Characterization of Silicon Drift Detectors with Electrons for the TRISTAN Project
S. Mertens, T. Brunst, M. Korzeczek, M. Lebert, D. Siegmann, A. Alborini, K. Altenmüller, M. Biassoni, L. Bombelli, M. Carminati, M. Descher, D. Fink, C. Fiorini, C. Forstner, M. Gugiatti, T. Houdy, A. Huber, P. King, O. Lebeda, P. Lechner, V. S. Pantuev, D. S. Parno, M. Pavan, S. Pozzi, D. C. Radford, M. Slezák, M. Steidl, P. Trigilio, K. Urban, D. Vénos, J. Wolf, S. Wüstling, Y.-R. Yen
CCharacterization of Silicon Drift Detectors with Electronsfor the TRISTAN Project
T. Brunst 𝑎 , 𝑏 M. Korzeczek 𝑐 M. Lebert 𝑎 , 𝑏 D. Siegmann 𝑎 , 𝑏 S. Mertens 𝑎 , 𝑏 , A. Alborini 𝑑 K. Altenmüller 𝑎 M. Biassoni 𝑒 L. Bombelli 𝑑 M. Carminati 𝑓 , 𝑔 M. Descher 𝑐 D. Fink 𝑏 C. Fiorini 𝑓 , 𝑔 C. Forstner 𝑎 , 𝑏 M. Gugiatti 𝑓 , 𝑔 T. Houdy 𝑎 , 𝑏 A. Huber 𝑐 P. King 𝑓 , 𝑔 O. Lebeda ℎ P. Lechner 𝑖 V. S. Pantuev 𝑗 D. S. Parno 𝑘 M. Pavan 𝑙 , 𝑒 S. Pozzi 𝑙 , 𝑒 D. C. Radford 𝑚 M. Slezák 𝑏 M. Steidl 𝑐 P. Trigilio 𝑑 K. Urban 𝑎 , 𝑏 D. Vénos ℎ J. Wolf 𝑐 S. Wüstling 𝑐 and Y.-R. Yen 𝑘 𝑎 Technical University of Munich, Arcisstraße 21, 80333 München, Germany 𝑏 Max Planck Institute for Physics, Föhringer Ring 6, 80805 München, Germany 𝑐 Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen,Germany 𝑑 XGLab srl, Bruker Nano Analytics, Via Conte Rosso 23, 20134 Milano, Italy 𝑒 INFN - Sezione di Milano - Bicocca, 20126 Milano, Italy 𝑓 Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy 𝑔 INFN - Sezione di Milano, 20133, Milano, Italy ℎ Nuclear Physics Institute of the CAS, v. v. i., 250 68 Ř ež, Czech Republic 𝑖 Halbleiterlabor of the Max Planck Society, Otto-Hahn-Ring 6, 81739 München, Germany 𝑗 Institute for Nuclear Research of Russian Academy of Sciences, Prospekt 60-letiya Oktyabrya 7a, Moscow117312, Russian Federation 𝑘 Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 𝑙 Università di Milano - Bicocca, Dipartimento di Fisica, 20126 Milano, Italy 𝑚 Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37831, USA
E-mail: [email protected] A ������� : Sterile neutrinos are a minimal extension of the Standard Model of Particle Physics.A promising model-independent way to search for sterile neutrinos is via high-precision betaspectroscopy. The Karlsruhe Tritium Neutrino (KATRIN) experiment, equipped with a novelmulti-pixel silicon drift detector focal plane array and read-out system, named the TRISTANdetector, has the potential to supersede the sensitivity of previous laboratory-based searches. In thiswork we present the characterization of the fi rst silicon drift detector prototypes with electrons andwe investigate the impact of uncertainties of the detector’s response to electrons on the fi nal sterileneutrino sensitivity.K ������� : Solid state detectors, Particle detectors, Neutrinos, Sterile Neutrinos, KATRIN Corresponding author ontents fi nal sensitivity 10 Sterile neutrinos are a minimal extension of the Standard Model of Particle Physics (SM) [1].A common candidate for sterile neutrinos are right-handed partners to the standard left-handedneutrinos. The existence of such right-handed partners would provide a natural way to introduceneutrino mass to the SM. A consequence of this SM extension is the existence of new neutrinomass eigenstates. These new neutrino particles can have an arbitrary mass scale 𝑚 s and a smalladmixture of the active neutrino component, governed by the so-called mixing amplitude sin ( Θ ) .This mixing allows them to interact with matter via the weak interaction. Throughout this work,we call these new neutrino mass eigenstates “sterile” neutrinos 𝜈 s .Light (eV-scale) sterile neutrinos are being widely discussed in the context of short-baselineneutrino oscillation anomalies, such as the reactor antineutrino anomaly [2, 3, 4]. Very heavy sterileneutrinos of at least the GeV-scale are typically introduced to generate both neutrino masses and thematter/anti-matter asymmetry of the universe [5, 6]. Finally, keV-scale sterile neutrinos are viablecandidates for dark matter [7, 8].Depending on their production mechanism sterile neutrinos can act as cold, cool, or warm darkmatter, which would impact structure formation of the universe in di ff erent ways. In particular thewarm type of sterile neutrino dark matter could potentially mitigate tensions between observations– 1 –nd cold-dark-matter predictions on small scales [9]. Sterile neutrinos constitute so-called decayingdark