Study of naturally occurring radionuclides in the ECHo set-up

The determination of the effective electron neutrino mass by analyzing the end point region of the 163\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{163}$$\end{document}Ho electron capture (EC) spectrum relies on the precise description of the expected 163\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{163}$$\end{document}Ho events and background events. In the ECHo experiment, arrays of metallic magnetic calorimeters, implanted with 163\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{163}$$\end{document}Ho, are operated to measure the 163\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{163}$$\end{document}Ho EC spectrum. 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This means, a control of the background level in the order of 10-5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$10^{-5}$$\end{document} day-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document} pixel-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-1}$$\end{document} is extremely important. We discuss the results of a Monte Carlo study based on simulations, which use the GEANT4 framework to understand the impact of natural radioactive isotopes close to the active detector volume in the case of the ECHo-1k set-up, which is used for the first phase of the ECHo experiment. For this, the ECHo-1k set-up was modeled in GEANT4 using the proper geometry and materials, including the information of screening measurements of some materials used in the ECHo-1k set-up and reasonable assumptions. Based on the simulation and on assumptions, we derive the expected background around QEC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q_{\mathrm {EC}}$$\end{document} and give upper limits of tolerable concentrations of natural radionuclides in the set-up materials. In addition, we compare our results to background spectra acquired in detector pixels with and without implanted 163\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{163}$$\end{document}Ho. We conclude that typical concentration of radioactive nuclides found in the used materials should not endanger the analysis of the endpoint region of the 163\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{163}$$\end{document}Ho EC spectrum for an exposure time of half a year.


Introduction
In the ECHo experiment, the 163 Ho electron capture (EC) spectrum is measured using low temperature metallic maga e-mail: alexander.goeggelmann@uni-tuebingen.de (corresponding author) netic calorimeters (MMCs), with 163 Ho enclosed in the absorbers via ion implantation [1]. The biggest effect of a finite electron neutrino mass on the spectrum can be found in the high energy part, just below the maximum energy available for the decay Q EC 2.8 keV, which corresponds to the mass difference between the parent atom 163 Ho and daughter atom 163 Dy [2]. The 163 Ho spectrum is characterized by several resonances, one for each of the excited states in which the daughter atom can be left and continuous structures related to the emission of X-rays and electrons to the continuum [3,4] (Fig. 1). Only a small fraction of the order of 10 −9 of all decays are located in the region of interest (ROI) of 10 eV below Q EC . The set-up used for the simulations based on the ECHo-1k design, which consists of an array of 72 MMCs based detector pixels [5]. Accordingly, a count rate of approximately 8 · 10 −5 day −1 pixel −1 is expected in the ROI.

Detection mechanism of MMCs
The energy E deposited by a particle in the absorber of a MMC leads to an increase in temperature δT of the MMC: δT where C is the total heat capacity of the MMC. The increase of the temperature of the paramagnetic sensor results in a change of magnetic moments in the sensor material and thus, in a change of magnetization δ M ∝ δT , which is measured with SQUIDS [6].

Objectives
We consider five background sources: Unresolved pile-up, electromagnetic noise, muons, co-implanted radioactive isotopes and, the topic of this work, naturally occurring radionuclides. In the ECHo experiment, the background level due to naturally occurring radionuclides and due to cosmic radiation Fig. 1 Expected 163 Ho EC spectrum (blue solid curve) following [3] and related unresolved pile-up spectrum for a pile-up fraction of 10 −6 (orange solid curve) and considering events with equal and opposite polarity. A Q-value of 2.833 keV and an energy resolution of FWHM = 10 eV are used to calculate the spectra. Inset: The effect of massive neutrinos on the summed spectrum is shown (mainly muons and secondary particles produced by muons) has to be reduced in a way that the unresolved pile-up remains the highest background contribution in the ROI. Preliminary Monte Carlo simulations, performed for the detector set-up of the ECHo-1k experiment [1], provided indicative upper limits on the tolerable concentration of radionuclides in the detector and surrounding materials [7,8].
Because of the small pixel size of 180 × 180 × 10 µm 3 , these limits of a few mBq are relatively high and can easily be fulfilled for most of the common radionuclides. In the following, new updated and more detailed Monte Carlo simulations based on screening measurements on some materials used in the ECHo-1k design are discussed in order to determine the expected background contribution due to the identified radionuclides and to give updated upper limits of tolerable concentrations.
In addition, background spectra measured with 163 Holoaded and non-loaded pixels are studied and compared to the simulations.

