Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Gallina, Giacomo
Doctor of Philosophy - PhD
University of British Columbia
Silicon PhotoMultiplier (SiPM) technology represents an unprecedented attempt to create an ideal solid-state photon detector, combining the low-light detection capabilities of the previous device generations with all the benefits of a solid-state sensor. For this reason, large-scale low-background cryogenic experiments, such as the next-generation Enriched Xenon Observatory experiment (nEXO), are migrating to a SiPM-based light detection system. nEXO aims to probe the boundaries of the standard model of particle physics by searching for neutrino-less double beta decay of ¹³⁶Xe. The nEXO experiment follows the same detection concept as the EXO-200 experiment, but uses 5 tonnes of liquid xenon inside a vacuum cryostat that is expected to be located at SNOLAB, the Canadian underground science laboratory. Decays in the xenon produce both light and ionization and it is important to measure both to achieve sufficient energy resolution and thus background rejection. In particular, electrons from the ionization drift in an applied electric field toward anode pads where they are measured. The light flash is simultaneously detected by an array of SiPMs. The technical goal of the proposed thesis is to study different SiPMs characteristics in order to choose the best SiPM technology for the nEXO experiment. This thesis will also introduce new mathematical models to better understand Geiger mode properties of SiPMs in order to optimize them for the next generations of double beta decay and dark matter experiments.
Development of a single vacuum ultra-violetphoton-sensing solution for nEXObyGiacomo GallinaA THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)April 2021© Giacomo Gallina, 2021The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the dissertation entitled:Development of a single vacuum ultra-violet photon-sensing solutionfor nEXOsubmitted by Giacomo Gallina in partial fulfillment of the requirements for thedegree of Doctor of Philosophy in Physics.Examining Committee:Prof. Reiner Kruecken, Department of Physics and Astronomy, University of BritishColumbia, Deputy Director, TRIUMFSupervisorProf. Fabrice Retiere, Department of Physics, Simon Fraser University, ScienceTechnology Department, TRIUMFCo-SupervisorProf. Vesna Sossi, Department of Physics and Astronomy, University of BritishColumbiaSupervisory Committee MemberProf. Janis McKenna, Department of Physics and Astronomy, University of BritishColumbiaSupervisory Committee MemberProf. Douglas Scott, Department of Physics and Astronomy, University of BritishColumbiaSupervisory Committee MemberProf. Scott Oser, Department of Physics and Astronomy, University of BritishColumbiaUniversity ExaminerProf. Russ Algar, Department of Chemistry, University of British ColumbiaUniversity ExaminerProf. Daniel McKinsey, Department of Physics, University of California, BerkeleyExternal ExamineriiAbstractSilicon PhotoMultiplier (SiPM) technology represents an unprecedented at-tempt to create an ideal solid-state photon detector, combining the low-light detec-tion capabilities of the previous device generations with all the benefits of a solid-state sensor. For this reason, large-scale low-background cryogenic experiments,such as the next-generation Enriched Xenon Observatory experiment (nEXO), aremigrating to a SiPM-based light detection system. nEXO aims to probe the bound-aries of the standard model of particle physics by searching for neutrino-less dou-ble beta decay (0νββ ) of 136Xe. The nEXO experiment follows the same detectionconcept as the EXO-200 experiment, but uses 5 tonnes of liquid xenon inside a vac-uum cryostat that is expected to be located at SNOLAB, the Canadian undergroundscience laboratory. Decays in the xenon produce both light and ionization and itis important to measure both to achieve sufficient energy resolution and thus back-ground rejection. In particular, electrons from the ionization drift in an appliedelectric field toward anode pads where they are measured. The light flash is simul-taneously detected by an array of SiPMs. The technical goal of the proposed thesisis to study different SiPMs characteristics in order to choose the best SiPM tech-nology for the nEXO experiment. This thesis will also introduce new mathematicalmodels to better understand Geiger mode properties of SiPMs in order to optimizethem for the next generations of double beta decay and dark matter experiments.iiiLay SummarySilicon PhotoMultiplier (SiPM) technology represents an unprecedented at-tempt to create an ideal solid-state photon detector, combining the low-light de-tection capabilities of the previous generations of devices with all the benefits ofa solid-state sensor. The nEXO experiment aims to probe the boundaries of thestandard model of particle physics by searching for neutrino-less double beta de-cay. Different SiPMs characteristics are studied in order to choose the best SiPMtechnology for this experiment. Moreover, new mathematical models are also in-troduced to better understand Geiger mode properties of SiPMs to optimize themfor the next generations of double beta decay and dark matter experiments.ivPrefaceThe work presented henceforth is original work that was conducted at TRI-UMF, the Canadian national laboratory for particle and nuclear physics, located inVancouver (BC). A version of Chapter 3 has been published in [G. Gallina, andet al. Characterization of the Hamamatsu VUV4 MPPCs for nEXO. Nuclear In-struments and Methods in Physics Research Section A, 940:371–379, 2019. ISSN01689002.] and in [G. Gallina and F. Retiere. Characterisation of a new generationof VUV low-light sensors. EPJ Web of Conferences, 227, 2020.]. I was the leadinvestigator, responsible for all the major areas of the experiment, such as setup de-velopment, data collection, data analysis and manuscript composition. F. Retieredeveloped the original setup design and contributed to the data analysis and paperwriting. P. Giampa also contributed to the data analysis and paper writing whileP. Margetak built the electronics for data taking. The other authors of the paperscontributed to the manuscript revision and writing. A version of Chapter 5 has beenpublished in [G. Gallina and et al. Characterization of SiPM Avalanche TriggeringProbabilities. IEEE Transactions on Electron Devices, 66(10):4228–4234,2019.].For this publication I was the lead investigator, responsible for all the major ar-eas of the experiment, such as setup development, data collection, data analysisand manuscript composition. F. Retiere contributed to the derivation of the model,data analysis and paper writing while P. Margetak built the electronic for the datataking and P. Giampa contributed to the paper figures and writing. The other au-thors of the paper contributed to the manuscript revision and writing. I was thelead investigator for the project presented in Chapter 4, where I was responsiblefor the development of the setup and for the data analysis. N. Massacret, L. Mar-tin, P. Margetak and R. Maharaj contributed to the development of the software,vhardware and electronic of the setup. F. Retiere contributed to the data analysis.Additionally, I was also the lead investigator for the model presented in Chapter 6.F. Retiere contributed to the model derivation and to the data analysis. M. Mahtabcontributed to Fig. 4.2 and Fig. 6.1.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Double beta decay search with the nEXO experiment . . . . . . . . 52.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Neutrinoless Double Beta Decay . . . . . . . . . . . . . . . . . . 82.2.1 Connections with Cosmology . . . . . . . . . . . . . . . 102.2.2 Decay rate and half life of the 0νββ decay . . . . . . . . 122.2.3 Energy signature of 0νββ decay . . . . . . . . . . . . . . 152.2.4 Discovery potential for next generation 0νββ decay ex-periments . . . . . . . . . . . . . . . . . . . . . . . . . . 16vii2.3 Liquid xenon for 0νββ search . . . . . . . . . . . . . . . . . . . 182.4 Double Beta Decay search with the nEXO Detector . . . . . . . . 212.4.1 The nEXO Charge Collection and Readout Subsystem . . 252.4.2 The nEXO Light Collection and Readout Subsystem . . . 262.4.2.1 VUV sensitive SiPMs for light detection in LXe 282.4.3 A model for the nEXO Energy Resolution . . . . . . . . . 342.4.3.1 Light subsystem . . . . . . . . . . . . . . . . . 372.4.3.2 Charge subsystem . . . . . . . . . . . . . . . . 402.4.3.3 Expected nEXO energy resolution . . . . . . . 412.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 Characterization of the Hamamatsu VUV4 MPPCs for nEXO . . . 433.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . 443.2.1 Hardware Setup . . . . . . . . . . . . . . . . . . . . . . . 443.2.2 Light Filtering Scheme . . . . . . . . . . . . . . . . . . . 453.2.3 Beam Position Mapping . . . . . . . . . . . . . . . . . . 453.2.4 Collected Data and Trigger Configurations . . . . . . . . 473.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 503.3.1 Signal Pulse Fitting Procedure . . . . . . . . . . . . . . . 503.3.2 Single PE Gain and Breakdown Voltage Extrapolation . . 513.3.3 Prompt Pulse Charge Distribution . . . . . . . . . . . . . 533.3.4 Noise Analysis . . . . . . . . . . . . . . . . . . . . . . . 533.3.4.1 Number of Correlated Avalanches per Pulse . . 553.3.4.2 Dark Noise Rate and Number of Correlated De-layed Avalanches per Pulse . . . . . . . . . . . 583.3.4.3 Number of Additional Prompt Avalanches . . . 603.3.5 Photon Detection Efficiency . . . . . . . . . . . . . . . . 623.3.5.1 Analysis of the reflectivity of the HamamatsuVUV4 MPPC and FBK LF SiPM . . . . . . . . 643.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674 Characterization of the FBK VUV HD 3 for nEXO . . . . . . . . . . 70viii4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.2 Experimental Details . . . . . . . . . . . . . . . . . . . . . . . . 734.2.1 Hardware Setup . . . . . . . . . . . . . . . . . . . . . . . 734.3 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . 774.3.1 Lamp Spectrum . . . . . . . . . . . . . . . . . . . . . . . 774.3.2 Beam Mapping Strategy . . . . . . . . . . . . . . . . . . 784.3.3 Collected Data and Trigger Configurations . . . . . . . . 794.3.4 Single PE Gain and Breakdown Voltage Extrapolation . . 794.3.5 Noise Analysis . . . . . . . . . . . . . . . . . . . . . . . 814.3.5.1 Number of Correlated Avalanches per Pulse . . 824.3.5.2 Dark Noise Rate and Number of Correlated De-layed Avalanches per Pulse . . . . . . . . . . . 844.3.5.3 Number of Additional Prompt Avalanches . . . 864.4 A new DC technique to measure the SiPM Photon Detection Effi-ciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.4.1 Calibration of the photon flux with a NIST Photo-Diode asreference . . . . . . . . . . . . . . . . . . . . . . . . . . 914.4.2 Temperature dependence of the Photo-Diode current . . . 934.5 Estimation of the nEXO energy resolution . . . . . . . . . . . . . 964.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015 A new detector for particle physics and beyond . . . . . . . . . . . . 1035.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.2 Characterization of SiPM Avalanche Triggering Probabilities . . . 1065.2.1 Parametrization of the SiPM PDE . . . . . . . . . . . . . 1075.2.1.1 Model for Single Photon Avalanche Diodes . . 1075.2.1.2 Modelling photon absorption and carrier transport 1085.2.1.3 Modelling the probability of triggering avalancheswithin the junction . . . . . . . . . . . . . . . . 1115.2.1.4 Inferring the electron-hole avalanche triggeringprobabilities . . . . . . . . . . . . . . . . . . . 1125.2.1.5 Evaluation of the ionization integral and Eq. 5.11 1135.2.1.6 Data analysis procedure . . . . . . . . . . . . . 115ix5.2.2 Model validation . . . . . . . . . . . . . . . . . . . . . . 1165.2.2.1 Analysis of the Hamamatsu H2017 MPPC . . . 1185.2.2.2 Analysis of the Hamamatsu VUV4 MPPC andFBK LF SiPM . . . . . . . . . . . . . . . . . . 1195.2.3 Design considerations for the next generation of SiPMs . . 1225.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1246 Nuisance Processes in p-on-n SiPMs . . . . . . . . . . . . . . . . . . 1266.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1266.2 Nuisance Processes in SiPM . . . . . . . . . . . . . . . . . . . . 1266.3 A model to explain the SiPM Dark Noise Rate . . . . . . . . . . . 1286.3.1 Diffusive contribution . . . . . . . . . . . . . . . . . . . 1286.3.2 Band to Band Tunneling . . . . . . . . . . . . . . . . . . 1296.3.3 Recombination via traps . . . . . . . . . . . . . . . . . . 1296.3.4 SiPM Dark Noise Rate . . . . . . . . . . . . . . . . . . . 1316.3.5 Evaluation of the field enhanced recombination integral . . 