matter. An interesting decay mode, from the observational point of view, is the decay to anactive neutrino and a mono-energetic x-ray photon. X-ray telescopes, such as the recently launchedeROSITA [10], can thus search for the existence of sterile neutrino dark matter. Current x-ray datalimit the mixing amplitude of sterile neutrinos to about sin ( Θ ) < − – 10 − in a mass range of2 keV to 10 keV, respectively. Below 2 keV mixing amplitudes above 10 − are disfavoured as theywould lead to an overproduction of sterile neutrino dark matter. However, these limits are rathermodel-dependent [11]. Laboratory searches reach exclusion limits of sin ( Θ ) < − – 10 − in amass range of 1 keV to 90 keV [12, 13, 14].A promising approach to search for sterile neutrinos in a laboratory-based experiment, whichwould be independent of cosmological or astrophysical models, is based on nuclear β - decays [15].In β − -decays, an electron anti-neutrino ¯ 𝜈 e is emitted alongside the β -electron. Thus, the electron’senergy spectrum is given as a superposition of spectra corresponding to the neutrino mass eigenstates 𝑚 𝑖 . A mass eigenstate 𝑚 s in the keV-range would correspond to a spectral branch with a muchreduced endpoint of 𝐸 = 𝐸 − 𝑚 s , where 𝐸 is the spectrum endpoint. Accordingly the sterileneutrinos would generate a kink-like signature at this energy and a broad distortion of the spectrumat lower energies. The relative probability of this decay branch is governed by the mixing amplitudesin ( Θ ) .The large-scale Karlsruhe Tritium Neutrino (KATRIN) experiment is currently the world-leading facility for precision spectroscopy of tritium. Its main objective is the direct measurementof the e ff ective electron anti-neutrino mass. In 2019, the collaboration set an improved upper limitof 𝑚 ( ¯ 𝜈 e ) < . fi dence level (C.L.) of 90 % [16]. The activity of its tritium sourceis ultra-high (10 decays per second) and stable (0 . cps, 2) to provide an energy resolution of about 300 eV full width at half maximum(FWHM) at 20 keV for electrons, and 3) to control the energy linearity at the ppm-level.In the framework of the Tritium Investigations on Sterile-to-Active Neutrino Mixing (TRIS-TAN) project, fi rst prototype detectors based on the Silicon Drift Detector (SDD) technology havebeen developed and tested [18]. SDDs are ideally suited for high-rate and high-energy-resolutionapplications. Thanks to their small read-out anode, even large pixel sizes of up to several millimeterskeep a small capacitance at the level of few hundreds of fF [19], which leads to a low serial noise.This in turn allows for short energy fi lter shaping times and is advantageous for measurements athigh rates. Typically, SDDs are used for x-ray measurements. In the case of TRISTAN these detec-tors will be applied for high-precision electron spectroscopy. In contrast to the x-ray application,the e ff ects of energy loss in an insensitive region at the entrance window and backscattering fromthe detector’s surface play a major role for the detection of electrons.In this work we present a detailed characterization of SDDs with mono-energetic electrons. Ascanning electron microscope (SEM) and a Rb/
Kr radioactive source were used as calibrationsources (see sec. 2). Based on the obtained spectra an empirical model describing the detector’s All masses are stated in natural units. – 2 –esponse to electrons was developed (see sec. 3). A special focus of this work is put on theestimation of the entrance-window thickness (see sec. 4). Finally, the impact of uncertainties in theelectron-response model on the fi nal sensitivity to sterile neutrinos is presented in sec. 5. A novelty of the TRISTAN detector system is the application of SDDs to high-precision electronspectroscopy. The penetration depth in matter is shorter for massive, charged particles as comparedto photons. This fact has several consequences: First, electrons deposit a signi fi cant fraction of theirenergy close to the entrance-window surface, where the electric fi elds are too weak to transport thecharge carriers to the read-out anode. Thus the energy of the electron is not fully detected but partlylost. Second, low-energy electrons have a probability of around 20 % or larger to scatter back fromthe silicon detector surface, again leading to a partial energy measurement [20]. Finally, due to theinteractions close to the surface, characteristic 1 .