Detector set-up
A simplified design of the ECHo-1k experimental set-up is used in the simulations as shown in Fig. 2. On top of a silicon ECHo-1k chip [9] of dimension 10 mm × 5 mm and a thickness of 350 µm, 36 MMC pairs are placed, resulting in 72 pixels positioned in an array of four lines with 18 pixels each (compare to the insert in Fig. 2). The pixels consist of gold absorbers of dimensions 180 µm × 180 µm × 10 µm, which are placed directly on top of Ag:Er sensors of dimensions 168 µm × 168 µm × 1.35 µm [9,10]. In the Fig. 2 Simplified design of the ECHo-1k experiment set-up used in the simulation. Inset: The region close to the ECHo-1k chip. On the purple-colored silicon ECHo-1k chip, 72 MMCs and large thermalization structures (a) are placed. Next to the ECHo-1k chip, four dc-SQUID chips (b) are located. All five silicon-based chips are directly glued on the copper holder (c). A circuit board (d) covers the full copper holder, except the region next to the ECHo-1k chip. Connectors (e) are placed at a distance of about 15 cm from the ECHo-1k chip. An aluminum box (f) surrounds the copper holder middle of the absorbers, thin layers of silver with a thickness of 200 nm and a surface of about 150 µm × 150 µm are placed as host material for 163 Ho. Close to the pixels, relatively large gold structures are positioned (Fig. 2a). Four silicon chips, representing the dc-SQUID chips (Fig. 2b), with dimensions of 6 mm × 2.5 mm and thickness of 350 µm, are positioned close to the ECHo-1k chip (Fig. 2, insert). The circuit board 1 (Fig. 2d) covering the copper T-shaped support (called copper holder, Fig. 2c) is modeled as a 0.7 mm thick layer of a bisphenol-based epoxy resins. The copper holder, obtained by a larger annealed oxygen free high conductivity (OFHC) copper piece, has a thickness of 0.7 cm. The T-shape is required in order to have the ECHo-1k chip and SQUID chips at a distance of about 13 cm from the aperture of an aluminum tube used as superconducting shield (Fig. 2f). The circuit board has a gap, so that the five silicon chips can directly be glued on top of a copper holder. A rectangular aluminum tube of 2.5 cm (width) × 0.9 cm (height) and a length of 15 cm surrounds the set-up. The wall thickness of the aluminum tube is 3 mm for the bottom and top side and 10.3 mm for the other sides. Last, nine carbon-based connectors 2 with a density of 1 g mol −1 are placed at a distance of about 15 cm away from the ECHo-1k chip (Fig. 2e).

Unresolved pile-up
The time profile of the voltage signal caused by the absorption of energy in a MMC is defined by the thermodynamical properties of the detector itself. The shape of the signal can be described by an exponential rise and decay. The rise time τ r of these pulses, limited by readout bandwidth, is about 500 ns for MMCs in the ECHo-1k phase, while the decay time is a few ms [9]. The rise time defines approximately the time resolution of the detectors i.a., if two decays occurred in the same MMC within a time interval shorter than τ r , they will be interpreted as a single signal with an amplitude corresponding to the sum of the energy released in the two decays. Since each detector channel consists of two pixels, which generate signals of opposite polarity, the unresolved pile-up rate is in first approximation given as twice the product of the activity per pixel A (assuming both pixels having the same 163 Ho activity) and the time resolution τ r . Therefore, the count rate is given by r pu = 2 · A 2 · τ r . In Fig. 1, the continuous blue line represents the expected 163 Ho spectrum, following the description in [3] and using a Q-value of 2.833 keV, while the orange line represents the pile-up spectrum. This pileup spectrum was calculated considering a time resolution of τ r = 500 ns and an activity of 1 Bq per pixel, leading to an unresolved pile-up fraction of f pu = 2 · A · τ r = 10 −6 . Note that, due to the different polarities of signals generated by the two pixels of the same channel, the total amplitude of a pile-up event can be smaller than the two single signal amplitudes. The pile-up rate in the last 10 eV is about 3 · 10 −6 day −1 pixel −1 .
At this point, we would like to note that a more precise shape of the unresolved pile-up spectrum depends on the data reduction algorithm, in particular in relation to pulse shape analysis, which might be more suitable to discriminate pileup events when the second events have energies above a few hundred eV, as described in [11].

Electromagnetic noise
Electromagnetic noise can couple to the readout chain of the detectors, resulting in additional background signals. These events can easily be rejected with an efficiency of almost 100 % based on their trigger time information [11].

Muons
Cosmogenic muons can interact with the MMCs and the material in their surrounding. Thus, muons can deposit energy directly in the MMCs and/or can generate secondary radiation, which can interact with the detector pixels. It was shown that these types of events can either be recognized with the use of an active muon veto, by searching for coincidence among pixels events and by their pulse shape [12]. Out of 242 ± 20 measured pixel-veto coincidences, 194 ± 12 events were also coincidences among pixels, leading to an efficiency of about (80 ± 8) % of detecting muon induced events by searching for coincidence among pixels.
In addition, by interacting with materials, muons can generate free neutrons, which can activate the materials. In copper, for example, radioactive isotopes of cobalt (like 60 Co) or other radionuclides (like 54 Mn) can be produced with an accumulated activity concentration of up to the order of mBq kg −1 [13].

Co-implanted isotopes
In the production process of 163 Ho, several other radioistopes, for example 166m Ho [14] or 170 Tm/ 171 Tm [15], are produced. In the ECHo experiment, a two-step separation is used to minimize these byproducts. In particular, a chemical separation is used to ensure that no isotopes different to holmium are left over from the production process [15], followed by mass separation of the holmium fraction at the RISIKO facility [16]. With this, a total 166m Ho/ 163 Ho ratio below 5 · 10 −10 is achieved in the MMCs.