1346.3.6 Fitting equation for the dark noise rate . . . . . . . . . . . 1346.3.6.1 Analysis of dependencies of Eq. 6.25 . . . . . . 1356.3.7 Comparison of analytical dark noise calculations with mea-surements . . . . . . . . . . . . . . . . . . . . . . . . . . 1366.4 A model to explain Correlated Avalanches in SiPMs . . . . . . . . 1426.4.1 Direct CrossTalk model . . . . . . . . . . . . . . . . . . 1426.4.1.1 Comparison of analytical DiCT calculation withmeasurements . . . . . . . . . . . . . . . . . . 1446.4.2 Correlated Delayed Avalanche Model . . . . . . . . . . . 1476.4.2.1 Comparison of analytical CDA calculation withmeasurements . . . . . . . . . . . . . . . . . . 1516.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1587 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164xList of TablesTable 2.1 Requirements for the nEXO light detection subsystem. See textfor explanation. . . . . . . . . . . . . . . . . . . . . . . . . . 33Table 3.1 Summary of the results derived for the characterization of theHamamatsu VUV4 MPPC useful for nEXO operation. . . . . . 68Table 4.1 Summary of the results derived from Chapter 3 and [1] for thecharacterization of the Hamamatsu VUV4 MPPC and FBK VUV HD 1Low Field (LF) SiPM. . . . . . . . . . . . . . . . . . . . . . . 71Table 4.2 Summary of the capacitance and breakdown voltage for severalphoton-sensors tested for nEXO. . . . . . . . . . . . . . . . . 81Table 4.3 Average dark current of the Photo-Diode as a function of thetemperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . 94Table 4.4 Summary of the parameters of Eq. 2.53. . . . . . . . . . . . . 98Table 4.5 Summary of the results derived in this chapter for the character-ization of the FBK VUV HD 3 SiPM. . . . . . . . . . . . . . . 101Table 5.1 Comparison of the fit parameters derived for the three testeddevices (1/2). . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Table 5.2 Comparison of the fit parameters derived for the three testeddevices (2/2). . . . . . . . . . . . . . . . . . . . . . . . . . . . 119Table 6.1 Summary of the parameters derived from the fitting of the darknoise data. Additionally, we reported the reduced χ2 of theglobal fit with NDF Number of Degrees of Freedom. . . . . . . 141xiTable 6.2 Parameters extracted from the fit of the DiCT data using Eq. 6.35for the two SiPMs tested: Hamamatsu VUV4 MPPC and FBK VUV HD 1SiPM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148Table 6.3 Parameters extracted from the fit of the afterpulse data usingEq. 6.42 for the two SiPM tested: Hamamatsu VUV4 MPPCand FBK VUV HD 1 SiPM. . . . . . . . . . . . . . . . . . . . 158Table 6.4 Summary of the f parameters derived in this chapter. . . . . . 158xiiList of FiguresFigure 2.1 Feynman diagrams representing two-neutrino double beta (2νββ )decay (left) and neutrinoless double beta (0νββ ) decay (right),as shown in Ref. [2]. . . . . . . . . . . . . . . . . . . . . . . 9Figure 2.2 Values of G0ν(Q,Z), Q and natural abundance of the initialisotope for several 0νββ decay processes [3]. . . . . . . . . . 13Figure 2.3 Values of the nuclear matrix element calculated with differentnumerical models. . . . . . . . . . . . . . . . . . . . . . . . 14Figure 2.4 Effective neutrino mass as a function of the mass of the lightestneutrino. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 2.5 Electron energy spectrum for the 0νββ decay mode and forthe 2νββ decay mode. The figure also includes the effect of a2% energy resolution smearing [4]. . . . . . . . . . . . . . . 16Figure 2.6 Experimental parameters for the older generation 0νββ ex-periments, with details on their sensitive exposure ε , half lifesensitivity, half life limit (represented as T 0νββ1/2 ) and effectivemass limit mββ [2] . . . . . . . . . . . . . . . . . . . . . . . 17Figure 2.7 Projected discovery sensitivity as a function of the sensitiveexposure ε and sensitive background B for three candidate iso-topes for 0νββ search [5]. . . . . . . . . . . . . . . . . . . . 18Figure 2.8 Ionization and scintillation processes in liquid xenon [2]. . . . 19Figure 2.9 Energy of events as measured by the ionization and scintil-lation channels while using a 228Th calibration source in theEXO-200 detector, the precursor of the nEXO detector. . . . . 20xiiiFigure 2.10 EXO-200 detector. . . . . . . . . . . . . . . . . . . . . . . . 22Figure 2.11 Sketch of the nEXO TPC located in the Cryopit at SNOLAB,the Canadian underground science laboratory [2]. . . . . . . . 23Figure 2.12 Sketch of the nEXO TPC [2]. . . . . . . . . . . . . . . . . . 24Figure 2.13 A close-up view of the TPC anode region showing the charge-collecting anode, the tensioned rods, and the SiPM staves be-hind the field cage [6]. . . . . . . . . . . . . . . . . . . . . . 25Figure 2.14 Schematic drawing of a prototype charge collection tile with10 cm edge and 3 mm pitch electrodes [6]. . . . . . . . . . . 26Figure 2.15 Energy resolution as a function of the overall light detectionefficiency of the nEXO TPC for a field of 400 V/cm and front-end electronic appropriate for internal (cryogenic) and external(room temperature and immediately outside of the cryostat)usage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Figure 2.16 Pulse shape produced by the discharge of one SiPM SPAD fortwo different temperatures (233 K and 173 K) for one SiPMtested for nEXO (Hamamatsu VUV4 MPPC). . . . . . . . . . 29Figure 2.17 Energy resolution as a function of the overall light detectionefficiency of the nEXO TPC for several electric fields [2]. . . 30Figure 2.18 Simulation of the photon Collection Efficiency (CE) of thenEXO TPC as a function of the Field Shaping Rings (FSR)sand cathode reflectivity. In the simulation the anode reflectiv-ity was set to 50% [2]. . . . . . . . . . . . . . . . . . . . . . 31Figure 2.19 Representation of the noise sources in SiPMs: Dark Noise(DN) and Correlated Avalanche (CA) noise. . . . . . . . . . . 32Figure 2.20 Estimated energy resolution for nEXO as a function of the overvoltage for the FBK VUV HD 1 SiPM in its Low Field (LF)and Standard (STD) version [1]. . . . . . . . . . . . . . . . . 34Figure 2.21 Comparison of the charge yields (a) and light yields (b) mea-sured by the EXO-200 detector with the NEST simulator for γand β particles [7, 8]. . . . . . . . . . . . . . . . . . . . . . . 35xivFigure 3.1 Hardware setup used for the characterization of the Hama-matsu VUV4 MPPC. . . . . . . . . . . . . . . . . . . . . . . 46Figure 3.2 Filtered xenon flash lamp spectrum measured after applicationof the 4 VUV filters. The shoulder effect around 190 nm is dueto the combination of the original xenon flash lamp spectrumand the different filters transmissions. . . . . . . . . . . . . . 47Figure 3.3 Position mapping of the VUV beam at the SiPM location. TheSiPM was moved in the x and y coordinates of Fig. 3.1 atincrements of 0.5 mm in each direction. . . . . . . . . . . . . 48Figure 3.4 Comparison between the measured beam map x-y projections(Blue) and the Monte Carlo model (Red) for the x-projection(Top) and y-projection (Bottom) of the beam map of Fig. 3.3. 49Figure 3.5 Schematic representation of the waveform analysis toolkit de-veloped for this study. See text for a detailed explanation. . . . 50Figure 3.6 Charge distribution (normalized to the average charge of 1 PEpulses) of first pulses following single PE trigger pulses as afunction of the time difference with respect to (wrt) their pri-mary pulse for T=163 K and for an over voltage of 5.1±0.2 V. 51Figure 3.7 Measured single PE gain (Eq. 4.3) as a function of the overvoltage for different SiPM temperatures. . . . . . . . . . . . . 52Figure 3.8 Charge distribution for prompt pulses obtained using dark datafor different SiPM temperatures and over voltages (Top: T=233 K.Bottom: T=163 K). . . . . . . . . . . . . . . . . . . . . . . . 54Figure 3.9 Histogram of the baseline subtracted integral of collected darkwaveform for an over voltage setting of 5.1±0.2 V and a tem-perature of 163 K. . . . . . . . . . . . . . . . . . . . . . . . 55Figure 3.10 Number of Correlated Avalanches (CAs) per primary pulsewithin a time window of 1 µs after the trigger pulse as a func-tion of the applied over voltage for different SiPM temperatures. 56Figure 3.11 Root Mean Square Error (RMS) of the number of CorrelatedAvalanches (CAs) per primary pulse within a time window of1 µs after the trigger pulse as a function of the applied overvoltage for different SiPM temperatures. . . . . . . . . . . . 57xvFigure 3.12 Relative fluctuation of the number of CAs in 1 µs measured at163 K and derived with Eq. 3.4 from the data of Fig. 3.10 andFig. 3.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Figure 3.13 Observed pulse rate R(t) normalized by the SiPM photon sen-sitive area as a function of the time difference with respect to(wrt) the primary pulse for a temperature of 163 K (5.1±0.2 Vof over voltage) (Blue) and 233 K (5.7±0.2 V of over voltage)(Red). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 3.14 Dark Noise (DN) rate normalized by the SiPM photon sensi-tive area as a function of the applied over voltage for differentSiPM temperatures. . . . . . . . . . . . . . . . . . . . . . . . 60Figure 3.15 Number of Correlated Delayed Avalanches (CDAs) per pri-mary pulse within a time window of 1 µs after the trigger pulseas a function of the applied over voltage for different SiPMtemperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . 61Figure 3.16 Number of Additional Prompt Avalanches (APAs) as a func-tion of the over voltage for different SiPM temperatures. . . . 61Figure 3.17 Position mapping of the VUV beam at the PMT location. ThePMT was moved in the x and y coordinates of Fig. 3.1 at in-crements of 0.5 mm in each direction. . . . . . . . . . . . . . 63Figure 3.18 Photon Detection Efficiency (PDE) as a function of the overvoltage for two Hamamatsu VUV4 MPPCs and three FBK-LFSiPMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65Figure 3.19 Specular reflectance as a function of the angle of incidence forfive samples measured at 175 nm. . . . . . . . . . . . . . . . 66Figure 3.20 Specular reflectance as a function of the angle of incidence forfive samples measured at 193 nm. . . . . . . . . . . . . . . . 67Figure 4.1 Image of a FBK VUV HD 3 SiPM. . . . . . . . . . . . . . . 72Figure 4.2 Hardware setup used for the characterization of the FBK VUV HD 3SiPM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 4.3 Vacuum Emission Reflectivity Absorption (VERA) setup atTRIUMF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74xviFigure 4.4 Configuration for efficiency and calibration measurements inthe VERA Setup. . . . . . . . . . . . . . . . . . . . . . . . . 75Figure 4.5 Particular of the motorized IRIS assembly inside the vacuumchamber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Figure 4.6 Lamp Spectrum of the Lyman-Alpha Resonance light source(Lamp temperature set point: 423 K) recorded by the refer-ence PMT (Bias Voltage: 1050 V) as a function of the VM200monochromator slit width. . . . . . . . . . . . . . . . . . . . 78Figure 4.7 Measured single PE charge as a function of the over voltagefor several devices tested for the nEXO experiment. . . . . . . 80Figure 4.8 Number of Correlated Avalanches (CAs) per primary pulsemeasured at 163 K within a time window of 1 µs after the trig-ger pulse as a function of the applied over voltage for severalphoton-sensors tested for nEXO. . . . . . . . . . . . . . . . . 83Figure 4.9 Root Mean Square Error (RMS) of the number of CorrelatedAvalanches (CAs) per primary pulse measured at 163 K withina time window of 1 µs after the trigger pulse as a function ofthe applied over voltage for several photon-sensors tested fornEXO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Figure 4.10 Relative fluctuation of the number of CAs in 1 µs measured at163 K and derived with Eq. 3.4 from the data of Fig. 4.8 andFig. 4.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Figure 4.11 FBK VUV HD 3 #1 charge distribution of first pulses follow-ing single PE trigger pulses as a function of the time differencewith respect to (wrt) their primary pulse for T=163 K and foran over voltage of 5.64±0.17 V. . . . . . . . . . . . . . . . . 86Figure 4.12 Observed dark pulse rate R(t) of the FBK VUV HD 3 #1 SiPMas a function of the time difference with respect to (wrt) theprimary pulse for a temperature of 163 K and for different overvoltages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87xviiFigure 4.13 Number of Correlated Delayed Avalanches (CDAs) per pri-mary pulse measured at 163 K within a time window of 1 µsafter the trigger pulse as a function of the applied over voltagefor several photon-sensor tested for nEXO. . . . . . . . . . . 