74 keV Si x-rays created by the electron can escapethe detector volume, again reducing the detected energy of the electron. All these e ff ects lead to acharacteristic shape of the energy spectrum for electrons.To characterize the response of SDDs to electrons, a 7-pixel TRISTAN prototype and twomono-energetic electron sources were used. In the following we describe the detector system andthe two calibration sources, and present the obtained spectra. Several 7-pixel SDD arrays have been manufactured at the Semiconductor Laboratory of the MaxPlanck Society (HLL) [19]. The chips are produced from monolithic silicon wafers with a thicknessof 450 µm. They feature a thin entrance window, terminated by a 10 nm thick SiO layer. Thehexagonal pixel shape enables an arrangement without dead area. For this work SDD chips with2 mm pixel diameter, shown in fi g. 1, were used. Each of these pixels features twelve drift rings anda small anode capacitance of approximately 100 fF.Each anode is wire bonded to a charge-sensitive preampli fi er (CSA) application-speci fi c in-tegrated circuit (ASIC), situated in close vicinity to the chip. The “CUBE” ASIC has beendeveloped by Politecnico di Milano and XGLab for applications in high-count rate and low-noisespectroscopy [21, 19] Its fi eld e ff ect transistor (FET) is based on complementary metal oxidesemiconductor (CMOS) technology and operates in pulsed-reset mode.The “DANTE” digital pulse processor (DPP) is used as a back-end electronics. DANTE isprovided by XGLab and features a waveform-digitizing analog-to-digital converter (ADC) with asampling frequency of 125 MHz and 16 bit resolution. Two trapezoidal fi lters are applied for eventtriggering and energy reconstruction, optimizing the system for high-count-rate applications [22].Characterization measurements of the TRISTAN SDD with Fe x-ray source demonstrated anenergy resolution of 139 eV (FWHM) at 5 . fi lter peaking times of about1 µs [18] and a detector temperature of − ◦ C. All measurements described in this work wereperformed at room temperature. – 3 – a) Read-out side. (b) Entrance-window side.
Figure 1 : Photographs of the TRISTAN detector chip. (a) The read-out side of the detector chip.Each pixel anode is surrounded by twelve drift rings and bonded to a CUBE preampli fi er ASIC. Thepixel size is 2 mm and the edge length of the silicon chip is 8 mm. (b) The entrance-window sideof the detector chip shows no structuring into individual pixels. Depletion voltage and guard-ringvoltage are supplied via wire bonds. Rb/
Kr source
The krypton calibration source consists of a mono-layer of Rb, evaporatedonto a highly oriented pyrolytic graphite (HOPG) carrier substrate [23]. Rb decays with a half-life of 86.2 days via electron capture to
Kr. In this decay, predominantly Kr-K α and Kr-K β x-rays are emitted. The occurrence of both photon and electron lines in one spectrum enables anin-situ calibration and characterization at the same time. The isomeric state Kr is the secondexcited state of krypton and has an energy of about 41 . γ -decays with 32 . . 𝐸 ce = 𝐸 γ + 𝐸 γ ( recoil ) − 𝐸 ce ( bind ) − 𝐸 ce ( recoil ) , (2.1)de fi ned by the energy of the gamma transition 𝐸 γ , the binding energy of an electronic shell ofthe krypton atom 𝐸 ce ( bind ) , and the recoil energies of the atom after the emission of the γ -ray 𝐸 γ ( recoil ) and the conversion electron 𝐸 ce ( recoil ) . The emission of a conversion electron fromthe K-shell ( 𝐸 ce ( bind ) = . fi c interest for this work are listed in tab. 1. All other lines aresituated in a low-energy continuum and thus unsuited for the investigation.A typical spectrum of Rb/
Kr measured with the TRISTAN SDD detector is shown in fi g. 2. While the photon peaks are symmetric, peaks from conversion electrons show a pronouncedlow-energy tail. Furthermore, the electron peak position ¯ 𝐸 𝑖 of a peak 𝑖 is shifted towards lowerenergies compared to the respective theoretical value ¯ 𝐸 th 𝑖 :¯ 𝐸 𝑖 = ¯ 𝐸 th 𝑖 − Δ ew 𝑖 − 𝛿 sc − 𝛿 Φ . (2.2)– 4 – able 1 : Listed are (a) photon and (b) electron lines of Rb/
Kr [25] used for the analysis inthis work. Some lines are not resolvable given the energy resolution of the detector and appear asa single peak in the spectrum. (a) Photons
Peak Line Energy (eV) γ -9.4 γ -9.4 9405 . ± . α K α
12 595 . ± . α
12 648 . ± . β K β
14 105 . ± . β
14 112 . ± . β
14 315 . ± . (b) Electrons Peak Line Energy (eV)K-32 K-32 17 824 . ± . -32 30 226 . ± . -32 30 419 . ± . -32 30 472 . ± . -32 31 858 . ± . -32 31 929 . ± . -32 31 936 . ± . -32 32 136 . ± . -32 32 137 . ± . Figure 2 : Spectrum of a Rb/
Kr source measured with a TRISTAN prototype detector. Thepeaks of speci fi c interest for this work are labeled.This shift is due to energy losses in the entrance window Δ ew 𝑖 of the detector, potential energy lossesin the source 𝛿 sc , and the potential di ff erence between source and entrance window 𝛿 Φ [26]. Scanning electron microscope