Natural radionuclides
The region of interest for the ECHo experiment is below 3 keV. Thus, especially low energy radiation, which could be produced directly in or next to the MMCs, has to be investigated. Radionuclides produce mostly low energy particles when decaying via the β-decay or EC decay. But also, Auger electrons and X-rays resulting from the rearrangement of the atomic shell, appearing by nuclear decays also including αdecays, have a probability to have low energies, below a few keV. In the following, the β-decaying daughters of the 238 Uchain 3 and 232 Th-chain 4 as well as 40 K are introduced, which represent the most frequent naturally occurring and relevant nuclides for the ECHo experiment. Only particles with energies less than 20 keV and an emission probability higher than 1 % per decay are listed. The following values are taken from [17] and [18]. The performed simulations include all decay modes, allowing therefore to investigate also low energy particles generated in scattering processes by α-particles and other energetic particles like γ -and δ-radiation.
4.1 238 U-chain 238 U can be found in the earth crust with an abundance of about 3 mg per kg [19] and thus, it also occurs in concrete and metals. The most prominent α-decaying daughter of 238 U is the gaseous 222 Rn, which can be accumulated in indoor air with concentrations of several tens of Bq per m 3 [20]. Further, radon atoms can be accumulated on surfaces and so, the 222 Rn daughters can be implanted in the detector materials due to the recoil after the α-decays. For example, concentrations of 210 Pb and 210 Po of the order of 10 −4 mBq cm −2 can be accumulated on the surface of OFHC copper [21]. 234 232 Th can be found in the earth crust with an abundance of about 10 mg per kg [19] and hence, 232 Th and its daughters also occur in metals. As 238 U, 232 Th has also gaseous daughters, however these and their daughters only have short lifetimes. Thus, these can not be accumulated very well on surfaces after the surface is no more exposed to air. 228 Ra decays to 228 Ac with a half life of about 6 years and a Q-value of about 46 keV. The daughter nuclide can be in excited states of about 6 keV (50 %), 20 keV (20 %) or 33 keV (30 %). This corresponds to small mean energies of the emitted electrons of about 3 keV to 10 keV. Due to the small excitation levels of a few keV, low energy gamma radiation can be emitted. Gamma radiation occurs with a probability of about 3 % with energies in the range of 13 keV to 16 keV. Actinium L X-rays with energies of 11 keV to 20 keV occur in about 1 % of all decays, as well as 6 keV to 20 keV actinium L Auger electrons. In addition, conversion electrons with energies around 2 keV (45 %), 5 keV to 10 keV (29 %) and 11 keV to 26 keV (12 %) are emitted. 228 Ac further decays to 228 Th. The Q-value is about 2124 keV and the half life about 6 hours. Almost in any transition, a relatively high energy electron (> 30 keV) is emitted and the daughter nuclide is in an excited state. Compared to the other decays, the probability of about 33 % of 11 to 20 keV thorium L X-rays is quite high, as well as the probability of 6 keV to 20 keV thorium L Auger electrons of about 37 %. 212 Pb has a half life of about 11 hours and decays with a Qvalue of about 574 keV to 212 Bi. 212 Bi can be in three states: The ground state (∼ 12 %), an excited state of an energy of about 239 keV (∼ 83 %) or of about 415 keV (∼ 5.2 %). 5 keV to 16 keV bismuth L auger electrons are emitted in about 22 % of all decays, while 9 keV to 16 keV bismuth L X-rays occur with a probability of about 14 %. 212 Bi is special, compared to the other discussed isotopes. The probability of β − -decay is only about 64 %, while 36 % of the decay are an α-decay. The half life is about 61 minutes and in case of the β-decay, the Q-value is about 2252 keV. The daughter nuclide 212 Po is in the ground state in about 86 % of all β-decays and in an excited state with an energy between 700 keV and 1805 keV in 14 %. X-ray and Auger electrons occur only in case of the α-decaying branch. The probability for these emissions after a β-decay is less than 0.5 %. Thus, thallium L X-rays with energies of 9 keV to 15 keV are emitted in about 7 % of all decays and thallium L Auger electrons with energies between 5 keV and 15 keV in about 12 %. 208 Tl decays to 208 Pb with a half life of about 3 minutes and a high Q-value of about 5000 keV. After the decay, the daughter nuclide is in one of 15 possible excited states in the range of 3197 keV to 4480 keV. 9 keV to 16 keV lead L X-ray occur in about 3 % and lead L Auger electrons with energies of 5 keV to 16 keV in about 5 %. 4.3 40 K 40 K is present in natural potassium with an abundance of 0.0117 % [17]. Its half life is 1.277 Gy and it has two decay branches. It decays to 40 Ca via a β − process (∼ 89 %) and a Q-value of around 1311 keV or to 40 Ar via electron capture (EC) decay or β + -decay (∼ 11 %) and a Q-value of about 1505 keV. While the daughter 40 Ca nucleus is always in the ground state, the 40 Ar nucleus is always in an excited state of 1461 keV. In case of the EC/β + -decay, argon K X-ray with energies around 3 keV are emitted with a probability of about 10 %, argon L Auger electrons with energies of about 300 eV with a probability of about 145 % 5 and argon K Auger electrons with energies between 2.5 keV and 3.2 keV in about 130 % 5 of all EC/β + -decays.