88Figure 4.14 Dark Noise rate measured at 163 K and normalized by theSiPM photon sensitive area as a function of the applied overvoltage for several photon-sensor tested for nEXO. . . . . . . 89Figure 4.15 Number of Additional Prompt Avalanches (APA)s measuredat 163 K as a function of the over voltage for several photon-sensor tested for nEXO. . . . . . . . . . . . . . . . . . . . . 90Figure 4.16 Observed pulse rate R(t) of the FBK VUV HD 3 #1 SiPMas a function of the time difference with respect to (wrt) theprimary pulse for a temperature of 163 K under 175 nm lightillumination. . . . . . . . . . . . . . . . . . . . . . . . . . . 91Figure 4.17 Observed photon induced pulse rate R0(t) extrapolated fromFig. 4.16 for the FBK VUV HD 3 #1 SiPM as a function of theover voltage, for a temperature of 163 K, under 175 nm lightillumination. . . . . . . . . . . . . . . . . . . . . . . . . . . 92Figure 4.18 Responsivity of the NIST calibrated Photo-Diode as a functionof the wavelength. . . . . . . . . . . . . . . . . . . . . . . . 93Figure 4.19 Photo-Diode photon current measured, as a function of thewavelength, for several Photo-Diode temperatures. . . . . . . 94Figure 4.20 Voltage recorded with the reference PMT during the Photo-Diode measurements reported in Fig. 4.19. . . . . . . . . . . 95Figure 4.21 omparison of two estimators used to account for the CA noisecontribution in the derivation of the nEXO energy resolutionfor the two SiPMs tested in this work. . . . . . . . . . . . . . 97Figure 4.22 nEXO predicted energy resolution as a function of the SiPMover voltage for the two SiPMs tested in this work. The overalldetector collection efficiency was set to 20%. . . . . . . . . . 99Figure 4.23 nEXO predicted energy resolution as a function of the SiPMover voltage for the two SiPMs tested in this work. The overalldetector collection efficiency was set to 33%. . . . . . . . . . 100xviiiFigure 5.1 Measured Single Photon Timing Resolution (SPTR) with a420 nm PiLas picosecond laser for several SiPMs . . . . . . . 104Figure 5.2 p-on-n SPAD simulated with Lumerical DEVICE. . . . . . . 109Figure 5.3 Single Photo-electron Equivalent (PE) charge as a function ofthe over voltage (difference between the reverse bias voltageand the breakdown voltage) for the three tested devices. . . . . 116Figure 5.4 Absolute PDE as a function of the over voltage for the Hama-matsu H2017 MPPC for wavelengths in the range 400−640 nm.118Figure 5.5 Fraction of Electron Driven Avalanches (EDA) ( f ∗e , derivedusing Eq. 5.9 and the fit results reported in Table 5.1 and Ta-ble 5.2) and saturation PDE (PDEMAX) plotted as a function ofthe wavelength for the H2017 Hamamatsu MPPC. . . . . . . 120Figure 5.6 Average number of photons detected by the Hamamatsu VUV4MPPC and the FBK LF SiPM (µSiPMλ , Eq. 5.23) as a functionof the over voltage for not calibrated light fluxes. . . . . . . . 121Figure 5.7 lectron and hole Avalanche Triggering Probability (ATP): Pe(dP)and Ph(dW ), for the three SiPMs analyzed in this chapter. . . . 122Figure 5.8 Number of ionization carriers produced along the carrier pathfor the three devices tested in this chapter . . . . . . . . . . . 123Figure 6.1 Model of the symmetric p-on-n junction used in this chapter. . 128Figure 6.2 Dark Noise Rate as a function of the over voltage for differentSiPM temperatures for the Hamamatsu VUV4 MPPC. . . . . 138Figure 6.3 Shockley-Read-Hall recombination rate (csrh) as a function of1/T for the Hamamatsu VUV4 MPPC. . . . . . . . . . . . . 138Figure 6.4 Shockley-Read-Hall thermal and trap-assisted rate rate as afunction of the over voltage for the Hamamatsu VUV4 MPPCat 233 K and 163 K . . . . . . . . . . . . . . . . . . . . . . . 139Figure 6.5 Dark Noise Rate as a function of the over voltage for differentSiPM temperatures for the FBK VUV HD 1. . . . . . . . . . 140Figure 6.6 Shockley-Read-Hall recombination rate (csrh) as a function of1/T for the FBK VUV HD 1 SiPM. . . . . . . . . . . . . . . 140Figure 6.7 Different types of Optical CrossTalk in SiPM. . . . . . . . . . 142xixFigure 6.8 Mean number of Additional Prompt Avalanches (APA) due todirect CrossTalk as a function of the over voltage for differentSiPM temperatures for the Hamamatsu VUV4 MPPC. . . . . 146Figure 6.9 Mean number of Additional Prompt Avalanches (APA) due todirect CrossTalk as a function of the over voltage for differentSiPM temperatures for the FBK VUV HD 1. . . . . . . . . . 147Figure 6.10 Distribution of FBK VUV HD 1 SiPM pulses as a functionof the time after the microcell was triggered. See text for adetailed explanation [1]. . . . . . . . . . . . . . . . . . . . . 148Figure 6.11 Observed pulse rate R(t) of the Hamamatsu VUV4 MPPC as afunction of the time difference with respect to (wrt) the primarypulse for a temperature of 233 K. . . . . . . . . . . . . . . . 152Figure 6.12 Number of Correlated Delayed Avalanches (CDA) per primarypulse (derived from Fig. 6.11) for the Hamamatsu VUV4 MPPCas a function of the over voltage. . . . . . . . . . . . . . . . . 153Figure 6.13 Total number of Correlated Delayed Avalanches (CDA) perprimary pulse for the Hamamatsu VUV4 MPPC as a functionof the over voltage, for different temperatures. Solid lines rep-resent fits performed with Eq. 6.42. . . . . . . . . . . . . . . 154Figure 6.14 Observed pulse rate R(t) of the FBK VUV HD 1 SiPM as afunction of the time difference with respect to (wrt) the primarypulse for a temperature of 233 K. . . . . . . . . . . . . . . . 155Figure 6.15 Total number of Correlated Delayed Avalanches (CDA) perprimary pulse for the FBK VUV HD 1 SiPM as a functionof the over voltage, for different temperatures. . . . . . . . . . 156Figure 6.16 FBK VUV HD 1 charge distribution of first pulses followingsingle PE trigger pulses as a function of the time differencewith respect to (wrt) their primary pulse for 233 K and for anover voltage of 4.81±0.13 V. . . . . . . . . . . . . . . . . . 157xxGlossary3D B-SiPM 3D integrated Back-side illuminated SiPMAOI Angle of IncidenceAPA Additional Prompt AvalancheCA Correlated AvalancheCDA Correlated Delayed AvalancheCE detector photon Collection EfficiencyCL confidence levelCP charge conjugation parity symmetryCT CrossTalkDAQ Data AcQuisition SystemDeCT Delayed CrossTalkDiCT Direct CrossTalkDN Dark NoiseEXO-200 Enriched Xenon Observatory-200FBK Fondazione Bruno KesslerFSRs Field Shaping RingsFWHM Full Width Half MaximumLF Low FieldxxiLXe liquid xenonMC Monte-Carlo modelMIDAS Maximum Integrated Data Acquisition SystemMPPC Multi-Pixel Photon CounternEXO next-generation Enriched Xenon ObservatoryPA Photosensitive AreaPD Photo-DiodePDE SiPM Photon Detection EfficiencyPE Photo-electron EquivalentPMNS Pontecorvo–Maki–Nakagawa–SakataPMT PhotoMultiplier TubesQE Quantum EfficiencyRF Radio-FrequencyRGA Residual Gas AnalyzerRMS Root Mean SquareROI Region of InterestSARF Single Avalanche Response FunctionSiPM Silicon Photo-MultipliersSM Standard ModelSPAD Single Photon Avalanche DiodeSPTR Single Photon Timing ResolutionTPC Time Projection ChamberVERA Vacuum Emission Reflectivity AbsorptionVUV Vacuum UltraVioletXe xenonxxiiAcknowledgmentsI came to Canada 4 years ago to start my Phd at UBC. First of all, I wouldlike to thank Les and Leslie. They welcomed me into their home and made mefeel at home. I would then say a big thanks to Maggie. Maggie is a bit f at doggyof 4 years old. I came here when she was just a puppy, few months old. I feelnow like she is part of my family. I would like to say thanks to her for the endlessamount of hours she spent waiting me for little walks, in particular during themonths I was studying for the comprehensive exam. I would then say thanks toDigby (the cat) not because I really like him, but otherwise I would feel guilty forthe rest of my life. I would then say thanks to Prof. Reiner Kruecken and to Prof.Fabrice Retiere. Reiner because he always helped and supported me during mystudies at UBC, Fabrice instead because he allowed me to work in his group andto prove my worth. I think I developed with him, during these years at TRIUMF, arelationship that goes beyond a usual student-supervisor relationship. I would liketo say thanks to him for this. I would then say thanks to my colleagues, in particularP. Margetak, N. Massacret, L. Martin, R. Maharaj, P. Giampa, M. Constable andP. Amaudruz, since I drove them crazy with my last minute requests for the last 4years and, no matter what, they always helped me. I would then say thanks to theErmenegildo Zegna Founder Scholarship that supported me in paying my tuitionfees at UBC. Finally, a heartfelt thanks goes to my parents, my uncle Stefano andmy aunt Nadia, and above all to my sister Camilla who supported and encouragedme in all circumstances. Thank you all; you helped make this work better.xxiiiChapter 1IntroductionIt is generally agreed that one of the most promising windows to the prop-erties of neutrinos and a further understanding of their mass would be from theobservation of a nuclear decay process known as neutrino-less double beta decay(0νββ ). This decay can only occur if the neutrino is its own antiparticle, in whichcase requiring a new mechanism that can give rise to mass [9]. Indeed the ob-servation of (0νββ ) decay would require lepton number violation and elementaryMajorana fermions. This is attractive because the neutrino mass is many ordersof magnitude smaller than that of the other fundamental particles of the standardmodel of particle physics, suggesting some new mechanism is at work and worthsearching for [10].Next-generation liquid xenon (Xe) detectors are emerging as the most promis-ing candidates for neutrinoless double beta decay searches, due to their scalabilityfor very large target masses and potential for extremely low background operations.Over the last few years, the next-generation Enriched Xenon Observatory(nEXO) collaboration has designed a new tonne-scale (0νββ ) decay experimentconceived to push the search to the next frontier. Specifically, nEXO aims to probethe boundaries of the standard model of particle physics by searching for (0νββ )of 136Xe.Among the candidate (0νββ ) nuclei [10], 136Xe is particularly attractive. The(0νββ ) Q value is high at 2458.07± 0.31 keV [9]. Xenon reserves in the atmo-sphere are practically unlimited and commercial production is sufficient to support1large scale experiments. As a noble gas, isotopic enrichment can be performedefficiently. Xenon is also readily purified of chemical contaminants, resulting inexceedingly low intrinsic radioactive backgrounds [11] and very long electron life-time [12]. Additionally, as a radiation detector medium, liquid xenon shows highscintillation and charge yield [13]. The high density ∼ 3 g/cm3 and atomic num-ber (Z = 54) result in short attenuation lengths for γ radiation. Finally, the xenonsupply can be recycled into upgraded detectors as technology improves.The current most stringent limit on (0νββ ) decay in 136Xe is 10.7× 1025 yrfrom the KamLAND-Zen experiment, with a corresponding sensitivity exposureof 504 kg× yr [14]. The diagnostic power of the liquid xenon (LXe) Time Pro-jection Chamber (TPC) allowed the Enriched Xenon Observatory-200 (EXO-200)experiment, the nEXO successful precursor, to reach a competitive sensitivity of3.7× 1025 yr with a substantially smaller exposure (178 kg× yr) and xenon mass(200 Kg) if compared with the KamLAND-Zen experiment [15].The nEXO detector follows the same concept of the EXO-200 detector, butusing 5 tonnes of LXe inside a TPC that is expected to be located at SNOLAB, theCanadian underground science laboratory [2]. At this time the nEXO collaborationis confident that a factor of ∼ 25 in the increase of the xenon mass, if comparedwith EXO-200, represents a natural progression in order to achieve a competitivesensitivity while at the same time relying on a conservative design [2].The nEXO TPC’s multiparameter measurement capability allows the simulta-neous determination of event energy, position, site multiplicity, and particle type [10].Energy loss in xenon produces in fact both light (scintillation) and electron-ionpair (ionization) and it is important to measure both signals to achieve sufficientenergy resolution and thus background rejection. In particular, electrons from thexenon ionization drift in an applied electric field towards anode pads where theyare measured. Xenon scintillation light is instead detected by an array of Sili-con Photo-Multipliers (SiPM)s. In contrast to the widely used PhotoMultiplierTubes (PMT)s or to the Large-Area Avalanche Photodiodes used in EXO-200,SiPMs are low-voltage powered, optimal for operation at cryogenic temperatures,and have low radioactivity levels with high gain stability over time in operationalconditions [16]. For these reasons, not only the nEXO experiment, but also other2large-scale