As a side product of the peak fitting for the FCCD/FAV analysis, the energy resolution is obtained for all analysis peaks. Fig. 7.26shows the energy resolution at 59.5 keV, 356.0 keV and 1332.5 keV FWHM for each detector. The resolution at the 1332.5 keV peak is taken as the FWHM from the Gaussian component of the fit; the low energy peak tail is not included in this number. All detectors apart from GD02D are well below a resolution of 2 keV FWHM at 1332.5 keV. Note, however, that the resolution is dependent on the amplifier electronics and the energy reconstruction algorithms. The obtained values are not representative for the energy resolution in Gerda Phase II inside LAr.
Figure 7.26 Energy resolution in FWHM at three different γ-lines of 59.5 keV, 356.0 keV and 1332.5 keV. The 1332.5 keV γ-line was fitted with an exponential low energy tail which is not included in the FWHM. The detectors are ordered in sequence of diode production at the manufacturer. Note that the 60Co measurement of GD35B was taken with an FADC and is not comparable with the other detectors.
The energy resolution can be correlated to the detector mass influencing the capacitance of the diode and the length of the charge trajectories. A correlation plot of the FWHM at the 1332.5 keV 60Co line with the detector mass is shown in Fig. 7.27a. However, no strong correlation is observed.
7.5 Conclusions 127
(a) FWHM vs mass
Figure 7.27 Correlations between energy resolution and detector mass. Note that the60Co measurement of GD35B was taken with an FADC and is not comparable with the other detectors.
7.5
Conclusions
The fully active volume (FAV) and the full charge collection depth (FCCD) has been de- termined for the Gerda Phase II BEGe detectors. The FAV is the active volume for processes that involve discrete spectral energies such as 0νββ decay and FEPs from γ-ray interactions. The FCCD can be interpreted as the dead layer thickness for these processes using the same terminology as in older literature. The FAV determined in this chapter is underestimating the active volume for processes involving continuous spectral energies such as 2νββ decay or 0νββ decay with Majoron emission. The FCCD should not be interpreted as a dead layer thickness for these processes. Especially for surface interac- tions such as beta particles penetrating the n+ electrode, an additional transition layer is required for an accurate description. A study of these cases is presented in the next chapter. Three methods based on 241Am, 133Ba and 60Co were applied to obtain first the FCCD and then calculate the FAV under the assumption of a homogeneous FCCD. The 241Am
and 133Ba methods probe the top surface FCCD with high precision. The 60Co method probes the full volume of the detector but is less sensitive to FCCD changes and influenced by large systematic uncertainties. The FCCD values determined with the three methods agree within uncertainties. However, systematic shifts were observed between the methods indicating a strong correlated uncertainty common to all detectors. For the final results, the 241Am and 133Ba values were combined into a single FCCD value for each detector.
Due to a much larger uncertainty budget of the60Co method, the results from the volume probe were not considered in the combination.
The assumption of homogeneity for the FCCD over the n+ electrode was extensively tested with collimated 241Am scans. The top and lateral surface was scanned for a subset of 22 detectors and no significant inhomogeneity was observed for all but two detectors (GD76B and GD89D). The FCCD difference between the lateral and bottom surface was tested for GD91C in the upside-down mount. Also here no significant difference was observed, thus strengthening the assumption of a homogeneous FCCD over the full detector surface.
Charge collection deficiencies in the corners were estimated with the surface scans to be smaller than 0.4 % of the total volume which cannot explain the observed FCCD difference between surface and volume probes.
The241Am scanning measurements were also used as a sensitive crosscheck of FCCD val- ues between the detectors using the 59.5 keV peak count rate. This very precise method is only sensitive to the FCCD difference between the detectors which can be compared to the difference obtained with the ratio methods. A strong correlation was found for 19 of 22 detectors strengthening the final FCCD results from the ratio methods.
The top surface FCCD measurements with the241Am and 133Ba ratio method were used to calculate the FAV of the detectors. The mass weighted average of 29 working BEGe detectors is fFAV = 0.919+0.007−0.004(corr.)+0.004−0.004(uncorr.). MC simulations of 0νββ decays were
performed for each detector to determine the detection efficiency of this process. The mass weighted average detection efficiency is fdet = 0.897± 0.002(corr.) ± 0.001(uncorr.). The
uncertainty budgets for all numbers are separated into a correlated and uncorrelated com- ponent between the detectors. This information can be incorporated into Gerda Phase II analyses: The uncorrelated component is reduced when considering multiple detectors in a dataset whereas the correlated component is intrinsic and is not reduced.
Finally, the energy resolution in the vacuum cryostats was determined for all BEGe de- tectors. The resolution of all 29 working BEGe detectors is better than 2 keV FWHM at 1332.5 keV. An investigation of the correlation between energy resolution and detector mass found no significant effect.