Screening measurement
In order to estimate the influence of naturally occurring radionuclides in the experimental set-up, screening measurements were performed to identify the presence of radionuclides in the materials used for the detector setup, as well as parts of the cryostat. The screening measurements were conducted in the shallow underground laboratories at Tübingen with a shielding against cosmogenic radiation of about 16 m.w.e. [22]. The sensitivity of the used high purity germanium detector [23] on radioactive contamination is mainly limited by the internal contamination of the detector itself. Dominant internal contamination features of the background spectrum correspond to about 15 · 10 −4 counts s −1 of the 40 K 1460 keV line, 12 · 10 −4 and 18 · 10 −4 counts s −1 for the 208 Tl 2615 keV and 583 keV lines respectively and 30 · 10 −4 counts s −1 of the 239 keV 212 Pb line. If no larger rates would be measured for the tested samples, an upper limit, the 95 % C.L., is calculated by using the internal limitations.
The screened samples are 50 g of cryostat copper used as high thermal conductivity holder for the detector set-up indicated with (c) in Fig. 2, a batch of 15 connectors ((e) in Fig. 2) with a total weight of 7.5 g and a printed circuit board with a weight of 13.63 g ((d) in Fig. 2). The results of the screening measurement are shown in Table 1 for bulk contaminations 5 More than one of these Auger electrons can be emitted per decay. The values are given in Bq kg −1 The values are given in mBq cm −2 and in Table 2 for surface contaminations. The latter are calculated by comparing the screening measurement with simulations of 40 K located one monolayer (10 −10 m) below the surface and 210 Pb, which is implanted in the material by the recoil of the decay of 222 Rn and its daughters. The typical measurement duration for these screening and background measurements was approximately a month each. Typical concentration of contamination in pure metals are in the order of 0.1 mBq kg −1 to 1 mBq kg −1 [24,25] and concentrations about 1 Bq kg −1 to 2 Bq kg −1 in non pure metals and alloys [26], mainly due to the 232 Th and 238 U chains. So, it is expected that for pure metals like the copper samples, only upper limits can be given. Concentrations of the order of 10 −4 mBq cm −2 [21] or of 17 mBq kg −1 to 40 mBq kg −1 [27] are expected for 210 Pb in the copper sample and concentrations of the order of 10 −3 mBq kg −1 for 232 Th and 238 U [28]. However, this is far below the sensitivity of the used detector. Smaller limits for the copper sample are given by a screening measurement including a similar copper sample with a mass of about 500 g, performed by the team of the Canfranc Underground Laboratory results in upper limits of about 40 mBq kg −1 for the 232 Th-chain, 6 about 120 mBq kg −1 for the 238 U-chain 7 and 25 mBq kg −1 of 40 K [29]. By comparing to the limits resulting from the screening measurement of the copper sample in Tübingen and assuming similar relations between the limits of 40 K surface to bulk contamination and 238 U bulk contamination to 210 Pb surface contamination, these limits leads to surface contaminations of less than 25 µBq cm −2 for 40 K and 28 µBq cm −2 for the 210 Pb-chain. Similar levels of contamination are also expected for pure aluminum samples [28].
The higher values for plastic (connectors) and the colored circuit board are as well expected. Crude oil and coal are often basic materials for plastics, binders (plastic disper- If a particle has too less energy to travel as far as the minimum range, the particle will not be created and its energy will be deposited locally. Larger volumes, marked with (*), contains sub volumes with smaller minimum range cuts (see Fig. 3) sions) and solvent. Both, crude oil and coal are known to have relatively large levels of concentrations of natural occurring radionuclides of about tens to hundreds of Bq kg −1 [30][31][32].
In newer MMC set-up for low background measurement, polyimide based circuit boards (Kapton) are used due to the very low concentration levels of natural radionuclides [29].

Monte Carlo simulation
The decays of the radionuclides are simulated using version 10.06.p03 of the GEANT4 toolkit [33]. To study accurately the effect of natural radionuclides located in the surrounding of the MMCs and to decrease computation time as much as possible, the predefined particle production energy thresholds are configured. If a potentially produced particle by a process with infrared divergence, such as bremsstrahlung or δ-ray production, the particle will only be generated, if its kinetic energy is above a given energy threshold. If the kinetic energy of the potentially produced particles is below the energy threshold, their kinetic energy is deposited locally. Particles generated by other processes like the radioactive decay or atomic de-excitation are not affected by this cut.