low-background cryogenic experiments, such as DarkSide-20k, are mi-grating to a SiPM-based light-detection system [17, 18].The technical goal of the proposed work is to study different SiPMs charac-teristics in order to choose the best SiPM technology for the light detection in thenEXO experiment. In particular, this work will focus on two aspects that are nowunder study by the nEXO collaboration: (i) analysis of the characteristics of sev-eral SiPMs candidates for nEXO; (ii) Theoretical study of Geiger mode properties(i.e. electric field and noise) of SiPMs. This last aspect will be crucial for the de-velopment in the near future of new generations of SiPMs to dramatically improveenergy and timing resolution of the next generation of noble liquid detectors.This work is organized as follows. In Chapter 2 I introduce the physics moti-vation behind the nEXO experiment. I discuss in particular the design of the nEXOdetector, along with the connections with its precursor, the EXO-200 detector. Inthe same chapter I also present the requirement of the photon-sensor portion ofthe nEXO experiment and the model used for the estimation of the overall nEXOenergy resolution, including the light and charge channel contributions.In Chapters 3 and 4, I report the characterization of the three most promisingSiPMs candidates for nEXO: the Hamamatsu VUV4 MPPC; the FBK VUV HD 1;and FBK VUV HD 3 SiPMs. A significant part of these chapters is devoted toexplain the construction of the two setups built for their characterization. Finally,at the end of Chapter 4, I estimate the overall nEXO energy resolution using thedata collected in Chapters 3 and 4.The last two chapters of this thesis (Chapters 5 and 6) are part of a broaderstudy that is not only limited to the nEXO experiment, but it looks forward thenext generation of noble liquid detectors. The outcome of this study will be thedevelopment of a new back side illuminated SiPM light sensor to dramatically im-prove energy and timing resolution of future noble-liquid detectors, significantlyenhancing their background rejection capabilities relative to the current generationof liquid-based dark matter and double beta decay experiments. More precisely, inChapters 5 and 6, I discuss the development of a new theoretical framework to bet-ter understand and optimize Geiger mode characteristics of SiPMs. In particular, Ipropose new models that are not only able to explain the wavelength and voltagedependence of the SiPM photon detection efficiency (Chapter 5), but also predict3the voltage and temperature dependence of several noise sources in SiPMs (Chap-ter 6). These models have been successfully applied to characterize two SiPMsand they can be naturally extended to other SiPMs. Furthermore, they provide keyinsight into the electric field structure within SiPMs, which can explain the limi-tation of the existing devices and be used to optimize the performance of the nextgeneration of SiPMs.4Chapter 2Double beta decay search withthe nEXO experiment2.1 IntroductionDefinitive evidence of non-zero neutrino masses from oscillation experimentshas been available for nearly two decades [19–22]. However, the incorporationof neutrino masses into the Standard Model (SM) of particle physics remains anopen issue [5]. In the SM of particle physics electron (e), muon (µ), tau (τ) andthe corresponding neutrinos (νe,νµ and ντ ) are spin 1/2 particles that belong tothe lepton class. The first three particles are charged (also known as the electron-like leptons) while the last three are neutral. The existence of the neutrino wasinitially posited in 1930 by Wolfgang Pauli to explain the otherwise missing spinand momentum observed in beta decays and was first detected by Clyde Cowanand Frederick Reines in 1956 [23]. Nevertheless, neutrinos are still poorly knownparticles. At the moment we know that there are three light neutrinos, much lighterthan their charged leptonic partners and they interact weakly with matter [23].More generally, neutrino phenomenology is described in the SM of particlephysics by three quantum flavor states νe, νµ and ντ , coupled to charged leptonsvia the weak interaction. These states do not have a fixed mass, but they are aquantum mechanic superposition of the three mass eigenstates ν1, ν2 and ν3, with5mass m1, m2 and m3, such thatνl =3∑i=1Uliνi (2.1)with l = e,µ,τ . The transformation between the mass and flavor bases is describedby the unitary Pontecorvo–Maki–Nakagawa–Sakata (PMNS) matrix [5]. In thestandard parametrization, the PMNS mixing matrix is characterized by: three mix-ing angles θ12,θ23 and θ13; a charge conjugation parity symmetry (CP)-violating δphase; and two possible CP-violating phases λ2 and λ3 [3] . Hence we can writeU = c12c13 s12c13 s13e−iδ−s12c23− c12s23s13eiδ c12c23− s12s23s13eiδ s23c13s12s23− c12c23s13eiδ −c12s23− s12c23s13eiδ c23c13D(λ2,λ3)(2.2)with cab ≡ cosθab, sab ≡ sinθab and the matrix D defined asD(λ2,λ3) =1 1 11 eiλ2 11 1 eiλ3 (2.3)Giving an initial neutrino state νl and a final neutrino state νl′ , defined accordinglyto Eq. 2.1, the probability for the transition νl −→ νl′ in vacuum is given by [3]P(νl −→ νl′) =∣∣∣δl′l+∑i 6=kUl′i(e−i ∆m2kiL2E −1)U∗li∣∣∣2 (2.4)where ∆m2ki ≡ (m2i −m2k). L is the distance between the neutrino detector and theneutrino source, and E is the neutrino energy. Equation 2.4 is crucial in neutrinophysics because it shows as, in the case of 3-neutrino mixing, neutrinos can trans-form from one flavor state to another during propagation, giving rise to neutrinooscillation, which remains to date the only observed phenomenon requiring non-zero neutrino masses.Equation 2.4 depends only on four mixing parameters θ12, θ23, θ13 and δ , andon two independent mass squared differences ∆m2ki ( ∆m212 and ∆m223) and not on the6three masses separately. The determination of the three masses is one of the mostchallenging tasks of contemporary physics and it has fundamental implications notonly in particle physics, but also in astrophysics and cosmology [24].The ∆m212 and ∆m223 mass squared differences are often referred as the solarand atmospheric neutrino mass square differences and denoted as ∆m2s and ∆m2a,respectively. Experimentally it has been found that [3]∆m212 ∼130∣∣∣∆m223∣∣∣ (2.5)However the existing data do not allow us to determine the sign of ∆m223. The twopossible signs correspond to the two types of neutrino mass spectrum, generallydenoted as :• Normal hierarchy: m1 < m2 < m3• Inverted hierarchy: m3 < m1 < m2Cosmology is sensitive to the sum of neutrino masses:Σ≡∑imi (2.6)for which several upper limits of about 0.1-0.2 eV are set by cosmological observa-tions [25]. Recent experiments also allowed us to constrain the values of ∆m2a and∆m2s . More precisely, from Super-Kamiokande data ∆m2a in the case of a normal(inverted) mass spectrum was found to be [26]1.9(1.7)×10−3eV2 ≤ |∆m2a| ≤ 2.6(2.7)×10−3eV2 (2.7)at the 90% of the confidence level (CL). From the combined analysis of all thesolar neutrino data and the data of the reactor KamLAND experiment, it has beenfound that ∆m2s is given by [27]∆m2s =(7.50+0.19−0.20)×10−5eV2 (2.8)From this it follows that the neutrino spectrum contains two masses (m1 and m2)7separated by the splitting ∆m2s (∆m212) , and a third mass m3 separated from the firsttwo by a larger splitting ∆m2a (∆m223), as also shown in Eq. 2.5 [4].2.2 Neutrinoless Double Beta DecayThe experimental observation of neutrino oscillations, which requires thatneutrinos have mass, indicates that the standard model description of neutrinosmust be extended. The introduction of Majorana-type particle fermions provides atheoretically compelling solution to the need to incorporate massive neutrinos intothe standard model. The most general mass term can be written in the Lagrangianas [2, 28]:−2L = mDνLνR+mD(νR)c(νL)c+mR(νR)cνR+h.c. (2.9)where (νR)c is the charge-symmetry conjugate of the right-handed neutrinochiral projection and (νL) is left-handed chiral projection. mR and mD are two massterms. The last equation can be written in matrix form as:−2L =(νL,(νR)c)(0 mDmD mR)((νL)cνR)+h.c. (2.10)The physical masses are the eigenvalues of the 2× 2 mass matrix of the previousequation, as given by:m± =12(mR±√m2R+4m2D)(2.11)Further making the assumption that mR >>mD, m± result in the following values:|m−|=m2DmR(2.12)|m+|= mR(1+m2Dm2R)∼ mR (2.13)This would explain both the absence of observational evidence for a heavy,right-handed neutrino and the suppression of the m− mass. If we choose the mass8scale for mR to be 1014−1016 GeV, and mD to be 100 GeV, we obtain a value for m−residing roughly in the observed neutrino mass splitting range of ∼ 1− 100 meV[29, 30]. This effect of a very massive, right-handed neutrino state driving downthe mass of the left-handed neutrino state is colloquially referred to as type-I see-saw mechanism and it is generally considered the most economical possibility [31].According to this mechanism, small neutrino masses are explained by new interac-Figure 2.1: Feynman diagrams representing two-neutrino double beta(2νββ ) decay (left) and neutrinoless double beta (0νββ ) decay (right),as shown in Ref. [2]. The (2νββ ) decay process conserves both baryonand lepton number separately. The (0νββ ) decay process instead is ex-plicitly a leptogenic process, creating two outgoing leptons. It is onlypossible if neutrinos are Majorana-type particles.tions beyond the standard model of particle physics which violates the total leptonnumber and, consequently, the lepton number violating neutrinoless double-betadecay process (0νββ ) of even–even nuclei is allowed1 [34]AZX =⇒ AZ+2Y+2e− (2.14)where A and Z are the numbers of nucleons and protons in the parent nucleus Xof mass MX . Here Y is instead the daughter nucleus with mass MY and number ofnucleons and protons equal to A and Z+2, respectively.1The Type-I see-saw mechanism for neutrino mass generation is only one of the many possibili-ties that could produce a 0νββ decay. Other theoretical prescriptions include Type-II (scalar (Higgs)triplet) and Type-III (fermionic triplet) see-saw mechanisms [32]. An additional set of contributionsto 0νββ could also arise by relaxing the assumption that the scale where lepton number is violatedis well above the electroweak scale [33].9Figure 2.1 shows not only the Feynman diagram representing the lepton vi-olating process (0νββ ), but also the Feynman diagram for the lepton conservingtwo-neutrino double beta decay process (2νββ ), represented byAZX =⇒ AZ+2Y+2e−+2ν (2.15)As clear from Eq. 2.14, the measurement of a 0νββ decay would immediatelydemonstrate the existence of lepton number violation. In addition, its observationwould confirm the existence of Majorana neutrinos, regardless of the decay mech-anism [35]. Such a discovery would be a fundamental departure from the pictureprovided by the standard model of particle physics, as all experimental measure-ments to date have shown lepton number to be a conserved quantity.2.2.1 Connections with CosmologyAntimatter is rare in the universe. The Big Bang should have created equalamounts of matter and antimatter in the early universe [36, 37]. But today, every-thing we see is made almost entirely of matter. There are three basic ingredientsnecessary to allow for the evolution of a matter dominated universe from an ini-tially symmetric state [38]:• Baryon Number Violation: There must be a violation of the Baryon num-ber (B).• C and CP violation: Even in the presence of B-non conserving interactions,a baryon asymmetry will not develop unless both C (charge conjugation) andCP (charge conjugation combined with parity) are violated. In the absenceof a preference for matter or antimatter, B-non conserving reactions will pro-duce baryon and antibaryon excesses at the same rate, thereby maintainingzero net baryon number.