Chapter 8
New Pulse Shape Model for
Surface Events in BEGe Detectors
Surface events are mainly created by beta emitting radioactive isotopes that are on the de- tector surface or are present in its vicinity. Roughly 96− 98 % of the surface of a Phase II BEGe detector is covered by the n+ electrode which has a thickness of 0.5 − 0.9 mm. Thus, the focus in this chapter is on n+ electrode surface events. Betas penetrating the n+ electrode can deposit energy inside the active volume. Clearly visible radioactive iso-
topes in Gerda Phase I are39Ar,42K and214Bi ([115] andSec. 5.5.2). Especially the42K betas with up to 3.5 MeV endpoint in the ground state transition (82 % probability) pose a background risk for 0νββ decay at 2039 keV.
MC simulations of n+ electrode surface events are difficult and have been largely ignored in the past. The non-existing electric field makes diffusion the dominating charge transport mechanism which results in significantly longer rise times (see alsoSec. 4.2.1). Due to the long rise time these events are called slow pulses. The isotropic diffusion of the charge carriers in the field-free region leads to a reduced charge collection efficiency when charges diffuse away from the active volume. This energy loss is dependent on the interaction depth below the surface.
Surface events dominate the background for BEGe detectors in Gerda. 39Ar is by far the largest overall background component and42K dominates the background around the ROI of 0νββ decay in Phase I with around 60 %. Yet, so far the energy spectra of these background components could not be adequately simulated. Furthermore, the slow pulse character of surface events allows strong suppression with pulse shape discrimination. A good understanding of this suppression is required to optimize PSD efficiencies. Addi- tionally, the n+ electrode accounts for roughly 10 % of the total detector volume and, to a smaller degree, also affects internal decays. Especially decays with continuous energy deposition such as the 2νββ decay and the 0νββ decay with Majoron emission are subject to a larger active volume when the n+ electrode is considered semi-active compared to simply ignoring it in the old approach. This effect becomes important when measuring the 2νββ decay with high precision.
The development of a new n+ electrode model is presented in this chapter. The goal is a
tool that can be used to post process existing Geant4 simulations to correctly describe surface events on the pulse shape level.
for228Th,90Sr and241Am calibration sources inSec. 8.1that can be used to design and test the new model1. In an intermediate step, a simplified ad-hoc model is developed inSec. 8.2 and used to extract and compare n+ electrode properties of the Phase II BEGe detectors with data from the HADES characterization. Then a more sophysticated n+ electrode model is constructed from first principles inSec. 8.3and folded into Geant4 simulations. Those simulations are compared with data from the upside-down mounting of GD91C at LNGS to test the validity of the model inSec. 8.5. Finally, in Sec. 8.6 the new model is extrapolated to surface background and signal events in Gerda and predictions are made for Phase II.
8.1
A/E Spectra of Calibration Sources
The pulse shapes in BEGe detectors can be effectively described by the A/E parameter (Sec. 4.2.3). Slow pulses result in a larger width of the current pulse, thus a smaller ampli- tude and thus a smaller A/E value compared to bulk events. A specific energy deposition in the n+ electrode leads to a reduced E measurement due to charge loss in the detec- tor and to an even more reduced A due to slowness. Hence the A/E is affected twofold compared to the same energy deposition in the bulk. Betas create charge carriers with ionization continuously along their trajectory. If betas pass through the n+ electrode, they will always have a fraction of their pulse influenced by this slow pulse character.
The A/E is reduced for both slow pulses and multi-site events (MSE) compared to single- site events (SSE) in the bulk (Fig. 4.10). The SSE topology of the 208Tl DEP is used as
a reference for A/E. If a 2614.5keV γ-ray from 208Tl is interacting via pair production, two 511.0 keV γ-rays from the positron annihilation can escape the detector. The detected 1592.5 keV energy of the electron is typically confined to a small volume2. The A/E versus E spectrum of a228Th calibration source is shown inFig. 8.1. The markings are explained below:
(a) A/E scatter plot (b) A/E slice
Figure 8.1228Th calibration source measurement. Shown is the A/E versus E scatter plot (left) and
A/E slices for given energy regions (right). Note that the spectra contain background. The spectral section is dominated by208Tl with the main features (A) DEP, (B) FEP and (C) SEP.
1
In principle also other pulse shape properties such as the rise time can be compared; however this work focuses on A/E as used in the Gerda analyses.
2
In some cases a wider spread of the energy deposition may occur if the electron or positron emit a Bremsstrahlung photon which can have a larger range in Ge. The average fraction of Bremsstrahlung energy loss at 1.5 MeV is around 3 % (seeFig. 4.4a). Another event topology creating MSE is caused by a Compton scattering followed by pair production.