Simulation set-up
In order to produce as many low energy particles as possible in the close surrounding of the MMCs, the energy threshold is reduced layer by layer. The discussed energy threshold is equivalent to a minimum distance the particles have to pass before getting absorbed. These minimum ranges are shown in Table 3 for different volumes. The larger volumes like the copper holder, aluminum shielding and the substrate of the ECHo-1k chip contain sub volumes as seen in Fig. 3, showing the profile of the set-up around the ECHo-1k chip. Picture taken from [12] The simulations are divided into two sets. If the radionuclides are uniformly distributed in the volume materials, they are called bulk-distributed and if the radionuclides are located only on the surface of the volumes, 7 they are called surfacedistributed. The full decay chains of the nuclides are simulated. The large number of simulated events of the order of 10 6 to 10 8 for each nuclide are needed to obtain high statistics describing the deposited energies of less than 6 keV in the MMC pixels to study the shape of the spectrum in this region. For levels of radioactivity as high as resulting from the screening measurement, the number of simulated decays corresponds to very long measuring times of the order of a few thousand days (compare to Tables 4 and 5). Since no screening measurements are available for the detector-pixels and the aluminum shielding until now, the upper limits of concentrations of the copper sample (from the measurement in the Canfranc Underground Laboratory) is used for the detector pixels, the shielding and copper holder. The two copper samples screened in Tübingen and Canfranc have different shapes. Nevertheless, the same ratio between bulk and surface contamination resulting from the measurement in Tübingen is also assumed for the copper sample used in Canfranc. In order to safe computation time, radionuclides are only placed at the first quarter (next to ECHo-1k chip) of the circuit board. Naturally occurring radionuclides in the connectors are not simulated. For comparison, the simulation of 28 · 10 6 decays of 238 U and its daughters in the bulk of the part of the circuit board next to the ECHo-1k chip results in 846 particles hitting the MMCs, while the simulation of 3·10 6 decays of 238 U and its daughters in the bulk of the rest of the circuit board results only in two hits. Thus, by considering Pixel-days 9.9 · 10 4 4.9 · 10 4 4.4 · 10 5 The equivalent experiment durations correspond to levels of activities as high as the results/limits of the screening measurement and a set-up including 72 pixels only events due to radionuclides in the circuit board, it can be assumed, that about 94 % of all particles hitting the detector pixels, are produced by particles created in the part of the circuit board, which is next to the detector pixels. The connectors are relatively far away from the active volume and the aluminum shielding is between the connectors and the active volume (except of the middle connector). They have similar levels of contamination as the circuit board, but result in a smaller solid angle coverage with respect to the active volume. Thus, radionuclides in the connectors should have less influence on the background, by comparing to radionulcides in the circuit board. Radionuclides in the substrate are also not simulated yet, because metallic contamination of less than 10 11 atoms cm −3 can easily be achieved [34,35], which is equal to an activity of less than 10 µBq kg −1 . Following, the values of expected count rates in the last 10 eV below Q EC are determined by fitting an exponential decay to the spectra in the 1 keV to 5 keV range and averaging of the 2.6 keV to 3 keV range. The obtained value is further scaled with the (upper limit) activity resulting from the screening measurement.

238 U-chain
The energy deposition caused by bulk-distributed radionuclides of the 238 U-chain in the absorbers of the MMCs is shown in Fig. 4. The colors indicate the fractions of the Pixel-days 2.5 · 10 6 2.2 · 10 6 Copper holder Simulated decays 3.0 · 10 6 6.0 · 10 7 Days 1.6 · 10 5 2.6 · 10 5 Pixel-days 1.2 · 10 7 1.8 · 10 7 Circuit board Simulated decays 2.6 · 10 6 6.7 · 10 6 Days 6.9 · 10 3 6.0 · 10 3 Pixel-days 5.0 · 10 5 4.3 · 10 5 The equivalent experiment durations correspond to levels of activities as high as the results/limits of the screening measurement and a set-up including 72 pixels summed spectra caused by the nuclides of the decay chain. The α-decaying isotopes have only a minor effect on the spectrum in the energy region below 6 keV and are not shown, except of 238 U. However, the emitted α-particles can leave the absorbers and hit the material surrounding the MMC array. Thus, structures at 1.5 keV and 1.7 keV can be identified, which corresponds to aluminum and silicon K-shell X-rays and Auger electrons generated in the aluminum shielding and the substrate. In addition, δ-ray produced by α-particles can deposit energy in the absorbers. Events caused by α-particles, hitting the surrounding, should show coincidences among pixels, meaning that in one pixel energy is deposited by products of the α-decay. Another pixel is hit by X-ray, Auger electrons and/or δ-ray generated by the α-particle in the surrounding. At higher energies, structures like the 47 keV 210 Pb edge, the peak at 73.9 keV due to the decay of the metastable J P state of 234 Pa and exemplary the edge around 72 keV caused by 238 U, are visible. By assuming an equilibrium of the members of the 238 U-chain and accumulated activity level of 0.12 Bq kg −1 , which is equal to about 7 · 10 8 atoms of the 238 U-chain in each MMC or 10 −8 of the absorber material, a signal count rate of about (3.8 ± 0.1) · 10 −9 day −1 pixel −1 is expected in the ROI. Figure 5 shows the spectrum caused by surface-distributed 238 U on the surface of an absorber. As in the case of bulk-distribution, the summed spectrum has no structures at low energies and the α-decaying isotopes have only a minor effect on the spectrum below 6 keV. On the other hand, many features can be observed at higher energies. Fig. 4 Simulated spectrum of deposited energies in the MMC absorbers caused by the bulk-distributed 238 U-chain. The fractions due to the single nuclides of this chain are colored. The summed spectrum is structure-less for low energies. Nuclides decaying by an α-decay change the spectrum only minor at low energies, exemplary shown for 238 U. However, α-particles can escape the absorber and hit the aluminum shielding or the substrate. Thus, aluminum K X-ray and Auger electrons and silicon (substrate) K X-ray and Auger electrons as well as δ-ray generated by α-particles can hit the absorbers These occur, because not all decay products deposit their energy in the absorber. The peaks due to the α-decaying isotopes are visible at energies of their Q-value reduced by the energy of the emitted α particles, which is the recoil energy of the daughter nucleus. For example 238 U: 4270 keV − 4198 keV = 72 keV. More than one peak is visible at these energies, because the energy released in deexcitation process of gold atoms (excited during the nuclear recoil) emitted either as Auger electrons or X-rays, which can escape the absorber. For surface-distribution, the 186 keV gamma of 226 Ra has a higher path length in the absorbers compared to bulk-distribution and so, has a higher probability to ionize. Thus, the 68 keV KL X-ray line of gold is visible. 234 Th provides many features, the 29 keV, 63 keV, 74 keV and 92 keV gamma levels as well as the corresponding X-ray escape peaks. Note that not only gold X-ray can The fractions due to the single nuclides of this chain are colored. The α-particles can be emitted by any isotope. For low energies, the summed spectrum has no structures. Nuclides decaying by an α-decay change the spectrum only minor at low energies. At higher energies however, these nuclides provide many features escape, but also X-ray emitted by the daughter nuclides. From 234 Pa, the 43 keV gamma level and from 214 Pb, excited during the α-decay, the 53 keV level can be identified. Also, at energies above 80 keV, α-particles generate more structures. Due to the recoil of the nucleus, the daughter nuclide of an α-decaying nuclide can leave the absorber. Thus, there is a chance that only the α-particle emitted by these daughters can deposit energy in the absorbers. Only 210 Pb and its daughters 210 Bi and 210 Po should be surface-distributed due to accumulated 222 Rn. 8 With an activity concentration of 0.028 mBq cm −2 , a count rate of about (1.9 ± 0.1) · 10 −8 day −1 pixel −1 is expected in the ROI from these radionuclides, which only corresponds to about 200 atoms on each MMC surface.