Scanning electron microscopes (SEM) are generally used tovisualize small structures, which cannot be resolved optically. In this work the SEM was used togenerate mono-energetic electrons as calibration source for the TRISTAN SDD detector.An image area is repeatedly scanned with an electron beam of about 10 nm diameter. The JEOL JSM-IT300 – 5 – igure 3 : Spectrum of a 14 keV mono-energetic electron beam from an electron microscopemeasured with a TRISTAN prototype detector.electrons are accelerated to 10 keV up to 30 keV and are focused by a fast-changing magnetic fi eldonto the sample inside a vacuum chamber. The beam intensity is determined by the temperatureof a heated tungsten spiral, from which the electrons are emitted. The TRISTAN detector waspositioned on the sample holder and electrically connected to the DAQ system via a feedthroughin a fl ange of the chamber. First investigations with a single channel detector have shown a goodapplicability of this method [27]. A typically recorded electron energy spectrum is displayed in fi g. 3. In order to describe the SDD response to electrons, an empirical analytical model was developed,where each physical e ff ect is modelled by a separate term. In the following the main features of thespectrum are explained and their corresponding analytical expression is given. The majority of electrons deposit almost their entire initial energy in the sensitivevolume of the detector, leading to a main peak in the energy spectrum. Its general shape is wellapproximated by a Gaussian function 𝐼 G ( 𝐸 ) = 𝐴 𝐺 · exp � − ( 𝐸 − 𝜇 ) 𝜎 � , (3.1)where 𝐴 𝐺 is the amplitude, 𝜇 is the mean and 𝜎 is the standard deviation. Low-energy tail
The entrance-window surface is covered with a 10 nm thick silicon oxide (SiO )layer. Charge deposited in this layer cannot be detected. Moreover, the electric fi elds in thesilicon volume close to this layer are too weak to e ffi ciently transport the charge carriers to the– 6 –ead-out contact. These undetected energy depositions lead to an asymmetry of the main peak atits low-energy shoulder, which is modelled with the following function: 𝐼 D ( 𝐸 ) = 𝐴 𝐷 · exp � 𝐸 − 𝜇𝛽 � � − erf � 𝐸 − 𝜇 √ 𝜎 + 𝜎 √ 𝛽 � � . (3.2)It is composed of a “washed-out” step function expressed by the error function and an exponentialtail towards lower energies. Amplitude and slope of the function are given by 𝐴 𝐷 and 𝛽 , respectively. Silicon escape peak
Incident radiation leads to the ionization of silicon atoms in the detector ma-terial, most often on the K-shell. In the subsequent K α de-excitation, an x-ray with Δ 𝐸 esc = .
74 keVis emitted. If this photon leaves the detector, the energy Δ 𝐸 esc remains undetected. Hence, thesilicon escape peak is modeled as a scaled projection of the main peak with amplitude 𝐴 esc , shiftedtowards lower energies by Δ 𝐸 esc : 𝐼 esc ( 𝐸 ) = 𝐴 esc · exp � − ( 𝐸 − [ 𝜇 − Δ 𝐸 esc ]) 𝜎 � . (3.3) Backscattering tail
A fraction of primary and secondary electrons scatter back from the detectorsurface or escape after incomplete energy deposition. The backscattering probability for electronswith energies of around 20 keV is about 20 % at perpendicular electron incidence and increaseswith the incident angle [20]. This e ff ect leads to a backscattering tail, dominating the spectralshape between silicon escape peak and detection threshold. The probability for an electron to bebackscattered is the largest at the detector surface and decreases with increasing penetration into thedetector material. Consequently, the backscattering tail rises towards lower energies. We describethis tail with a multiplication of two power functions given by 𝐼 B ( 𝐸 ) = 𝐴 𝐵 · � 𝐸𝜇 − 𝑎 � 𝑏 · � − 𝐸𝜇 � 𝑐 . (3.4)The fi rst term with exponent 𝑏 describes the low-energy region just above the threshold energy 𝑎 , whereas the second term with exponent 𝑐 describes the higher end of the backscattering tail.Parameter 𝐴 𝐵 is the overall amplitude of the function. Each mono-energetic electron peak measured with
Kr or at the electron microscope is fi t withthe sum of the terms described above. In the case of the K-32 and M-32 peaks, the terms 𝐼 𝐵 ( 𝐸 ) and 𝐼 esc ( 𝐸 ) are not considered, as the fi t is only performed in a region close to each conversion electronpeak because various peaks are overlapping. An example of the fi t to the K-32 peak is shown in fi g. 4a. The fi t to the obtained spectrum at the electron microscope measurement is displayed in fi g. 4b.A very good agreement of the empirical model to the data is found. The dependence ofthe model parameters on both energy and angle can be investigated by measuring the response atvarious energies and incident angles. For the analysis of the continuous tritium β -decay spectrum,it is conceivable to use this empirical description of the detector response to obtain a model of themeasured tritium spectrum. To this end, the mono-energetic spectra are combined into a response– 7 – a) Fit to a krypton K-32 peak. (b) Fit to an electron microscope spectrum. Figure 4 : Fits of the electron response model to measured spectra. (a) The krypton K-32 lineat around 17 . fi g. 2. All subfunctions of the model add up to a good fi t( χ / dof = /