• Non-Equilibrium Conditions: In chemical equilibrium the entropy is maxi-mal when the chemical potentials associated with all non-conserved quantumnumber vanish. Further, particles and antiparticles masses are guaranteed tobe equal by the CPT invariance (charge, parity, and time reversal symmetry).10The conditions were proposed by Andrei Sakharov [39]. Modern physics researchhas shown that all three conditions can be present in the frameworks of the standardmodel [2].For example, early experimental work studying Parity (P) symmetry violationin weak decays in 1957 implied the presence of a C-symmetry violation througha theorem from Lee and Yang. Later in 1964 studies of the neutral K-mesonsshowed the existence of CP-symmetry violation. Together these existing observa-tions demonstrated, for example, as the second of Sakharov’s three conditions isalso present in nature. However, experimental research on K-mesons showed asthe magnitude of the CP-violation present in K-meson systems was not sufficientto explain the matter-antimatter asymmetry of the universe [40].Thus the search continues for a process to fulfill the requisite magnitude ofCP-violation, potentially in some other area of the SM, such as the lepton sector,where neutrinos remain less than fully understood. In fact, the last two decadesof developments in neutrino physics research have revealed a number of intriguingresults. The simple, mass-less neutrinos of the SM have actually been found to bemassive particles and potentially contain CP violation hidden within the completeformal description of flavor-oscillating massive neutrinos.Additionally, neutrinos will also provide clues to the matter-antimatter asym-metry in the universe.While, in fact, different possibilities exist to create such an asymmetry, themost popular scenario is baryogenesis via leptogenesis, as it allows to additionallyaddress open questions of neutrino physics like the mechanism of neutrino massgeneration and mixing [36]. The two common approaches are via: (i) leptogenesisfrom out-of-equilibrium decays, (ii) leptogenesis from oscillations.In the first approach, in order to feature small enough neutrino masses and atthe same time a large enough baryon asymmetry, the right handed neutrino mass isbounded from below [41].In this type of leptogenesis an asymmetry is created by violating out-of-equilibrium decays of new heavy degrees of freedom that provide a new sourceof CP violation. As long as these decays generate a net asymmetry above the elec-troweak scale baryogenesis via leptogenesis becomes possible. The CP violationrelevant for baryogenesis is usually parameterized by the CP asymmetry ε per de-11cay of heavy particles. In some leptogenesis models ε is proportional to the massesof both, the light neutrinos and the heavy ones. Given the tiny value of light neu-trino masses (compared to the electroweak scale), the leptogenesis scale set by themass of the heavy neutrinos has to be very high in order to generate a large enoughlepton asymmetry [36].In the second approach, instead, while the total lepton number is approxi-mately conserved, flavor oscillations create an asymmetry in between the differentflavor sectors [42]. The singlets that are in thermal equilibrium are able to transfertheir asymmetry to the active neutrino sector and thus create a baryon asymme-try [36].A number of experiments will explore the lepton flavor sector with more accu-racy in the future. Particularly important are: (i) Neutrino oscillation experiments;(ii) Neutrinoless double beta decay searches [36]. The first kind of experimentswill search for leptonic CP violation in light neutrino mixing. The oscillation prob-abilities are sensitive to the light neutrino mixing angles, mass differences and theCP phase: δ , of the PMNS matrix (Eq. 2.2). Although existing accelerator neu-trino experiments such as T2K and NOνA are sensitive to δ , their sensitivity israther limited and will be improved significantly in the future with the experimentDUNE [43].Double beta decay experiments instead will perform measurements sensitiveto low-scale seesaw scenarios as the heavy neutrinos can give a significant contri-bution to the amplitude for masses below 1 GeV.2.2.2 Decay rate and half life of the 0νββ decayThe experimentally observable measurement for the 0νββ search is its decayrate, which is proportional to the inverse of its half-life time. Assuming that thisprocess is induced by Majorana neutrino masses and mixing the 0νββ decay rateis given by [3]Γ0ν ≡( 1T 0ν1/2)= G0ν(Q,Z)|M0ν |2 |mββ |2m2e(2.16)where G0ν(Q,Z) is the known integral over the phase space that depends on Z (thenumber of protons in the parent nucleus) and on the reaction Q-value. This last12quantity is defined as the total energy released in the nuclear decay process and it isequal to Q≡ (MX−MY −2me) with me the electron mass. |M0ν | is the nuclear ma-trix element. The numerical values of G0ν(Q,Z), Q and the natural abundance ofFigure 2.2: Values of G0ν(Q,Z), Q and natural abundance of the initial iso-tope for several 0νββ decay processes [3].nuclei for which the 0νββ decay is theoretically allowed are presented in Fig. 2.2.The quantity mββ is instead the effective Majorana mass defined asmββ ≡∑iU2eimi (2.17)This last quantity, in addition to the nuclear matrix element |M0ν |, is a crucialparameter, since the measurement of the half-life of the (0νββ )-decay, accordingto Eq. 2.16, gives the product of the effective Majorana mass with the nuclearmatrix element |M0ν | and not only the effective Majorana mass [3].Fig. 2.3 shows the value of the nuclear matrix element computed with severalnumerical models. It is evident that there is a large discrepancy between values of|M0ν | computed with different models. The nuclear matrix element computation istherefore still an open field of research. The strongest limits on the half-life of the0νββ decay rate are from the KamLAND-Zen and GERDA experiments, givingat 90% CL for two different isotopes [5]T1/2(136Xe)> 10.7×1025 yr (2.18)13Figure 2.3: Values of the nuclear matrix element calculated with different nu-merical models. QRPA represents the Quasi-particle Random PhaseApproximation. EDF is the Energy Density Functional method. PHFBis the Projected Hartree–Fock–Bogoliubov approach. IBM-2 is the In-teracting Boson Model-2 and LSSM is the Large-Scale Shell Model.For more details see Ref. [3].and [44]T1/2(76Ge)> 5.3×1025 yr (2.19)respectively.Generally, the effective Majorana mass is examined as a function of the low-est neutrino mass, as shown in Fig. 2.4, for the two different neutrino mass hierar-chies (normal or inverted) introduced in Sec. 2.1. Uncertainty in the parameters ofEq. 2.17 produces in Fig. 2.4 allowed bands (green and red) under the assumptionthat neutrinos are Majorana particles.The current generation of 0νββ decay experiments are probing |mββ | downto 100 meV. Figure 2.4 also shows the target sensitivity level for the next generation0νββ decay experiments, which is roughly |mββ | ∼15 meV [2].14Figure 2.4: Effective neutrino mass as a function of the mass of the light-est neutrino. Current limits and expected limits from past and ongoingexperiments are shown as grey and blue horizontal bands. The green(for inverted hierarchy) and red (for normal hierarchy) bands show theexpected ranges under the assumption that neutrinos are Majorana par-ticles. Next-generation tonne-scale experiments aim to probe the effec-tive Majorana neutrino mass down to 15 meV, shown as a horizontaldashed line [2].2.2.3 Energy signature of 0νββ decayIn addition to its half-life, the most important experimental signature for a0νββ decay is a mono-energetic peak in the measured electron energy spectrumat the Q-value of the decay, produced when the two electrons emitted in the pro-cess are both absorbed in the detector active volume, as shown in Fig. 2.5. Theelectron energy is therefore the main observable for the discovery of the 0νββ de-cay [5]. This feature allows us to separate 0νββ from 2νββ events, even if thecorresponding decay rate for the 0νββ mode is much smaller than the one for the2νββ mode.15Figure 2.5: Electron energy spectrum for the 0νββ decay mode and for the2νββ decay mode. The figure also includes the effect of a 2% energyresolution smearing [4].2.2.4 Discovery potential for next generation 0νββ decayexperimentsThe number of detectable 0νββ decays (N0νββ ) occurring in a mass m of anelement containing a candidate 0νββ isotope of half-life T1/2 follows as [5]N0νββ =ln2 ·NA · εMββT0νββ1/2(2.20)where NA is Avogadro’s number, Mββ is the molar mass of the target isotope, andT1/2 is the half-life of the decay. ε is often called sensitive exposure and it is givenbyε ≡ {a ·m · εlive · εdet · t} (2.21)where a is the isotopic abundance (the enrichment), εdet is the detector detectionefficiency in the energy Region of Interest (ROI) (Fig. 2.5) to observe 0νββ decayevents, and t is the elapsed observation time with a detector live-time fraction of16εlive [2]2. The number of background events in the ROI can be written as [5]Nbkg = B · ε (2.22)where B is often called sensitive background and represents the number of back-ground events in the ROI region divided by ε , defined in Eq. 2.21. Sensitive ex-posure and sensitive background can then be used to estimate, using a likelihoodmethod [5, 45], the discovery sensitivity of old and next generation 0νββ experi-ments, as reported in Figs. 2.6 and 2.7. More precisely, Fig. 2.7 plots the projectedFigure 2.6: Experimental parameters for the older generation 0νββ experi-ments, with details on their sensitive exposure ε , half life sensitivity,half life limit (represented as T 0νββ1/2 ) and effective mass limit mββ [2] .discovery sensitivity for a number of selected experiments as a function of ε and B.The discovery sensitivity was defined in Ref. [5] to be the value of T 0νββ1/2 or mββfor which an experiment has a 50% chance to measure a signal above backgroundwith a significance of at least 3σ . The computation was performed for T 0νββ1/2 andthe result converted to a range of mββ values by using Eq. 2.16. The experimentsin Fig. 2.7 are divided accordingly to the candidate isotopes used for the 0νββsearch. Uncertainty in the nuclear matrix element is represented as bands. Pastor current experiments with published background level and energy resolution (redmarks) are shown according to the average performance in their latest data taking2Note as m and Mββ are significantly different. m, in fact, represents the total mass of the element(Xe, for example), measured in kg, while Mββ is the molar mass of the enriched isotope (136Xe, forexample), measured in kg/mol. Xenon, for example, can be enriched to significantly high level, upto 90% (a= 0.9) and it is one of the best candidates for 0νββ searches, see Fig. 2.2.17phase. Among several experiments, the next-generation Enriched Xenon Observa-Figure 2.7: Projected discovery sensitivity as a function of the sensitive expo-sure ε and sensitive background B for three candidate isotopes for 0νββsearch [5]. Uncertainties in the nuclear matrix elements are representedas bands. Past or current experiments with published background leveland energy resolution (red marks) are shown according to the averageperformance in their latest data taking phase.tory experiment (nEXO) is the only Xe-based next generation experiment able toprobe the effective Majorana mass down to ∼ 15 meV.2.3 Liquid xenon for 0νββ searchLXe (boiling point: 165.03 K, melting point: 161.36 K) is a particularly at-tractive candidate for 0νββ search for several reasons [28].• It serves as the source of the decay and as the detector.• It can be isotopically enriched to very high levels.• Its high atomic mass and density make it efficient at stopping gamma back-grounds (this property is often called self-shielding).• Being a liquid, it allows to build monolithic detectors.• It can be reliably purified to facilitate long electron lifetimes.