232 Th-chain
The effect of bulk-distributed 232 Th is shown in Fig. 6. As in the case of bulk-distributed 238 U, α-decaying isotopes have only a negligible effect on the spectrum at low energies. The summed spectra has no structures in the low energy region, but a few features can be identified at higher energies. The three 228 Ra edges at around 6.5 keV, 20 keV and 33 keV can be seen. Also, the 58 keV excitation level of 228 Th, the daughter of 228 Ac is visible as well as exemplary the edge of 232 Th. In case of 228 Ra, there is a chance that 228 Ac with a half life of about 6 hours decays simultaneously (the time interval used in the simulation to generate pile-up events is δt < 1 ms) and thus, higher energies than the Q-value of 228 Ra of about 46 keV can be measured. For an activity concentration of 0.04 Bq kg −1 (about 10 9 atoms per MMC or 10 −8 of the absorber material), a count rate of Fig. 7 Simulated spectrum of deposited energies in the MMC absorbers caused by the bulk-distributed 40 K in the absorbers. The βspectrum is flat for low energies and the Ar shell levels due to the EC/β + -decay can be seen about (4.5 ± 0.1) · 10 −10 day −1 pixel −1 is expected in the ROI.

40 K
The resulting simulated spectrum of bulk-distributed 40 K in an absorber can be seen in Fig. 7. The only visible features are the Ar shell levels due to the EC/β + -decay at 0.3 keV and 3.2 keV. The β-spectrum is flat for energies below 6 keV.
For an activity concentration of 0.025 Bq kg −1 (about 10 8 atoms per MMC or 7 · 10 −9 of the absorber material), a count rate of about (3.2±0.1)·10 −9 day −1 pixel −1 is expected in the last 10 eV below Q EC . Figure 8 shows the spectrum caused by surface-distributed 40 K on the surface of an absorber. Compared to bulk-distributed 40 K, the lines due to the EC/β +decay are broader. This happens, because not all Auger electrons and X-ray deposit all their energy in the absorber. For an activity concentration of 0.025 mBq cm −2 (about 3 · 10 10 atoms per MMC-surface or 0.5 % of the surface atoms), a count rate of about (2 ± 1) · 10 −7 day −1 pixel −1 is expected in the ROI.

238 U-chain
The resulting simulated spectra for bulk-and surfacedistributed 238 U in the aluminum shielding can be seen in Figs. 9 and 10 respectively. In case of bulk-distribution, mainly higher energy electrons/β-particles deposit energy in the absorbers and thus, mainly the β-decaying isotopes with higher Q-values (≥ 1 MeV) are listed, but also the excited daughters of 214 Po can often emit high energy conversion electrons. The α-particles can generate much δ-radiation, which can deposit energy in the absorbers. Mainly the Landau distribution [36] caused by these electrons can be seen. For comparison, the Landau distribution caused by 500 keV electrons passing the absorbers is plotted. Similar to the surfacedistribution of 238 U on the absorbers, the spectrum resulting Fig. 9 Simulated spectrum of deposited energies in the MMC absorbers caused by the bulk-distributed 238 U-chain in the aluminum shielding. No special structures are observable. Mainly, electrons (βparticles) deposit energy in the absorbers. A Landau distribution [36] is expected to be caused by these electrons and can be compared to a Landau distribution for 500 keV electrons passing the absorbers [37] from surface-distributed 238 U in the shielding shows peaks from α-decaying isotopes, which can be seen at energies at the Q-values minus the energy of the emitted α-particle. Also, the α-particles can produce δ-radiation and X-ray, which results in deposited energies lower than 6 keV. An activity concentration of bulk-distributed 238 U of 0.12 Bq kg −1 results in a count rate of less than 2.7 · 10 −8 day −1 pixel −1 at 90 % C.L. in the ROI and surface-distributed 210 Pb and daughters with a level of 0.028 mBq cm −2 result in a count rate of about (6 ± 1) · 10 −8 day −1 pixel −1 in the ROI.