90) to the measured data. (b) The energy of the SEM was set to 14 keV. Siliconescape peak and noise pile-up are approximated with two additional functions. The fi t yields χ / dof = / β -decay spectrum. A parameterization of theresponse is particularly advantageous as it allows one to easily include systematic uncertainties inthe data analysis. The feasibility of this approach has been demonstrated in [28]. In this section we focus on a detailed investigation of the entrance-window thickness. As describedabove, charge carriers created in a volume close the detector surface are only partially collected.Approximately the fi rst 10 nm of the detector are fully insensitive, due to an SiO layer. In the siliconbulk the charge-collection e ffi ciency increases steeply. In this work, we assume a sharp transitionbetween the dead and active detector areas for simplicity, which we refer to as a “dead-layer model”.In the following we describe the measurement strategy and we present the resulting estimationof the dead-layer thickness, which is obtained by comparing the measurement results to MonteCarlo (MC) simulations. To eliminate possible in fl uences of the bias voltage 𝛿 Φ and source e ff ects 𝛿 sc on the peak positionshift (see equ. 2.2), the tilted beam method is applied [29]. By tilting the detector relative to theelectron source by an angle 𝛼 , the e ff ective dead-layer thickness for incoming electrons increases.This concept is illustrated in fi g. 5. By comparing a measurement with and without tilt angle, thein fl uence of the entrance window Δ ew 𝑖 is isolated as a relative shift of the main energy peaks Δ 𝐸 = 𝐸 ( 𝛼 ) − 𝐸 ( ) . (4.1)– 8 – igure 5 : Scheme of the tilted beam method. The distance that electrons travel through the entrancewindow (grey region) before reaching the sensitive detector volume (green region) is e ff ectivelyincreased (orange arrow) by tilting the detector by an angle 𝛼 .measurements were performed with the scanning electron microscope and the Rb/
Kr sourcewith perpendicular electron incidence ( 𝛼 = 𝛼 = fi t with the empirical response model described in sec. 3.1. The resulting peak positiondi ff erences Δ 𝐸 are calculated and illustrated in fi g. 6a. For a 14 keV electron Δ 𝐸 =
50 eV, and, asexpected, the energy loss decreases to about Δ 𝐸 =
30 eV at incident energies of about 30 keV.
In this study we describe the region of incomplete charge collection at the entrance window witha single parameter, the dead-layer thickness 𝑑 DL . To relate the observed shift in energy Δ 𝐸 to adead-layer thickness, MC simulations of electrons are performed with two incident angles of 𝛼 = 𝛼 =
60° and for several incident energies 𝐸 𝑖 . For each case the simulation is performed with14 di ff erent dead-layer thicknesses in a range of 40 – 65 nm. The simulations are performed withthe KESS software, which was developed by the KATRIN collaboration speci fi cally to describescattering of low-energy electrons in silicon [30].Fig. 6b shows a good agreement of the measured and a MC simulated spectrum. A minimizationof the squared data-to-simulation residuals for each measured energy yields the best dead-layerthickness and uncertainty of 𝑑 DL = ( ± ) nm . (4.2)Using this dead-layer thickness, an overlay of the simulated and measured energy shifts is illustratedin fi g. 6a. The fi nal aim of the TRISTAN project is to reach a sensitivity to a spectral distortion at the ppm-level.This requires two key ingredients: 1) an excellent energy resolution and 2) a precise understandingof the measured spectral shape. In the following, we discuss the impact of the entrance-windowthickness on the energy resolution, and secondly the impact of an imprecise knowledge of thedetector response to electrons on the sterile-neutrino sensitivity.– 9 – a) Energy dependent peak position shift. (b) Simulated and measured spectrum. Figure 6 : Comparison of the measurements with MC simulations at perpendicular electron inci-dence using KESS. (a) Energy shifts extracted from measurements with an electron microscopeand a Rb/
Kr source. The values are compared to a simulation based on a dead-layer modelwith 𝑑 DL =
48 nm. (b) Spectrum of mono-energetic electrons from a measurement with an electronmicroscope and the corresponding simulation.