• There are no long-lived radioactive isotopes of Xe produced via activationfrom cosmogenic sources.18• Scintillation and ionization are anti-correlated in LXe, and this can be usedto achieve good energy resolution.The response of LXe to ionizing radiation has been studied extensively in the liter-ature, both experimentally [13] and numerically [7].Energy loss in xenon produces both light (scintillation) and electron-ion pair(ionization) and it is important to measure both signals to achieve sufficient energyresolution and thus background rejection. The ionization point can be preciselymeasured by incorporating the LXe in a TPC [46].More generally, when particles deposit their energy in LXe, they produce anumber of electron-ion pairs and excited xenon atoms often called “excitons”. InFigure 2.8: Ionization and scintillation processes in liquid xenon [2].the scintillation process, two routes are then possible: either direct excitation of theXe atoms or electron-ion recombination.The resulting Xe+ ions and Xe∗ atoms recombine with other Xe atoms to formexcited molecules (Xe∗2 ) that decay emitting 175 nm Vacuum UltraViolet (VUV)photons (174.8± 10.2 nm [47]). Due to this fast decay time, the majority of the19scintillation signal is collected by the TPC photon-light sensors within 100 ns fromthe original energy deposition.The final ratio of light over charge is strongly dependent on the type of par-ticle that interacts with the liquid xenon, allowing particle identification. Alphasgenerate much more light than betas/gammas due to their higher density of ioniza-tion, resulting in larger amounts of recombination. As an example, a 2.5 MeV be-ta/gamma event generates about 104 k photons and 125 k electrons, while a 5 MeValpha event generates about 350 k photons and 10 k electrons in an electric field of400 V/cm [8]. The relative number of electrons and photons produced by an energydeposition not only depends on the type of particle, but also on the electric fieldapplied to the TPC. This property was first measured in Ref. [48]. As the electricfield increases in the TPC, more ionized electrons can be drifted away from theinteraction site, reducing the number of photons produced through recombination.This anticorrelation between the light and charge channel can be used as a pow-Figure 2.9: Energy of events as measured by the ionization and scintillationchannels while using a 228Th calibration source in the EXO-200 de-tector, the precursor of the nEXO detector. The energy resolution isconsiderably improved by forming a linear combination of both mea-surements [2, 49].erful tool to dramatically improve the energy resolution, since it allows to linearlycombine the information provided by the light and charge channels reducing there-fore the fluctuations of the two channels while considered individually, as shownin Fig. 2.9 [48, 49].20In addition to this property, LXe is also ideal for the implementation of back-ground rejection strategies. Shielding the inner detector from the energy depositionof other particles that constitute its natural background is crucial for an effective0νββ search. Discrimination of 0νββ events from gammas coming from the222Rn decay chain is the key for the success of most of the 0νββ experiments.External gammas are in fact the dominant background source and they can depositan energy near the Q-value of the 0νββ [50]. Gammas tend to Compton scatter, sothey can produce more multiple energy deposition (multi-site) events than singleenergy deposition (single-site) events. Moreover, even for single-site events, thereare differences between the ionization electron cloud topology produced by gam-mas and beta particles (used instead for 0νββ identification). An additional wayto discriminate gamma particles in LXe is to reconstruct their original position ofenergy-deposition. Gamma rays with an energy comparable to the Q-value of the0νββ decay in fact have an attenuation length in LXe smaller than 8.7 cm [28].This means that a large enough LXe detector would have an inner volume isolatedfrom external gamma rays. Therefore, all gammas interactions that happen closeto the detector edges can be suppressed with fiducial-volume cuts.This last property, usually called self-shielding, is due to the high atomic mass,density and homogeneity of LXe and it is crucial for 0νββ searches with LXeTPCs. It will be used, in addition to the measurement of the cloud charge size, asa powerful background rejection strategy in several next generation xenon basedexperiments. Additionally, it has already been successfully implemented in theEXO-200 experiment, the nEXO precursor.2.4 Double Beta Decay search with the nEXO DetectorThe nEXO detector is based on a Time Projection Chamber (TPC) filled with 5tonnes of liquid xenon (5109 kg) enriched 90% at 136Xe [51]. As shown in Fig. 2.7,it will be the only 0νββ next generation Xe-based detector able to probe the effec-tive Majorana mass down to 15 meV. Additionally, the 5109 kg of LXe are chosento achieve a competitive sensitivity. This last aspect can be easily understood usinga simple estimation based on Eq. 2.20. Requiring a minimum 0νββ event rate of1 event/year and assuming a half life limit of T 0νββ1/2 ≥ 9.7× 1027 years, the total21mass of xenon that is necessary to have to achieve the required event rate is about5000 kg. This simple estimation, based on the law of radioactive decay shows thatonly large mass detectors can achieve a sufficient number of events in the ROI toperform a successful 0νββ search.According to the nEXO baseline design, the nEXO TPC will be a monolithicsingle-phase detector with a completely free volume filled with LXe. This is asignificantly different approach if compared with the design of its precursor: theEXO-200 detector, which instead had an optical transparent cathode in the centreof the TPC used to create the electric field [12], as shown in Fig. 2.10.Figure 2.10: EXO-200 detector. PTFE (Polytetrafluoroethylene) tiles (1) in-stalled inside the field-shaping rings serve as reflectors for the scin-tillation light. The aluminum-coated side of the large-area avalanchephotodiodes platter (2) is visible, as well as the field cage (3), ioniza-tion wires and flexible cables (4) [12].As shown in Sec. 2.2.2 the current most stringent limit on the (0νββ ) de-cay in 136Xe is 10.7× 1025 yr from the KamLAND-Zen experiment, with a cor-responding sensitivity exposure of 504 kg× yr [14]. The diagnostic power of a22LXe TPC allowed the EXO-200 experiment to reach a competitive sensitivity of3.7× 1025 yr with a substantially smaller exposure (178 kg× yr) and xenon mass(200 Kg) if compared with the KamLAND-Zen experiment [15]. A careful selec-tion of the TPC material, with also the intrinsic capability to simultaneously detectsignal and background, will be the primary strength of the nEXO detector follow-ing the same path of its precursor. The nEXO design is in fact conservative andvery few assumptions of material radio-purity were made beyond what was alreadyexperimentally demonstrated and measured with the EXO-200 detector [52].Fig. 2.11 shows a sketch of the nEXO LXe TPC located inside a vacuuminsulated cryostat. A thicker shield will be also obtained with a large water tank,Figure 2.11: Sketch of the nEXO TPC located in the Cryopit at SNOLAB,the Canadian underground science laboratory [2].which acts as an active cosmic-ray veto detector. The location of the nEXO detectoris not yet finalized and, according to the nEXO baseline design, it will be locatedin the Cryopit at SNOLAB, the Canadian underground science laboratory. As amonolithic detector, surface αs and β s can be rejected by a fiducial volume cutafter position reconstruction, as introduced in Sec. 2.3.Decays producing αs inside the LXe bulk can also be easily rejected by alight-to-charge ratio cut, since α events create much denser charge clouds thanelectrons, and therefore a larger amount of scintillation light is produced from re-23Figure 2.12: Sketch of the nEXO TPC [2].combination. Moreover, the self-shielding capabilities of a large detector whoselinear dimensions exceed 1 m are ideal to identify and suppress γ ray backgroundin the energy region of interest (Sec. 2.3).The energy resolution around the Q-value of the 0νββ decay is the crucialparameter in the 0νββ search, since it is the only instrument to effectively separate2νββ decays from 0νββ decays (Sec. 2.2.4). nEXO is designed to optimize thischaracteristic, providing the best possible energy resolution for a LXe TPC witha final design goal of 1% energy resolution (σ/Q) for the 0νββ decay of 136Xe(Q-value at 2458.07±0.31 keV [9]).In order to achieve this objective, the nEXO TPC is designed to read outwith high efficiency both the charge clouds and the light produced by the LXeionization and scintillation, respectively. This will allow it to take advantage of theanticorrelation between the two channels and improve therefore the final energyresolution, as discussed in Sec. 2.3. Fig. 2.12 shows a sketch of the nEXO TPCwith the location of the channels used for the charge and photon detection. Theelectric field in the TPC is created thanks to 58 Field Shaping Rings (FSRs) heldtogether by 24 1.2 meters long sapphire single-crystal rods and spaced by 1.6 cmlong cylindrical spacers [2]. The sapphire rods are held in tension by springs above24Figure 2.13: A close-up view of the TPC anode region showing the charge-collecting anode, the tensioned rods, and the SiPM staves behind thefield cage [6].the anode region. The field is graded from anode to cathode by a set of custom-made, low-mass, low-radioactivity resistors, connected to the FSRs.Charge collection is achieved at the top of the TPC with silica tiles patternedwith crossed metallic strips [6], as shown in Fig. 2.13. Scintillation light is in-stead collected with a large-area array (∼ 5 m2) of VUV-sensitive Silicon Photo-Multipliers (SiPMs). This is a significant difference if compared with the EXO-200 light detection system that was constituted by large-area avalanche photodi-odes [53]. Vacuum Photo-multipliers are in fact too radioactive to be used innEXO. The array of VUV sensitive SiPMs is expected to be located behind thefield-shaping rings [54]. In this way it will be possible to achieve a higher lightcollection efficiency, compared with the EXO-200 detector, in which the large-areaavalanche photodiodes were located behind the anode crossed-wire planes.2.4.1 The nEXO Charge Collection and Readout SubsystemIn nEXO we plan to use a segmented anode composed of an array of tilesfor the readout of the charge produced by the ionization of LXe [6, 55]. Eachtile consists of a dielectric substrate covered with an array of 60 orthogonal metalcharge-collecting strips for the charge collection. Each strip consists of 30 squarepads that are 3 mm across the diagonal and daisy-chained at their corners. Indi-25vidual strips can be read out as an independent channel. A schematic drawing of a10 cm by 10 cm prototype tile with a strip pitch of 3 mm is shown in Fig. 2.14. ThisFigure 2.14: Schematic drawing of a prototype charge collection tile with10 cm edge and 3 mm pitch electrodes [6].prototype tile was already tested in a LXe TPC test chamber, where good agree-ment was achieved between the measured ionization spectrum of a 207Bi sourcerecorded with the tile and the one predicted by simulations [6, 55].The characteristics of the nEXO charge readout subsystem are driven by theobjective to achieve a 1% energy resolution at the decay Q-value. The main contri-bution of the charge subsystem to the overall nEXO energy resolution is, however,not coming from the electron collection and extraction efficiency in LXe (whichgenerally approaches 100%), but instead it mainly depends on the readout elec-tronic noise of the charge channels. Fig. 2.15 shows, for example, the energy reso-lution at 400 V/cm for different readout configurations, as a function of the overallphoton collection efficiency of the nEXO light detection subsystem. As it can beseen the overall energy resolution can be significantly degraded by the electronicnoise in the charge channel (here represented as a function of the readout boardlocation and therefore temperature), while keeping unaltered the charge collectionand extraction efficiency in LXe.2.4.2 The nEXO Light Collection and Readout SubsystemThe readout of scintillation light is crucial to provide a prompt signal at theinteraction time that can be used not only to obtain the best possible energy resolu-26Figure 2.15: Energy resolution as a function of the overall light detection ef-ficiency of the nEXO TPC for a field of 400 V/cm and front-end elec-tronic appropriate for internal (cryogenic) and external (room temper-ature and immediately outside of the cryostat) usage. The curve for theupgraded (Phase-II) EXO-200 detector is also shown for reference [2].tion, but also as trigger for the charge readout channel [51]. This thesis will focuson studying the performances of the candidates photo-detectors that will be used inthe photon-sensor portion of the nEXO experiment. In order to achieve a 1% en-ergy resolution at the Q-value of the 0νββ decay of 136Xe, these photo-detectors,and their readout electronics, need to fulfill strict requirements to not degrade theoverall energy resolution. This last quantity tends in fact to be dominated by fluc-tuations in the scintillation light channel because its detection efficiency is signif-icantly smaller compared with the one achievable with the charge channel, whichgenerally approaches 100% (Sec. 2.4.1).According to the discussion of Sec. 2.3, when a particle deposits energy inLXe, it produces singlet and triplet molecules that decay quickly (∼30 ns) emit-ting 175 nm VUV photons (174.8± 10.2 nm [47]). Simulations show that, whenincluding the photon transport time, 99.9% of scintillation photons arrive at thephoto-detectors within 100-150 ns of the interaction time [2].In nEXO we plan to have a maximum photon-charge integration time afterthe trigger of 1 µs. This will allow not only to collect all the light produced by the27original interaction, but also to fully reconstruct the photo-detector signal, as willbe shown in the next section.2.4.2.1 VUV sensitive SiPMs for light detection in LXenEXO plans to use VUV sensitive Silicon Photo-Multipliers (SiPMs) as photon-sensors for the detection of the 175 nm scintillation light of LXe [56]. In contrastto the widely used Photomultiplier Tubes (PMTs), SiPMs are low-voltage pow-ered, optimal for operation at cryogenic temperatures, and have low radioactiv-ity levels with