232 Th-chain
232 Th in and on the aluminum shielding results in the same structures like the ones resulting from 238 U in the shielding, the Landau distribution caused by electrons. Bulk-distributed 232 Th with a level of 0.04 Bq kg −1 results in a count rate of (6 ± 2) · 10 −9 day −1 pixel −1 in the ROI.

40 K
The spectra resulting from 40 K show no structures. Bulkdistributed 40 K with a level of 0.025 Bq kg −1 results in a count rate of (8 ± 3) · 10 −9 day −1 pixel −1 in the ROI and results surface-distributed and with a level of 0.025 mBq cm −2 in a count rate of about (4±2)·10 −7 day −1 pixel −1 in the ROI.

Radionuclides in the copper holder
Naturally occurring radionuclides located in the copper holder results in similar spectra as resulting from radionu- Fig. 10 Simulated spectrum of deposited energies in the MMC absorbers caused by the surface-distributed 238 U on the aluminum shielding. Lines caused by the α-decaying isotopes can be identified. Also, low energy particles generated by α-particles in the surrounding of the MMCs can hit the pixels clides in the aluminum shielding, but with lower intensities. With the same concentrations as used for the absorbers and shielding, nuclides of the 238 U-chain cause a count rate of (6 ± 1) · 10 −9 day −1 pixel −1 in the ROI for bulkdistributed nuclides and (6 ± 2) · 10 −9 day −1 pixel −1 for surface-distributed 210 Pb. For bulk-distributed 232 Th, a count rate of about (2 ± 1) · 10 −9 day −1 pixel −1 in the ROI is expected. Bulk-distributed 40 K results in a count rate of less than 8 · 10 −9 counts day −1 pixel −1 in the ROI at 90 % C.L. and in about (1.7 ± 0.3) · 10 −8 day −1 pixel −1 , if surfacedistributed.   Fig. 11 and are similar to the ones caused by 238 U and its daughters in the aluminum shielding. For bulk-distributed 232 Th with a level of 128 Bq kg −1 , a count rate of about (2 ± 1) · 10 −6 day −1 pixel −1 is expected in the ROI. Bulk-distributed 40 K with a level of 6.2 Bq kg −1 results in about (3 ± 1) · 10 −7 day −1 pixel −1 in the ROI and in about (5 ± 2) · 10 −7 day −1 pixel −1 , if surface-distributed with a level of 0.53 mBq cm −2 .

Upper limits
Upper limits of tolerable concentrations of naturally occurring radionuclides are obtained by fitting an exponential distribution to the spectra and scaled, so that the count rate in the last 10 eV below the Q-value of the 163 Ho EC is equal to the expected rate of unresolved pile-up of about 10 −6 day −1 pixel −1 . The resulting concentration limits for bulk-and surface-distributed radionuclides are listed in Tables 6 and 7.  Compared to the results of the screening measurement of Chapter 5, the upper limits of tolerable concentrations are much larger than the upper limits determined in the screening campaign, except of the limits for the circuit board. By assuming that 40 K is only surface-distributed, a total count rate of (6 ± 1) · 10 −6 day −1 pixel −1 is expected in the ROI, mainly due to radionuclides in the circuit board (about 87 %), which is in the same order than the unresolved pile-up. The expected background spectrum is shown in Fig. 12. In future stages of the ECHo experiment, the circuit board will be made of polyimide-based materials, resulting in lower concentrations of radionuclides. However, the background level of the order of 10 −6 day −1 pixel −1 does not danger the ECHo-1k phase, since this background results in a count rate of about 10 −5 day −1 pixel −1 in the energy range of Q EC ±100 eV and thus, only one background event is expected with an exposure of five month and 64 pixels.

