0.4 % in the data compared to 33.9± 0.2 % in the best fit model. In ROI 2 the fractions are 40.1 ± 0.7 % and 42.5 ± 0.2 % respectively. It is not clear if the difference between data and MC is due to a mismatch in number of p+ electrode events or a mismatch in the number of events in the other regions. The SSB band itself is dominated by background in the data and only 32 % of SSB events can be attributed to 90Sr in ROI 1 and only 23 % in ROI 2. The large subtraction of background creates a significant uncertainty on the quantitative comparison.
The maximum of the SPB is best reproduced by the 0.002 model. However, the gap be- tween SPB and SSB is not qualitatively reproduced since the SPB is significantly wider in the data. Also the extension to the lowest A/E values is wider in the data. A possible explanation are local variation in the n+ electrode which are not modeled in the MC and which would widen any slow pulse component of an A/E distribution. This goes along with the observation of a larger than expected variety of slow pulses in the A/E versus E spectrum of241Am (Fig. 8.20).
Table 8.2 A/E event fractions in % in the two ROIs of90Sr. The data is background corrected and the
MC is based on the best recombination model.
ROI 1 [650− 1000 keV] ROI 2 [1000 − 1450 keV]
region range data MC data MC
A/E < 0.98 69.1± 0.6 62.8± 0.2 59.0 ± 0.8 55.8± 0.3 0.98 < A/E < 1.07 1.4± 0.2 3.3± 0.1 0.9± 0.2 1.7± 0.1 A/E > 1.07 29.5± 0.4 33.9± 0.2 40.1 ± 0.7 42.5± 0.2
Even with the qualitatively different shape of the SPB between data and MC, an A/E cut at 0.98 separates the SPB and the SSB maximally in both cases. The fraction of events in the low A/E region and the SSB region is also shown inTab. 8.2 and compared between data and MC. The fractions are defined with respect to all events in the respective ROI and sum up to 100 %. The fraction of SSB events can be interpreted as the survival fraction of 90Sr events with an A/E cut of 0.98 < A/E < 1.07 and is crucial for understanding surface events of BEGe detectors in Gerda. The survival fraction is measured with about 1 % in both energy ranges and shows the strong discrimination capability of surface events. The prediction by the MC is about a factor of 2 to 3 larger. The mismatch between data and MC might be explained by a few arguments concerning the experimental setup. (1) The beta beam of the 90Sr source was focused on the n+ electrode but a large popula- tion of scattered betas is interacting on the p+ electrode and groove surface creating high A/E events. This scattering is highly dependent on the exact geometrical implementation of the setup such that small systematic uncertainties introduce a large bias in the high A/E population. Such an influence would be reduced in an alternative measurement on a different side of the detector where the p+ electrode is not partially exposed. (2) Events in the SSB band are dominated by background and small systematic differences between the background and source measurement as e.g. introduced by correcting the efficiency of quality cuts, propagate strongly into the 90Sr SSB population and thus into the survival
fraction via background subtraction. (3) The high A/E tail on the SSB might slightly change the event separation between data and MC which can have a strong effect on the few surviving events in the SSB. But in any case, the discrepancies result in a conservative overestimation of the survival fraction of surface events in the MC.
(a) ROI 1 (b) ROI 2
Figure 8.26 Separation of simulated90Sr events in majority bulk events and majority n+ events. The event by event separation is based on the region in which the largest energy fraction is deposited. The simulation is based on the best fit recombination model.
Finally, the A/E distribution from the MC can be separated into majority bulk events and majority n+ events depending on the location of the deposited energy. This is shown for the best recombination model in Fig. 8.26. If a larger fraction of energy is deposited in the n+ electrode the event is counted as n+ event and included in the green histogram; the mutually exclusive case of a larger energy fraction in the bulk or FAV of the detector is shown in the blue histogram19. It becomes clear that the events in the slow pulse band are events were the major part of the energy is deposited in the bulk. Those events define the gap between SPB and SSB. It can be also seen that this effect is increased for larger measured energies. Hence, the mismatch of the gap in the MC is created by event topologies where less energy is deposited in the n+ electrode. This would e.g. occur if the charge recombination is locally larger20. The same effect would be expected if the FCCD were locally thinner which is however, not supported by the data from the 241Am scans
(Sec. 7.2). On the other hand, events with a larger energy deposition in the n+ electrode have significantly lower A/E values and will be vetoed with any A/E cut.
8.5.3 Conclusion
The n+ model developed in the previous section was compared with calibration data of GD91C. The model is based on the measured FCCD, the dimensions and the impurity concentration of an individual detector. The recombination rate of charges in the RDR is left as a free parameter and was tuned to data from 241Am and 90Sr. The two differ- ent event types are best described by the same recombination rate of 0.002 per ns. The
19
Note that the separation is based on the original Geant4 energy deposition of the event. Also energy in largely dead detector volume is counted.
20This may sound counter intuitive but can be observed in Fig. 8.25. A larger charge recombination
would give less slow pulse character to an event with a given beta trajectory. The measured energy of this event would also be smaller; however, by definition such an event has sufficient energy to populate the energy region of the A/E spectrum. Hence, for a larger charge recombination rate, the SPB moves closer to the SSB for events in a certain energy range.