high gain stability (∼ 106) over the time in operational conditions[16, 57]. For these reasons not only nEXO, but other large-scale low-backgroundcryogenic experiments such as Darkside-20k, are migrating to a SiPM-based lightdetection system [17, 18]. SiPMs consist of an array of tightly packed Single Pho-ton Avalanche Diode (SPAD) acting as an avalanche photodiode that can behavein the Geiger mode regime when the device is reverse biased above a thresholdvoltage (breakdown voltage). In the conventional SiPM design each SPAD is con-nected to a series resistor (called the quenching resistor) that limits the currentflowing during the breakdown and thus ensures that the avalanche current is even-tually quenched [58]. The total charge realised from the SPAD defines the devicegain and it depends on the SPAD capacitance CSPAD and applied bias voltage suchthat Q =CSPADOV. The quantity OV is defined as the over voltage and it is equalto (V −VBD) whereV is the applied bias voltage andVBD is the breakdown voltage,defined as the minimum bias voltage for which an avalanche can be self sustained,i.e. when a pulse is actually produced [59]. When the avalanche current flowsin the quenching resistor it induces a voltage drop on the SPAD itself that bringsthe voltage across the diode back to the breakdown voltage. After the avalancheis quenched the SPAD starts its recharging phase where it slowly returns to theoriginal bias voltage. For a detail electrical characterization of SiPMs we refer thereader to Ref. [60]. An example of a SiPM pulse, that corresponds to the dischargeof one SiPM SPAD is reported in Fig. 2.16. The most important SiPMs char-acteristic is their capability to detect light i.e. their Photon Detection Efficiency(PDE), which represents the combined probability that a photon is absorbed in theactive volume of the device with a subsequently triggered avalanche, i.e. the pro-28time [ns]50 100 150 200 250 300 350 400 450 500Current [A]0123456−10×Temperature:233 [K]163 [K]Figure 2.16: Pulse shape produced by the discharge of one SiPM SPAD fortwo different temperatures (233 K and 173 K) for one SiPM tested fornEXO (Hamamatsu VUV4 MPPC). The complete characterization ofthis device is reported in Chapter 3. The SiPM pulse shape depends onthe SiPM temperature, since the quenching resistor used to quench theavalanche can have a strong temperature dependence [61].duction of a pulse, as shown in Fig. 2.16. Only recently different companies andresearch institutions developed SiPMs with sensitivity extending to the 175 nm re-gion. Fondazione Bruno Kessler (FBK), for example, produced several batches ofVUV SiPMs for the nEXO experiment. Hamamatsu Photonics Inc. also developedfour generations of SiPMs for applications in LXe.In order to guide the discussion about the photo-detector specifications fornEXO, it is necessary to first introduce the SiPM characteristics that define thecontribution of the light detection subsystem to the total nEXO energy resolution.Fig. 2.17 shows the nEXO energy resolution as a function of the overall pho-ton collection efficiency. A requirement of 1% in the energy resolution automat-ically sets a requirement on the overall light detection efficiency of the TPC thatneeds to be bigger than or equal to 3%. It is useful to define the overall lightdetection efficiency of the TPC (called εp) as the product of two quantities, thenEXO detector photon Collection Efficiency (CE), and the SiPM Photon Detection29Figure 2.17: Energy resolution as a function of the overall light detection ef-ficiency of the nEXO TPC for several electric fields [2].Efficiency (PDE).εp ≡ CE×PDE (2.23)The CE is defined as the probability a photon produced randomly in the nEXO de-tector arrives to the SiPM surface; while the PDE represents instead the probabilitythat a photon that is hitting the SiPM surface is subsequently absorbed by the SiPMand triggers an avalanche.Fig. 2.18 shows a simulation of the photon CE (called photon transport effi-ciency in the figure) as a function of the overall reflectivity of Field Shaping Rings(FSR)s and cathode. If we consider a 15% SiPM PDE at the scintillation wave-lengths of LXe, it is necessary to achieve, accordingly to Eq. 2.23, a photon CEof 20%. From Fig. 2.18 this means a ∼ 50% reflectivity of the cathode, anodeand field shaping rings. The value of 15% for the SiPM PDE is considered as thebaseline for the nEXO design. It is a conservative value, but, as it will be shown inChapters 3 and 4, it represents the average PDE achievable by the current genera-tion of VUV SiPMs.In addition to their light detection capabilities, SiPMs suffer from severalsources of intrinsic noise. Dark and correlated avalanche noise are in fact crucialSiPM parameters that can eventually reduce the overall nEXO energy resolution30Figure 2.18: Simulation of the photon Collection Efficiency (CE) of thenEXO TPC as a function of the Field Shaping Rings (FSR)s and cath-ode reflectivity. In the simulation the anode reflectivity was set to50% [2].since they can artificially increase the fluctuations in the number of photons de-tected by the SiPMs.Dark Noise (DN) pulses are charge signals generated by the formation ofelectron-hole pairs due to thermionic or field enhanced processes [62]. The moststringent constraint on the SiPM dark noise rate for the nEXO energy resolutioncomes from the requirement to trigger on scintillation pulses with energy as lowas 500 keV, useful for background rejection strategies, for which a dark noise rate≤ 50 Hz/mm2 is required.Correlated Avalanche (CA) noise is due instead to at least two processes: theproduction of secondary photons during the avalanche in the gain amplificationstage detected in nearby cells; and the trapping and subsequent release of chargecarriers produced in avalanches. The latter process is usually referred to as after-pulsing, while the former is usually called crosstalk. Afterpulse events can triggerthe same cell in which the original avalanche happened multiple times. If we defineas one Photo-electron Equivalent (PE) the charge realized by the discharge of oneSiPM SPAD, the charge realized by one afterpulse event is, on average, smaller ifcompared with the original one PE discharge, since afterpulse events trigger the31cell during its recharging time. The mechanism of detrapping, that is at the basis ofthe afterpulse [63], is, however, a function of the temperature and it is not unlikelyat 163 K to have afterpulses that trigger the original cell several ms after the origi-nal discharge. In this case, the charge realised from an afterpulse event is equal to1 PE, since the original SPAD had enough time to be completely recharged.CrossTalk (CT)s photons produce instead nearly simultaneous avalanches tothe primary one (Direct CrossTalk (DiCT)) or delayed by several ns (DelayedCrossTalk (DeCT)), as shown in Fig. 2.19. Since Crosstalk photons trigger SPADsthat are completely charged, the additional charge realized by a DiCT or DeCTevent is a multiple of one PE, depending on the number of cells discharged [64].In general, the subset of the CAs constituted by afterpulses and delayed crosstalkActiveregionPhotonPrimary PulseReflectionCarrierproductionand diffusionCT-P CT-DDNFigure 2.19: Representation of the noise sources in SiPMs: Dark Noise (DN)and Correlated Avalanche (CA) noise. DN are charge signals gener-ated by the formation of electron-hole pairs due to thermionic or fieldenhanced processes. CA noise is instead mainly due to the produc-tion of secondary photons (called Cross Talk (CT) photons) during anavalanche in the gain amplification stage of one cell detected in nearbycells. Generally CT events are categorized accordingly to the timedifference with respect to the primary discharged cell that originatedthem. If prompt (∼ ps) they are called: Prompt CT (CT-P in the figure);if delayed (∼ ns) they are called Delayed CT (CT-D in the figure).events is named Correlated Delayed Avalanche (CDA)s. Unlike DN events, CAs(and therefore CDAs) are correlated with a primary signal and therefore they arepresent only if an avalanche happens i.e. a SiPM SPAD is discharged with thesubsequent production of a pulse.Independently of the mechanism responsible for their generation, all CAs pro-32Parameter RequirementPhoton Detection Efficiency at 175 nm > 15%Dark Noise Rate < 50 Hz/mm2Relative Fluctuation of the mean number of CA in 1 µs < 0.4Equivalent noise charge < 0.1 PE r.m.sTable 2.1: Requirements for the nEXO light detection subsystem. See textfor explanation.duce an extra charge (measurable in PE) in the nEXO 1 µs acquisition window,therefore artificially increasing the total number of photons detected. Simulationsshow as the contribution of correlated avalanches to the resolution is subdominantwhen the relative fluctuation of the mean number of correlated avalanches per pulseis smaller than 0.4 [2]. This requirement sets a corresponding upper bound on theover voltage since the correlated avalanche rate increases with voltage, as will beshown in Chapters 3 and 4. Table 2.1 summarizes the SiPMs requirements for thejust introduced nEXO light detection subsystem.In addition to the SiPMs requirements, we include in Table 2.1 one more re-quirement to account for the electronic readout noise in the photon channel (Equiv-alent noise charge). In this case we require an electronic noise to be smaller than0.1 PE r.m.s. to be able to detect and then trigger on single photoelectrons whosecharge, by definition, is equal to 1 PE [65]. Figure 2.20 shows the predicted energyresolution including the contribution of the charge and light channel, as a functionof the SiPM over voltage, for one of the SiPMs produced by FBK for the nEXOexperiment and tested in Ref. [1]: the FBK VUV HD 1, with its Low Field (LF)and Standard (STD) version. The most dominant feature of the three curves inFig. 2.20 is the existence of a minimum. Furthermore, the minimum does not co-incide with the largest operational over voltage, which in general results in a worseenergy resolution due to the increase of the SiPM correlated noise. Overall theFBK VUV HD 1 SiPM in its LF version satisfies, at an over voltage roughly be-tween 2 and 3 V, the requirement on the nEXO energy resolution to be smaller orequal to 1% for the 0νββ decay of 136Xe (Q-value at 2458.07±0.31 keV [9])33Figure 2.20: Estimated energy resolution for nEXO as a function of the overvoltage for the FBK VUV HD 1 SiPM in its Low Field (LF) and Stan-dard (STD) version [1].2.4.3 A model for the nEXO Energy ResolutionIn this section we introduce a model for the prediction of the expected energyresolution in nEXO. This model differs from the one used in Ref. [1] to constructFig 2.20. The main difference is the estimation of the correlated avalanche noisecontribution. In [1] CAs are in fact treated as Poisson processes. This approxima-tion is justified at small over voltages, like the ones shown in Fig. 2.20, but tends tounderestimate the contribution of the CAs to the overall energy resolution at highover voltages, as will be shown in Sec. 4.5 of Chapter 4.The model derived in this section is based on the assumption that each recom-bining electron-ion pairs produces an exciton (excited xenon atom) which in turnproduces a photon. The appropriateness of this approximation will be discussedin more details in Sec. 2.4.3.3. More generally, when particles deposit an energyE in LXe, they produce a number of electron-ion pairs and excitons. Some of theelectrons produced in the initial energy deposition, however, can either recombine(depending on the density of the tracks realised by the initial particle), or they canbe lost due to the inefficiency of the extraction electric field (Sec. 2.3). Regardlessof the specific situation, when an electron-ion pair recombines, it produces an exci-ton, which in turn produces a photon. If we denote with r the fraction of recombin-34ing electrons, the maximum number of detectable electrons (nq) and photons (np)for an initial population of ni electron-ion pairs and nex excitons (produced by theinitial energy deposition), can be written asnq = (1− r)ni (2.24)andnp = (nex+ rni) (2.25)respectively.Under these assumptions, it is possible to define a recombination-independentvalueW ≡ Enq+np(2.26)which corresponds to the energy required to create a single quantum of either type(light or charge). Equation 2.26 is independent from the recombination (and there-Figure 2.21: Comparison of the charge yields (a) and light yields (b) mea-sured by the EXO-200 detector with the NEST simulator for γ and βparticles [7, 8].fore from the extraction electric field), since the quantity nq+np is independent ofr, in fact(nq+np) = {(1− r)ni+nex+ rni}= {nex+ni} (2.27)35In addition to these definitions, it is also possible to define the energy required toproduce a single electron-ion pair prior to recombination asWi ≡Eni(2.28)Due to the anti-correlation between the light and charge channel in nEXO (in agree-ment with what was done in EXO-200) E can be decomposed using a rotated en-ergy scale defined as [8]E ∝ {cos(θ)〈Eq〉+ sin(θ)〈Ep〉} (2.29)where 〈Eq〉 and 〈Ep〉 are the mean energy deposited in the charge and light chan-nel, respectively. Here θ represents the rotation angle and it indicates the optimalweighting of the charge and light signals in order to minimize the overall energyresolution.The mean number of quanta (of both types) produced by a single energy depositionof energy E can then be written as〈n〉= 〈E〉W∝ 〈nq〉+ 〈np〉 (2.30)where np =〈Ep〉W and nq =〈Eq〉W . In what follows we will assume that 〈E〉 is equal tothe Q-value of the 0νββ decay in 136Xe (2458.07±0.31 keV [9]) and W equal to11.5±0.5 (syst).