Background measurement
Due do the double-meander pick-up coil geometry of the MMCs, two pixels are readout by the same SQUID. In the following, these pairs of pixels are called channels. The ECHo-1k high statistics spectrum has been acquired in two independent runs between Dec 2019 and May 2020. In both runs, several channels of two ECHo-1k chips have been used. A description of the detectors used for this ECHo-1k measurement can be found in [9]. Here, we describe the analysis of events acquired in five asymmetric channels, meaning channels in which only one pixel was implanted with 163 Ho. The pixels without 163 Ho can therefore be used for background measurements. In total, about 241 pixel-days of data of pure background have been analyzed.
The thermodynamical properties of the two pixels of one channel are nearly identical. In order to separate events caused by particles, which deposit their complete energies in the pixels from events caused by particles, which are not fully stopped in the pixels, signals due to the decay of 163 Ho of the implanted pixels are analyzed first. The signal pulse shape can be described by several parameters and are calibrated by using 163 Ho events, which correspond to events due to particles fully stopped in the pixels. This calibration, as well as the energy calibration, are adapted for the analysis of events in the background pixels.
The pulse shape analysis is based on the analysis developed to recognize muon induced events [12,38] and modified to select 163 Ho-like events. Five parameters are obtained from each pulse, its integral, rise time and amplitude on the one hand, and on the other hand, the pulse is compared to a template and is correlated with the same template. Events, caused by particles depositing their complete energy in the pixels, are identified by comparing these parameters to each other. Events with energies above 3 keV are chosen from the data set containing data of the five 163 Ho-loaded pixels. Above 3 keV, only unresolved pile-up events and background events are expected, while above 6 keV only background events are expected. However, due to ADC settings the pulse height is limited to about 5 keV. We measured four events with energies between 3 keV and 5 keV in 241 pixel-days after pulse shape analysis. In the same energy region, we expect about 0.7 counts due to unresolved pile-up events. However, by considering the pile-up spectrum, the probability that one count of these events is caused by pile-up is about 22 % and less then 0.2 % that more then one of these counts are caused by pile-up. The expected pile-up spectrum normalized to the 3 keV to 5 keV energy region and the measured events are shown in Fig. 13. Thus, these events are more likely caused by a different background source. Assuming a flat background level, this results in a background level of (8 ± 4) · 10 −5 pixel −1 day −1 in the last 10 eV before Q EC , which is higher than the estimated background due to radionuclides of 6 · 10 −6 pixel −1 day −1 .
The energy spectrum recorded by the background pixels, which are not loaded with 163 Ho, is shown in Fig. 14. After the pulse shape analysis, no events above 3 keV are measured. This looks like a contradiction to the observation from the 163 Ho-loaded pixels. However, the 95 % confidence intervals for the mean of the Poisson distribution are [0, 3.69) for no observations and [1.09, 10.24) for four counts. Accordingly, there is an overlap of the sets. 166m Ho can be excluded as background source, since a fraction of 166m Ho/ 163 Ho > 10 −5 would be needed to explain these events [8] and is more than four orders of magnitudes higher than achieved. A fraction of 10 −4 can be achieved due to chemical purification [15] and a further reduction of five orders of magnitude by mass sepa- Fig. 14 Energy distribution of non-coincidental events measured by the background pixels. The blue spectrum shows all measured events. The orange spectrum shows the actual background spectrum ration [16], resulting in a fraction of 166m Ho/ 163 Ho < 10 −9 . Measurements over a larger energy range are planned within the coming ECHo runs in order to be sensitive to structures at higher energies, which could be used to improve the understanding of the background sources. A 163 Ho-like background can be observed in the spectrum recorded by the background pixels. This spectrum can be observed for each pixel and can neither be described by any simulations of natural radionuclides described in Sect. 6 so far or by muon caused events [12]. The measured spectrum could correspond to an activity of about 30 µBq of 163 Ho per pixel, which corresponds to about 6 · 10 6 atoms per pixel. The observed lines, which could represent the M lines around 2 keV and N lines round 400 eV of the 163 Ho EC, are slightly shifted to lower energies compared to the 163 Ho EC spectrum. Also, the fraction of number of events of the N line to the number of events of the M line of 5 ± 1 is larger than expected from theory with 2.3. The energy shift of the lines and the higher N/M-ratio could be explained by 163 Ho located at the surface of the background pixels, because multiple particles could be emitted by the decay. Further, if this is the case, a surface contamination of about 93 mBq cm −2 can be assumed for the whole detector chip. The endpoint region should not be affected by surface-distributed 163 Ho, because the 163 Ho activity in the pixels is five orders of magnitude higher than the potential surface contamination. If the source of this spectrum has different origins, a background level of about 8·10 −5 pixel −1 day −1 can be assumed, since one event was measured between 2.5 keV and 3 keV in 241 pixel-days. In addition, the 1.49 keV line of aluminum X-rays could be observable.

Summary
Different natural radionuclides were simulated in different parts of the ECHo set-up. The background in the ROI of the ECHo experiment is aimed to be dominated the unresolved pile-up of about 10 −6 day −1 pixel −1 in the ROI for the ECHo-1k phase with a 163 Ho -activity per pixel of 1 Bq and a time resolution of 500 ns. The simulations show that concentrations of radionuclides of the order of 10 Bq kg −1 or a few hundreds of µBq cm −2 are needed to result in signal count rates as high as the signal due to the unresolved pile-up. Screening measurements were performed and concentration levels are given for connectors (which are not used in the simulations) and circuit boards. For copper, only upper limits are given, pointing out that the material is quite pure. The same can be expected for aluminum. In total, a count rate of about (6 ± 1) · 10 −6 day −1 pixel −1 is expected in the ROI due to naturally occurring radionuclides in materials in the next surrounding of the detector arrays. This value is higher than the rate of unresolved pile-up, but low enough for the ECHo-1k phase with an exposure of about less than one year. For the future stage of the ECHo experiment, ECHo-100k, different materials (Kapton) are foreseen as material for circuit boards. This should reduce the background due to natural radionuclides of about 90 %. Further, a 163 Ho activity of a few Bq per pixel is foreseen, which increases the signal count rate as well as the pile-up.
Background measurements including 163 Ho-loaded and -unloaded pixels were analyzed using pulse shape discrimination methods. Only events above the Q-value of the 163 Ho EC are considered for data of 163 Ho-loaded pixels, which can either be caused by unresolved pile-up events or by other sources. We measured a background level of about 8 · 10 −5 day −1 pixel −1 in the ROI. This count rate is higher compared to the pile-up limit and the expected background due to the simulated radionuclides and muons. On the other hand, the background pixels did not measure any events in the same energy region of above 3 keV. The spectrum measured by these background pixels could be caused by surfacedistributed 163 Ho with about 30 µBq per pixel, from which a count rate of less than 10 −8 day −1 pixel −1 is expected in the ROI.