To reach the targeted sterile-neutrino sensitivity an energy resolution of approximately 300 eV at20 keV is required [31]. An excellent energy resolution is needed to avoid washing out the charac-teristic kink-like signature of a sterile neutrino. The ability to detect or rule out this local signature,makes the search for sterile neutrinos robust against large classes of systematic uncertainties.Energy loss in the dead layer is a statistical process and thus di ff erent for each incident electron.This variation leads to a smearing of the spectrum and can be interpreted as a worsening of theenergy resolution. Fig. 7 illustrates the resulting additional contribution to the energy resolutionfor di ff erent dead-layer thicknesses. This contribution is especially large at low energies, where theenergy loss in the dead layer is the largest. With the measured e ff ective dead-layer thickness (seeequ. 4.2) the requirement on energy resolution is met. fi nal sensitivity To reach ppm-level sensitivity to sterile neutrinos, systematic e ff ects which in fl uence the spectralshape need to be described with high precision. As presented in this work, the shape of the responseof SDDs to electrons depends on the entrance-window thickness and the backscattering probability.To estimate the impact of an uncertainty of these properties, we performed a sensitivity study basedon a semi-analytical detector model [32].For the study, we assume a di ff erential measurement with total statistics of 10 electrons(corresponding to three years’ data taking with KATRIN at a 100-fold reduced column density).The detector response function is based on multiple interpolated MC simulations with KESS. Theindividual MC simulations were performed in a fi ne grid of various incident energies and incidentangles. For this study, the detector response model takes into account the e ff ect of the so-called– 10 – igure 7 : Simulation of the additional broadening of the energy resolution in FWHM, for di ff erentdead-layer thicknesses. An equivalent noise charge of 9 electrons is considered [18]. To reach thetargeted sensitivity a FWHM of less than 300 eV is required.post-acceleration electrode. This electrode, boosts the kinetic energy of all electrons by up to 20 keVon their way to the detector [33]. We investigate the impact of the uncertainty of a parameter of the response function (e.g. theentrance-window thickness), by generating 10 MC samples of the measured spectrum, each timevarying the parameter of interest. From these MC samples the variance of all data points and theircovariance is deduced, i.e. the covariance matrix 𝐶 is constructed.The sensitivity of the experiment is derived by minimizing the squared data-to-model residualsfor 40 ×
40 grid points in the ( 𝑚 𝑠 , sin ( Θ ) )-plane: 𝜒 ( 𝑚 𝑠 , sin Θ ) = � 𝑟 T 𝐶 − � 𝑟 , (5.1) � 𝑟 ≡ � 𝑟 ( 𝑚 𝑠 , sin Θ ) = � 𝑅 model ( 𝑚 𝑠 , sin ( Θ )) − � 𝑅 truth ( , ) , (5.2)where � 𝑅 model depicts the model expectation in case of a sterile neutrino with mass 𝑚 𝑠 and mixingamplitude sin ( Θ ) , and � 𝑅 truth depicts the MC truth, for which no sterile neutrino is assumed.At each grid point a minimization with respect to the spectrum normalization 𝑁 , a constantbackground rate 𝐵 and the spectrum endpoint 𝐸 is performed. The sensitivity at 90 % C.L. isgiven by the contour of Δ 𝜒 = 𝜒 − 𝜒 = .
6, where 𝜒 is the 𝜒 value found for the case( 𝑚 𝑠 , sin ( Θ ) ) = (0, 0).In the fi rst study we investigate the impact of an uncertainty on the entrance-window thicknessof 10 %. As shown in fi g. 8a, a 10 % uncertainty on a 50 nm thick dead layer reduces the sensitivityby up to a factor of ten in certain mass ranges. The e ff ect is signi fi cantly reduced for a smallerdead-layer thickness of 10 nm. Moreover, the e ff ect can be almost fully eliminated by applying apost-acceleration energy of 20 keV, as the increased energy of the β -electrons reduces the relativefraction of energy loss in the dead layer. In the current KATRIN design the post-acceleration energy is limited to 12 keV for technical reasons. – 11 – a) E ff ect of uncertainty on the dead layer. (b) E ff ect of uncertainty on the incident angle. Figure 8 : Sensitivity study of the impact of detector uncertainty on the sterile-neutrino sensitivity.The solid blue line represents the sensitivity after three years’ data taking with KATRIN at a100-fold reduced column density. No uncertainty on the dead-layer thickness or the incident angleis considered. (a) In certain mass ranges, a 10 % uncertainty on a 50 nm thick dead layer reducesthe sensitivity by a factor of ten (orange dash-dotted). Applying a post-acceleration (PA) energy of20 keV almost fully recovers the sensitivity (orange dotted). The e ff ect is signi fi cantly reduced for asmaller dead-layer thickness of 10 nm (green dashed). (b) A 0 . fi cantly reduces the sensitivityof the experiment (orange dash-dotted). A post-acceleration can also mitigate this e ff ect (orangedotted).In the second study we test the impact of an uncertainty of the backscattering probability. Thisuncertainty can for instance arise from an uncertainty of the incidence angle of the electrons, whichitself could arise from an uncertainty of the exact orientation of the detector. For this study, weemulate this e ff ect by assuming electrons with an incident angle of ( ± ) °. This translates to anuncertainty in the backscattering probability of 0 . .
