Discrimination of the individual iSticks

It is observed that the pulse shape of different detectors slightly varies despite the same geometry and the same production process. The three iStick thermometers measured in the present work were produced on the same silicon wafer and processed simultaneously (see chapter 6). The pulse shapes observed in the iStick channel are investigated in the following.

In figure 7.13 the decay time parameter of all iStick events is shown against the pulse height measured in the iStick channel. The decay time parameter is calculated by the analysis software and describes the time of a pulse necessary to decay from the maximum sample to 1/eof the total pulse height. For pulse heights &1 V (corresponding to an energy of ∼20 keV) three clearly separated populations are visible in the decay time parameter calculated for the pulses measured in the iStick channel. For smaller pulse heights a high noise contribution increases the uncertainty of the decay time parameter.

Figure 7.13: Decay time parameter of iStick events versus the pulse height measured in the iStick channel. For pulse heights above∼1V (corresponding to an energy of∼20keV) three populations can be discriminated. In total 1798 events are marked in magenta, 2176 events in violet and 1889 in green. The similar number hints that the energy scale of the three iSticks is roughly similar.

A more elaborated pulse-shape analysis⁷ might improve the discrimination for smaller pulse heights.

The three populations are marked in colors for pulse heights&1 V. They contain a similar amount of events of 1798 events (magenta), 2176 events (violet) and 1889 events (green). This hints that the energy scale of the three iSticks is roughly similar.

For each distribution a standard event is produced from pulses with a pulse height of

∼3 V and is shown in figure 7.14. The standard events of the three different populations are well distinguishable by eye. They slightly differ in their rise time (τn,1 = 0.4 ms, τn,2 = 0.6 ms,τn,3= 0.7 ms) and strongly in their decay time (τ_{f ilm,1}= 2.7 ms,τ_{f ilm,2}= 4.4 ms,τ_{f ilm,3}= 8.8 ms). The differences are explainable by discrepancies in the thermal couplings. A difference in the glue spot connecting the TES-carrier to the CaWO4stick can cause a difference in the rise time. The decay time can be influenced by differences in the thermal coupling to the heat bath, which varies due to differences in the bonding process of the gold wire providing the thermal coupling. Moreover, the thermal coupling between the stick and the holder can vary, due to a difference in the pressure of the clamp pressing the stick against the absorber crystal.

The amplitude of a pulse determined in the template fit depends on the template

7Several parameters can be used to distinguish pulses with different shapes. In CRESST-II phase 2 a pulse-shape analysis has been performed to distinguish pulses from the main absorber crystal and the TES-carrier. The discrimination power of several single parameters as well as a pulse-shape analysis based on artificial neural networks was investigated in [76].

Figure 7.14:Template pulses of the three iSticks with an amplitude normalized to one. Each standard event is generated from one of the three populations visible in figure 7.13 of pulses with a pulse height of∼0.3V. A clear difference in the pulse shape can be seen. The rise time differs slightly (τ_n,1= 0.4 ms,τ_n,2= 0.6 ms,τ_n,3= 0.7 ms), while the decay time varies strongly (τ_{f ilm,1}= 2.7 ms,τ_{f ilm,2}= 4.4 ms,τ_{f ilm,3} = 8.8 ms).

used. For this reason the correct amplitude can only be determined if pulses from the different sticks can be separated⁸. As it is not necessary to know the exact amplitude in a veto channel, the pulse height parameter can be used as estimator for the amplitude.

In figure 7.15 the pulse height measured in the iStick channel against the amplitude measured in the phonon detector is shown for all events. The events are colored ac-cording to figure 7.14 for iStick pulse heights of & 1 V, so that the events occurring in each stick are shown in different colors. Events of each iStick appear in a wide distribution with the largest density occurring in two bands. This means that for a certain energy deposited in one iStick a different amount of energy is transferred into the phonon detector. This can be explained by a difference in the thermal coupling of different parts of the stick. The feedthrough of the housing for the sticks couples the middle of the stick to the housing and, thus, to the heat bath. For this reason, phonons produced in the part of the stick inside the housing are more likely to be transferred into the absorber crystal than in the iStick TES. In contrast, phonons produced in the outer part of the stick are more likely to be transferred into the iStick TES than in the absorber crystal. In conclusion, it seems that events occurring close to the absorber crystal transfer a larger amount of energy in the absorber crystal compared to events

8A fit with different templates is also a method to discriminate events with different pulse shapes.

Typically, the RMS from the fit is low if the template describes the pulse shape well. When a pulse is fitted with different templates, the template that results in the smallest RMS value is the best estimator for the true pulse shape.

Figure 7.15: Distribution of events of the respective iSticks. The same events as in figure 7.11 are shown here but with different colors. The iStick events are colored as the respective populations shown in figure 7.13. While the distribution of events of the two iSticks with the longer decay times overlap (green and violet), the distribution of the iStick 1 (magenta) is observed at lower pulse heights in the iStick channel. All three distributions of the respective iSticks seem to appear in two bands, which probably correspond to events occurring inside or outside the housing. All events which could not be attributed to one iStick are shown in gray color.

close to the TES-carrier.

The distributions of two iSticks overlap (iStick 2 in violet and iStick 3 in green), while the distribution of iStick 1 (magenta) appears at smaller pulse heights measured in the iStick channel. The reason for this can be either a worse performance of one iStick thermometer or a difference in the transfer of phonons into the absorber crystal, e.g. due to a different pressure between the absorber crystal and one iStick.

In contrast to the phonon signal, there is no visible difference in the light signal of events in the three iSticks. It seems that the produced photons are distributed more evenly in the stick than the phonons after an energy deposition.

It is not necessary to discriminate the individual detectors of the iStick channel to act as a veto channel. However, these results demonstrate that it is possible to discriminate events from several detectors operated with only one SQUID. A more sophisticated analysis of the pulse shape might discriminate events occurring in the different iSticks to even lower energies. Such an analysis is possible with CRESST-III data as it exhibits a smaller pile-up component.