Calibration and Selection of the 10.37 keV Calibration Events

The five measurements channels are saving the voltage of their associated sensors in ADU unit specific to each considered channel. In order to proceed with the estimation of the heat E_heat, ionizationEIon.and recoilERenergies, it is now necessary to determine the conversion rates be-tween ADU units and eV for each channelCH. This calibration coefficientαCH are determined experimentally thanks to the intrinsic germanium 10.37 keV calibration line inducing electronic recoils of known heat energyEheat = 10.37 keVeeand ionization energy EIon. = 10.37 keV. This subsection first describes the calibration of the ionization channel. Then, it discusses the selec-tion of the 10.37 keV calibraselec-tion events for the calibraselec-tion of the heat channel.

The most straightforward calibration method is to determine the position of this calibration peak on the amplitude spectra of the electrodesA,B,C,D. Indeed, according to the charge sig-natures (eq.6.7) of the events in the detector RED80, the charge are induced on the two collecting electrodes with equal amplitude. However, due to the oblique propagation of the electrons, a

0

Figure 6.15: Histogram and CDF derived from the experimental estimation of the cabling capac-itanceC_cabling,22andC_cabling,44for each Bulk events in the REDN1 detector.

significant fraction of the 10.37 keV events does not possess these archetypal ionization signature but rather a linear combination. Although this phenomenon affects only slightly the calibration of the collect electrodes Band Ddue to the high fraction of bulk events with complete charge collection, the low amount of well reconstructed guard events render the precise calibration of the guard electrodes AandCimpossible.

The alternative calibration method, used in this work, permits the precise calibration of all the electrodes by benefiting from the non-ideal ionization signatures being linear combination of the bulk, guard and guard-collect events. The figure 6.16illustrates this ionization calibra-tion method for the RED80 data streams relative to the neutron background measurement. The graphics shows the cross-talk corrected amplitudesA^corr._X of all the quality events as red points.

The left graphic shows that all events produce negative amplitudes on the electrodes AandB which is consistent with the fact that at the default polarization6.6, Aand Bcollect electrons.

Similarly, the electrodesCandDcollect holes inducing signals with positive amplitude.

The blue points are quality events which are selected with the following conditions:



with A^corr._tot the total ionization amplitude. This selection crudely corresponds to the 10.37 keV calibration events with a complete charge collection EIon. ≈ 10.37 keV. As the electrons (resp.

holes) are collected by both theAandB(resp. C and D) electrodes, the ionization energyEIon.is split between the two electrodes. The calibration of the electrodes of REDN1 is done using the same method with the difference that the electrons are collected by the electrodes B,Cand the holes by A,Dwith the default polarization6.10of the detector REDN1.

The black lines are linear laws adjusted to the blue population using orthogonal distance

Figure 6.16: Calibration of the electrodes A,B,C,D of the detector RED80 on the data stream tg18l005. The left graphic displays the cross-talk corrected amplitudesA^corr._A versus A^corr._B . Simi-larly, the right graphic plotsA^corr._C versusA^corr._D . All the quality events are represented in red. The blue events correspond to 10.37 keV calibration quality events with complete charge collection.

Their amplitudes is adjusted with a linear law yielding the amplitudesA⁰_Xof the fully collected 10.37 keV peak.

regression. The parameters of the linear laws, A⁰_X, are the positions of the calibration peaks when fully collected by either one of the electrodes.

The calibration coefficientαXare defined for each electrodesXas:

αX= ^{10.37 keV}

|^A0_X| ^(6.40)

The calibrated amplitudes in keV are called the electrode specific ionization energiesEXand defined as:

∀^X∈ {^A,B,C,D}^{, E}X =αX·^Acorr.X (6.41)

The ionization energyEX is proportional to the charge QX induced on the electrodeX and es-timates the fraction of the ionization energyEIon.measured by this electrode. One should note that within this convention negative ionization energies are possible. The estimation of the ion-ization energyEIon. created by the recoil is the quantity E^tot_Ion. called the total ionization energy.