38 % ( fi g. 5).The result, displayed in fi g. 8b shows, that an uncertainty on the backscattering probabilityof 0.4% signi fi cantly reduces the sensitivity of the experiment. Again, the post-acceleration ofelectrons can fully mitigate the e ff ect as high-energy electrons reach further into the detector andare less likely to backscatter. The KATRIN experiment, equipped with a novel multi-pixel silicon drift detector (SDD) focal planearray, has the potential to perform a search for keV-scale sterile neutrinos with an unprecedentedsensitivity, compared to previous laboratory experiments. In the framework of the TRISTANproject, fi rst SDD prototypes have been developed and an excellent performance with x-rays wasdemonstrated. – 12 –n this work, mono-energetic electrons in the keV range from a scanning electron microscopeand a radioactive Kr source were used to characterize the prototype detectors. An excellentagreement between the observed electron spectra and an empirical analytical and a Monte-Carlo-based model was found.The entrance-window thickness, a key parameter of the detector response to electrons, wasdetermined by tilting the detector and determining the relative shift of the main electron energy peak.Assuming a step-like dead-layer model, a thickness of ( ± ) nm was derived by comparing themeasured energy shifts to Monte Carlo simulations. With this result the requirements with respectto the energy resolution are met.Finally, the impact of uncertainties of the SDD response to electrons on the fi nal sterile-neutrinosensitivity was studied based on Monte Carlo simulations. Assuming an entrance-window thicknessof ( ± ) nm and a backscattering uncertainty of 0.4% reduces the sensitivity by about a factor of10 for sterile neutrino masses above 10 keV. Reducing the entrance-window thickness and absoluteuncertainty to ( ± ) nm would mitigate this degradation. As a major result, we fi nd that therequirements on the uncertainty of dead-layer thickness and backscattering probability are reducedto an almost negligible level, when boosting the energy of the electrons with a post-accelerationelectrode.The next stage of the TRISTAN project will be the integration of a SDD module with166 channels in the KATRIN monitor spectrometer in 2021 [34]. The fi nal system, consistingof 21 modules, will prospectively be integrated in the KATRIN beamline after successful comple-tion of the neutrino mass measurement. Acknowledgments
We acknowledge the support of Helmholtz Association (HGF), Ministry for Education and ResearchBMBF (05A17VK2 and 05A17WO3), the doctoral school KSETA at KIT, the Max Planck ResearchGroup (MaxPlanck@TUM) program, and the Deutsche Forschungsgemeinschaft DFG (GSC-1085-KSETA and SFB-1258). This project has received funding from the European Research Council(ERC) under the European Union Horizon 2020 research and innovation program (grant agreementNo. 852845). This work is further supported by the U.S. Department of Energy, O ffi ce of Science,O ffi ce of Nuclear Physics under Award Number DE-AC05-00OR22725 and by the Ministry ofEducation, Youth and Sport (CANAM-LM2015056, LTT19005). References [1] K. N. Abazajian, M. A. Acero, S. K. Agarwalla, A. A. Aguilar-Arevalo, C. H. Albright, S. Antuschet al.,
Light Sterile Neutrinos: A White Paper , arXiv e-prints (2012) , [ ].[2] G. Mention, M. Fechner, T. Lasserre, T. Mueller, D. Lhuillier, M. Cribier et al., The ReactorAntineutrino Anomaly , Phys. Rev. D (2011) 073006, [ ].[3] C. Giunti and T. Lasserre, eV-scale Sterile Neutrinos , Ann. Rev. Nucl. Part. Sci. (2019) 163–90,[ ]. – 13 –
4] S. Böser, C. Buck, C. Giunti, J. Lesgourgues, L. Ludhova, S. Mertens et al.,
Status of Light SterileNeutrino Searches , Prog. Part. Nucl. Phys. (2020) 103736, [ ].[5] L. Canetti, M. Drewes and M. Shaposhnikov,
Sterile Neutrinos as the Origin of Dark and BaryonicMatter , Phys. Rev. Lett. (2013) 061801, [ ].[6] R. N. Mohapatra and G. Senjanovic,
Neutrino Mass and Spontaneous Parity Nonconservation , Phys.Rev. Lett. (1980) 912.[7] R. Adhikari, M. Agostini, N. A. Ky, T. Araki, M. Archidiacono, M. Bahr et al., A White Paper on keVsterile neutrino Dark Matter , J. Cosmol. Astropart. P. (2017) 025.[8] A. Boyarsky, M. Drewes, T. Lasserre, S. Mertens and O. Ruchayskiy,
Sterile Neutrino Dark Matter , Prog. Part. Nucl. Phys. (2019) 1–45, [ ].[9] M. R. Lovell, V. Eke, C. S. Frenk, L. Gao, A. Jenkins, T. Theuns et al.,