8.1 A/E Spectra of Calibration Sources 131
A Double escape peak (DEP) at 1592.5 keV: Two annihilation γ-rays escape. Used as reference for SSE in the bulk.
B Full energy peak (FEP) at 2614.5 keV: Likely Compton scattering or pair production at higher energies. This results in MSE topologies and reduced A/E in most cases3. C Single escape peak (SEP) at 2103.5 keV: One annihilation γ-ray escapes and the other is detected. This often results in a very defined MSE: An energy deposition of 511.0 keV in one place and 1592.5 keV in another. If the energy depositions occur in sufficiently different locations in the detector such that the charges arrive separately and no Bremsstrahlung occurs, the A value is that of the larger energy deposition and A/E is constant. This can be seen inFig. 8.1at 2103.5 keV and A/E=0.76. The A/E value is the ratio of the two energy depositions 2103.5 keV−511.0 keV2103.5 keV .
The maximum range of a42K 3.5 MeV electron in germanium is 5 mm. The typical depth
at which charges are fully collected is about 0.5−0.9 mm for the Phase II BEGe detectors. Hence, only a small fraction of the pulse shape is influenced by n+ electrode effects which reduce the A/E with respect to 208Tl DEP events in the bulk. This results in a band of
events that collectively have a smaller A/E value than bulk events.
A90Sr calibration source (2.28 MeV beta endpoint of90Y) is used to investigate the effect
of high energetic betas such as from42K. An A/E versus E spectrum of a90Sr calibration source is shown in Fig. 8.2. The A/E is calibrated such that the DEP of 208Tl has the value 1. The following features are visible:
(a) A/E scatter plot (b) A/E slice
Figure 8.2 90Sr calibration source measurement. Shown is the A/E versus E scatter plot (left) and
A/E slices for given energy regions (right). The spectral section is dominated by90Y betas with the
main features (A) SSB and (B) SPB.
A Single site band (SSB): A band of events with the same A/E values as the DEP. These evens are created by background radiation as e.g. Compton scattered γ-rays from the outside. Another source is Bremsstrahlung induced by90Y betas in material between source and the active detector volume e.g. source material, cryostat wall, inactive germanium material on the outer side of the n+ electrode.
B Slow pulse band SPB: A band of events with commonly shifted A/E values. This shift is similar for a specific initial beta energy in which a certain fraction of the
3Note that the A/E can still be equivalent to a SSE if two energy depositions are in locations with
energy is deposited in the n+ electrode. For larger energies this fraction is smaller and the SPB is closer to the SSB. For smaller energies the argument reverses. In the continuous 90Sr spectrum, this can be seen as a widening of the gap between SSB and SPB towards lower energies in Fig. 8.2a and 8.2b. However, the separation of SSB and SPB is always strong.
To avoid the complications with the continuous energy depositions from a beta source, the 59.5 keV γ-ray from241Am is used for investigations with point-like interactions. 59.5 keV γ-rays interact 10 times more likely via the photoelectric effect than via Compton scattering and have an attenuation length of 1 mm in germanium. The A/E versus E spectrum of an 241Am calibration source is shown in Fig. 8.3. The A/E values are normalized to the 59.5 keV peak. The following features can be seen in the spectrum:
(a) A/E scatter plot (b) A/E slice
Figure 8.3241Am calibration source measurement. Shown is the A/E versus E scatter plot (left) and
A/E slices for given energy regions (right). The main features are (A) FEP, (B) 241Am SSE, (C)
slow pulse degraded 59.5 keV events, (D) the minimum A/E value and (E) DAQ effects on the A/E reconstructions at low energies.
A Full energy peak (FEP) at 59.5 keV: Events interacting in the FAV below the FCCD. The resolution of A/E is significantly worse at low energies and the SSB is much wider.
B Other events: Events that are Compton scattered outside the detector. Low energy Compton backscattering results only in a small energy loss of the scattered γ-ray. C Energy degraded 59.5 keV events: Events interacting in the n+ electrode are mea-
sured with a reduced energy. The further above the FCCD, the stronger the energy loss, the slower the pulse and the smaller the A/E. This forms an arc below the peak which is an important feature that has to be reproduced by the model.
D Minimal observed A/E value due to noise and the trigger threshold.
E DAQ effects: The trigger becomes less effective for slow pulses at low energies. The A/E reconstruction results in large variations due to a stronger influence of the noise on the current pulse maximum. Typically the noise increases A rather than decreasing it such that A/E values > 1 can be reconstructed below 10 keV.
To understand and reproduce these A/E features with MC simulations is the main goal of this chapter. 90Sr is used as a proxy for 42K. However, the initial step of the model construction is performed with241Am which has a more defined point-like event signature.