In its default polarization, the total ionization energy for the detector RED80 is expressed as:

E^tot_Ion.= −^EA−^EB+EC+ED

2 (6.42)

In the case of REDN1 with default polarization, the total ionization energy becomes:

E^tot_Ion. = ^EA−^EB−^EC+ED

2 (6.43)

The calibration of the heat channel is also based on the 10.37 keV calibration events. This

Figure 6.17: Reconstructed Ionization Energy as a function of the Reconstructed Heat Energy, for the quality events of the Calibration configuration. The plot is zoomed up to 12 keV for an easier view of the calibration peaks.

calibration process is illustrated for the detector RED80 on the stream tg18l005. The figure6.17 presents the total ionization energy E^tot_Ion. of all the quality events versus their heat amplitude Aheat.

Thanks to high rate of calibration events, we easily recognize the band of the 10.37 keV cal-ibration events. This band follows a linear law stretched between two remarkable points. The first corresponds to the 10.37 keV calibration peak, formed by events with a complete charge collection yielding a complete Luke-Neganov boost, located at A_heat ≈ ^{1200ADUand Etot}Ion. = 10.37 keV. The second point is situated at Aheat ≈ ^700ADUand E^tot_Ion. = 0 keV. It corresponds to 10.37 keV calibration events with no charge collection: the electron-hole pairs recombine im-mediately after the recoil and there is no Luke-Neganov boost on the heat channel. All the calibration events between these points have an incomplete charge collection with only partial Luke-Neganov boost.

The blue events on the figure correspond to the manual selection of the calibration events.

This selection is made manually with a graphical lasso selection. All the events of these selection are designated in the analysis as "calibration events" and they are used to determine precisely the heat amplitudes of the two extreme points of the calibration bands. The amplitude of the completely collected calibration peak isA_heat^peak. The heat amplitude of the calibration events with no charge collection is A^HO_heat. The exponent HO refers to "Heat-Only", as these events do not induce any ionization signal. The selection of calibration events is adjusted with the linear law:

E^tot_Ion. = ^10.37

A_heat^peak−^A_heat^HO(Aheat−A_heat^HO) (6.44)

using an orthogonal distance regression algorithm. The calibration coefficient αheat associated with the heat channel is calculated as:

αheat = ^{10.37 keVee}

A^peak_heat (6.45)

The calibrated heat amplitude called the heat energy of an event is defined as:

Eheat =αheat·^Aheat (6.46)

This heat energy is expressed in the unit keVee where the indexee refers to "electronic equiva-lent". This unit expresses the heat energyEheat generated by an electronic recoil of quenching factorQER =1 and recoil energyERaccording to the equation4.24:

Eheat= ER· As such, the heat calibration assumes that every event is induced by an electronic recoil, which is false in the case of neutron recoils with a lower quenchingQNR. This means that apart from the electronic recoils, this experimental heat energyEheathas no physical meaning. However, it is used to access the recoil energyER of an event expressed in keV. This recoil energyERtakes into account the experimental quenching factor of an eventQand the Luke-Neganov BoostENL

associated .

Combining the equations4.2and4.23, the Luke-Neganov energy of an event is derived from the ionization energy as:

ENL =E^tot_Ion.Vbias

2.97 (6.48)

The recoil energyERof an event is calculated as:

ER =EC·

and the associated quenching factor is derived using the usual formula4.2 with experimental estimation:

The charge conservation cut aims at discarding events which does not respect the charge con-servation. Indeed, some events might demonstrate charge collection issue. Drifting charges can be trapped in the germanium and may not end up being collected. In section6.2.7, the ionization energies EX are obtained from amplitudesA^corr._X of the decorrelated voltage signal V_X^decor.. For the definition the charge conservation cut only, the termEXrefers to the ionization energies cal-culated from the raw voltage signalVXwithout decorellation. As such,EXis proportional to the charges collected on the electrodeXof the detector. We define the energy of charge conservation ECC as:

ECC = ¹

2(EA+EB+EC+ED) (6.51)

By construction, this quantity is proportional to the excess or lack of total induced charges on the electrodes of the detector. Contrary to the total ionization energyE^tot_Ion., this quantity is common to RED80 and REDN1 as it is independent from the polarization of the electrodes.