The haloes of bright satellitegalaxies in a warm dark matter universe , Mon. Not. R. Astron. Soc. (2012) 2318–24.[10] A. Merloni, P. Predehl, W. Becker, H. Böhringer, T. Boller, H. Brunner et al., erosita science book:Mapping the structure of the energetic universe , arXiv e-prints (2012) , [ ].[11] A. Boyarsky, O. Ruchayskiy, D. Iakubovskyi and J. Franse, Unidenti fi ed line in x-ray spectra of theAndromeda galaxy and Perseus galaxy cluster , Phys. Rev. Lett. (2014) 251301.[12] J. N. Abdurashitov, A. I. Belesev, V. G. Chernov, E. V. Geraskin, A. A. Golubev, P. V. Grigorievaet al.,
First measurements in search for keV sterile neutrino in tritium beta-decay in the Troitsknu-mass experiment , .[13] E. Holzschuh, W. Kündig, L. Palermo, H. Stüssi and P. Wenk,
Search for heavy neutrinos in the 𝛽 -spectrum of Ni , Phys. Lett. B (1999) 247–55.[14] E. Holzschuh, L. Palermo, H. Stüssi and P. Wenk,
The 𝛽 -spectrum of S and search for the admixtureof heavy neutrinos , Phys. Lett. B (2000) 1–9.[15] R. Shrock,
New tests for and bounds on neutrino masses and lepton mixing , Phys. Lett. B (1980)159–64.[16] KATRIN collaboration, M. Aker, K. Altenmüller, M. Arenz, M. Babutzka, J. Barrett, S. Bauer et al., Improved upper limit on the neutrino mass from a direct kinematic method by KATRIN , Phys. Rev.Lett. (2019) 221802.[17] S. Mertens, T. Lasserre, S. Groh, G. Drexlin, F. Glück, A. Huber et al.,
Sensitivity of next-generationtritium beta-decay experiments for keV-scale sterile neutrinos , J. Cosmol. Astropart. P. (2015)020.[18] S. Mertens, A. Alborini, K. Altenmüller, T. Bode, L. Bombelli, T. Brunst et al.,
A novel detector systemfor KATRIN to search for keV-scale sterile neutrinos , J. Phys. G Nucl. Partic. (2019) 065203.[19] P. Lechner, C. Fiorini, R. Hartmann, J. Kemmer, N. Krause, P. Leutenegger et al., Silicon driftdetectors for high count rate x-ray spectroscopy at room temperature , Nucl. Instrum. Meth. A (2001) 281–7. – 14 –
20] E. H. Darlington and V. E. Cosslett,
Backscattering of 0.5–10 keV electrons from solid targets , J. Phys.D: Appl. Phys. (1972) 1969–81.[21] L. Bombelli, C. Fiorini, T. Frizzi, R. Alberti and A. Longoni, “CUBE”, A low-noise CMOSpreampli fi er as alternative to JFET front-end for high-count rate spectroscopy , IEEE Nucl. Sci. Conf.R. (2011) 1972–5.[22] V. T. Jordanov and G. F. Knoll,
Digital synthesis of pulse shapes in real time for high resolutionradiation spectroscopy , Nucl. Instrum. Meth. A (1994) 337–45.[23] D. Vénos, M. Zbo ř il, J. Kašpar, O. Dragoun, J. Bonn, A. Kovalík et al., Erratum to: “Development ofa super-stable datum point for monitoring the energy scale of electron spectrometers in the energyrange up to 20 keV” , Meas. Tech. (2010) 573–81.[24] E. McCutchan, Nuclear Data Sheets for A = 83 , Nucl. Data Sheets (2015) 201–394.[25] D. Vénos, J. Sentkerestiová, O. Dragoun, M. Slezák, M. Ryšavý and A. Špalek,
Properties of
Krconversion electrons and their use in the KATRIN experiment , J. Instrum. (2018) T02012.[26] M. Lebert, T. Brunst, T. Houdy, S. Mertens and D. Siegmann, Characterization of the DetectorResponse to Electrons of Silicon Drift Detectors for the TRISTAN Project , arXiv e-prints (2020) ,[ ].[27] M. Gugiatti, M. Biassoni, M. Carminati, O. Cremonesi, C. Fiorini, P. King et al., Characterization of asilicon drift detector for high-resolution electron spectroscopy , arXiv e-prints (2020) , [ ].[28] T. Brunst, T. Houdy, S. Mertens, A. Nozik, V. Pantuev, D. Abdurashitov et al., Measurements with aTRISTAN prototype detector system at the “Troitsk nu-mass” experiment in integral and di ff erentialmode , J. Instrum. (2019) P11013.[29] G. A. Johansen, Development and analysis of silicon based detectors for low energy nuclearradiation . PhD thesis, University of Bergen, 1990.https://inis.iaea.org/collection/NCLCollectionStore/_Public/23/002/23002484.pdf.[30] P. Renschler,
KESS - A new Monte Carlo simulation code for low-energy electron interactions insilicon detectors . PhD thesis, Karlsruhe Institute of Technology, 2011. 10.5445/IR/1000024959.[31] S. Mertens, K. Dolde, M. Korzeczek, F. Glueck, S. Groh, R. D. Martin et al.,
Wavelet approach tosearch for sterile neutrinos in tritium 𝛽 -decay spectra , Phys. Rev. D (2015) 042005.[32] M. Korzeczek, Sterile neutrino search with KATRIN – modeling and design-criteria of a noveldetector system . PhD thesis, Karlsruhe Institute of Technology, 2020.[33] J. F. Amsbaugh et al.,
Focal-plane detector system for the KATRIN experiment , Nucl. Instr. Meth. A (2015) 40–60.[34] M. Erhard, S. Bauer, A. Beglarian, T. Bergmann, J. Bonn, G. Drexlin et al.,
High-voltage monitoringwith a solenoid retarding spectrometer at the KATRIN experiment , J. Instrum. (2014) P06022.(2014) P06022.