±0.1 (stat.) eV [8]. From this it follows that〈n〉= 〈E〉W= 2.14×105 (2.31)The values of np and nq can be derived knowing the decay Q-value and the lightand charge yields (Fig. 2.21). Using for these two quantities the values measuredin EXO-200 (0.037 γeV and 0.050eeV [8]), np and nq follow asnp = 90946 (2.32)nq = 122900 (2.33)36In term of quanta, the relative standard deviation of Eq. 2.30 (also called the energyresolution for the 0νββ decay or optimum estimator) can then be computed asσn〈n〉 =√σ2q +σ2p +2Covq,p+σ2Xe〈n〉 (2.34)where σ2q and σ2p are the variances of nq and np, respectively. The first three termsin Eq. 2.34 follow directly using the theory of error propagation for correlatedquantities. The last term, instead, represents an additional variance that was addedto Eq. 2.34 to include the intrinsic fluctuations in the number of quanta not due torecombination (i.e. some loss due to heat). It can be written asσ2Xe = fXe〈n〉 (2.35)where fXe is defined as the LXe Fano Factor measured to be 0.059 [13] which rep-resents a deviation from the Poisson statistic assumed by Eq. 2.35. More detailsof the LXe Fano Factors can be found in Ref. [66]. Compared to other mecha-nisms (readout charge noise and photon noise) this additional fluctuation can beneglected.2.4.3.1 Light subsystemIn nEXO we plan to use VUV sensitive SiPMs in a photon counting mode.The number of avalanches measured by the SiPMs can be written asnav = (npεp+nDC)(1+ 〈Λ〉) (2.36)where 〈Λ〉 represents the mean number of extra avalanches and nDC representsthe number of Dark Counts (DC) in the acquisition window. np, as introducedin the previous section, is the number of photons produced by the initial energydeposition and it is equal to the maximum number of photon detectable. Note asformally in Eq. 2.36 photon induced avalanches and dark induced avalanches aretreated in the same way, i.e. as random continuous variables. Additionally, εprepresents the total light detection efficiency defined in Eq. 2.23. This quantity willbe assumed constant in what follows.37The number of photons detected can then be defined asnd ≡ npεp (2.37)Using this last equation, Eq. 2.36 can be written asnav = (nd+nDC)(1+ 〈Λ〉) (2.38)and inverted to derive np asnp =nav−nDC(1+ 〈Λ〉)εp(1+ 〈Λ〉)=[ navεp(1+ 〈Λ〉)− nDCεp](2.39)Its variance follows asσ2p =σ2av(εp(1+ 〈Λ〉))2+σ2DCε2p+σ2r (2.40)where: σ2av is the variance of nav; σ2DC is the variance of nDC and σ2r is an additionalterm that accounts for the fluctuation in units of quanta, resulting from recombina-tion. As will be shown in Chapters 3 and 4, the number of dark count events in theacquisition window, as well as its fluctuation, is completely negligible at cryogenictemperatures, therefore Eq. 2.40 can be simplified asσ2p ∼σ2av(εp(1+ 〈Λ〉))2+σ2r (2.41)Error propagation of Eq. 2.38 givesσ2av =(∂nav∂nd)2σ2d +( ∂nav∂ 〈Λ〉)2σ2〈Λ〉+( ∂nav∂nDC)2σ2DC (2.42)withσ2〈Λ〉 =σ2Λ〈nDC〉+ 〈nd〉(2.43)with σ2Λ and 〈Λ〉 the variance and mean of the number of additional avalanches inthe acquisition window and 〈nDC〉+ 〈nd〉 the total number of avalanches detected.38σ2Λ and 〈Λ〉 can be measured from the SiPM dark noise data by constructing ahistogram of the charge of all the pulses within the nEXO acquisition window (thatextends up to 1 µs from the trigger pulse), and scaling it such that the single Photo-electron Equivalent (PE) avalanche charge is equal to one.Assuming: (i) a binomial distribution for the number of photons detected withprobability to be detected equal to εp (σ2d = εp(1− εp)np, 〈nd〉 = npεp) and (ii)a Poisson distribution for the number of Dark Counts events in the acquisitionwindow (σ2DC = 〈nDC〉, 〈nDC〉= nDC), we getσ2av = (1+ 〈Λ〉)2εp(1− εp)np+(〈nDC〉+ 〈nd〉)2σ2〈Λ〉+(1+ 〈Λ〉)2〈nDC〉+η2noise(2.44)The last term in Eq. 2.44, η2noise, accounts for an additional noise contribution dueto avalanches misreconstructed by the photon-readout noise channel. This quantitycannot be calibrated until the photon-readout for nEXO is finalised, and thereforeit will be neglected in what follows.Eq. 2.41 then becomesσ2p =(1+ 〈Λ〉)2εp(1− εp)np+(〈nDC〉+ 〈nd〉)2σ2〈Λ〉+(1+ 〈Λ〉)2〈nDC〉(εp(1+ 〈Λ〉))2+σ2r(2.45)Simplification givesσ2p =(1− εp)npεp+(〈nDC〉+ 〈nd〉)2σ2〈Λ〉(εp(1+ 〈Λ〉))2+〈nDC〉ε2p+σ2r (2.46)Using Eq. 2.43, Eq. 2.46 then becomesσ2p =(1− εp)npεp+(〈nDC〉+ 〈nd〉)σ2Λ(εp(1+ 〈Λ〉))2+〈nDC〉ε2p+σ2r (2.47)The mean number of dark noise events in the acquisition window 〈nDC〉 can beestimated from the dark noise data by measuring the dark noise rate at 163 K andintegrating it for a time length equal to the nEXO acquisition window (1 µs). Itis, however, a sub-dominant contribution, due to the extremely low dark noise rateof SiPMs at 163 K. Therefore, using the same approximation done with Eq. 2.41,39Eq. 2.47 becomesσ2p ∼(1− εp)npεp+〈nd〉σ2Λ(εp(1+ 〈Λ〉))2+σ2r (2.48)The quantity 〈nd〉 = npεp is complicated to measure, since it depends on the to-tal detector light collection efficiency (εp) which can only be estimated with acombination of light propagation simulations in the TPC (for the light CollectionEfficiency (CE)) and SiPM Photon Detection Efficiency (PDE) measurements at175 nm.2.4.3.2 Charge subsystemThe contribution of the charge subsystem to the overall nEXO energy resolu-tion can be derived with the same approach introduced in the previous section. Inparticular, the number of charges detected ndq can be written asndq = εqnq (2.49)where εq is the charge collection efficiency. From this follows thatnq =ndqεq(2.50)Assuming binomial statistics for the number of detected charges with probabilityto be detected equal to εq, we getσ2q =(1− εq)nqεq+σ2q,noiseε2q+σ2r (2.51)where σ2q,noise accounts for the noise contribution in the charge channel and σ2r isthe variation in units of quanta in the charge channel due to recombination fluctu-ations. The charge collection efficiency is assumed to be function of the drift timet such that εq = e− tτ with t = l/v (l = 0.65 m and v = 2 mm/µs [2]). The elec-tron lifetime τ depends on the xenon purity and it is set in this model to be 10 ms,accordingly to the nEXO baseline design [2]. Overall these parameters bring to40a charge collection efficiency of εq = 0.97 %. Finally, the noise contribution inthe charge channel, which depends on the design of the pixel pitch, is predicted tobe ∼ 1100 e−[2].2.4.3.3 Expected nEXO energy resolutionIn Sec. 2.4.3 we assumed perfect anticorrelation between the light and chargechannels, such that every recombined electron generates a VUV photon. Withthis assumption we derived Eq. 2.51 and Eq 2.48 introducing in both equations aterm σ2r that represents the recombination fluctuation for the two channels. Withthe same assumption it follows that the covariance between the two channels inEq. 2.34 is simply Covq,p =−σ2r .This assumption was tested by the EXO-200 collaboration in Ref. [8] and it wasfound to be true with a recombination efficiency equal to 97%. In other words,a recombined electron generates a VUV photon in 97% of the cases. Due to theexcellent agreement of the EXO-200 data with this assumption, in the nEXO esti-mation of the energy resolution we will assume that this condition holds true at alltimes. If we substitute the contribution of the light channel (Eq. 2.48) and chargechannel (Eq. 2.51) in Eq. 2.34, we can derive an estimation of the energy resolutionas followsσn〈n〉 =√((1−εp)npεp+ 〈nd〉σ2Λ(εp(1+〈Λ〉))2+σ2r)+((1−εq)nqεq+σ2q,noiseε2q+σ2r)−2σ2r〈n〉(2.52)Simplification givesσn〈n〉 =√((1−εp)npεp+ 〈nd〉σ2Λ(εp(1+〈Λ〉))2)+((1−εq)nqεq+σ2q,noiseε2q)〈n〉(2.53)This last equation will be used in Chapter 4 for the estimation of the expectednEXO energy resolution using all the measurements done in Chapters 3 and 4 ofthis work for two SiPMs candidates for nEXO: the Hamamatsu VUV4 MPPC andthe FBK VUV HD 3 SiPM.412.5 ConclusionsIn this chapter we introduced the main motivation behind the need for a 0νββsearch. We also introduced liquid xenon (LXe) as an attractive candidate for thistype of physics, since it not only serves as the source of the decay, but also asits detector. Moreover its anticorrelation and self shielding properties allow us toimplement extremely precise particle identification and background suppressiontechniques that are crucial for a low background cryogenic experiment. In the sec-ond part of the chapter we introduced the nEXO experiment that will be one ofthe most promising candidates to perform a successful 0νββ search, allowing usto probe the effective Majorana mass down to 15 meV. We also introduced the re-quirement of the nEXO charge and light subsystem. The next two chapters of thisthesis will focus on the nEXO light detection subsystem. In particular they willshow the characterization of several SiPM photocandidates for the nEXO experi-ment, comparing their performance against the nEXO requirements, summarised inTable 2.1. Custom setups were built at TRIUMF specifically to test these devices.A significant part of the next two chapters will therefore be devoted to explain theirconstruction. Finally, at the end of Chapter 4, we will use all the measurementsof Chapters 3 and 4 to estimate the contribution of the tested SiPMs to the overallnEXO energy resolution, using the model introduced in Sec. 2.4.3 of this chapter.42Chapter 3Characterization of theHamamatsu VUV4 MPPCs fornEXO3.1 IntroductionSilicon Photo-Multipliers (SiPMs)1 have emerged as a compelling photo-sensorsolution over the course of the last decade [57]. nEXO aims to probe the boundariesof the standard model of particle physics by searching for neutrino-less double betadecay (0νββ ) of 136Xe [10].The requirements of the photo-sensor portion of the nEXO experiment aresummarised in Table 2.1. More precisely, the VUV SiPMs that will be used innEXO and their readout electronic must meet the following requirements [2]: (i)Photon Detection Efficiency (PDE) greater than 15% for light at 174.8±10.2 nm(scintillation light in liquid xenon [47]), (ii) relative fluctuation of the mean numberof correlated avalanches per pulse (within a time window of 1 µs after the triggerpulse2) below 0.4, (iii) dark-noise rate lower than 50 Hz/mm2, (iv) electronic noise(equivalent noise charge) smaller than 0.1 Photo-electron Equivalent (PE) r.m.s.1This chapter was published in [54] and [67]. Its content was adapted to fit the thesis structure.2In nEXO, the maximum charge integration time after the trigger will be 1 µs, as introduced inChapter 2.43According to the discussion introduced in Chapter 2, the first three requirementsare in fact sufficient to achieve an energy resolution of 1% for the (0νββ ) decayof 136Xe. In Fig. 2.20, it was shown that these requirements could be met withFBK VUV HD 1 SiPMs developed by Fondazione Bruno Kessler (FBK, Trento,Italy) for nEXO. The aim of this chapter is to assess the performance of HamamatsuVUV4 Multi-Pixel Photon Counter (MPPC) (S/N: S13370-6152) developed forapplication in liquid xenon as a possible alternative solution to FBK SiPMs. Thedevices tested have a micro-cell pitch of 50 µm and an effective photosensitive areaof 6× 6 mm2. Similar characterizations for the same generation of HamamatsuVUV4 devices, but with different series, can be found in [16, 68].3.2 Experimental Details3.2.1 Hardware SetupA setup was developed at TRIUMF to characterize the response of SiPMs atVUV wavelengths, as illustrated in Fig. 3.1. The measurement setup is installed ina dark box, kept under constant nitrogen gas purge and mounted on an optical plat-form. Humidity was monitored constantly with a HH314A Omega controller [69].Light from a Hamamatsu L11035 xenon flash lamp [70] shines through: (i) a 1 mmdiameter collimator, (ii) a VUV diffuser (Knight optical DGF1500 [71]) and (iii)a CaF2 lens (eSource optic CF1220LCX [72]). The diffuser is placed at the focalpoint of the lens in order to uniformly illuminate the lens and to produce a parallelbeam. The whole assembly is housed in a Radio-Frequency (RF) copper box (RFShield #1 in Fig. 3.1) to shield against electromagnetic emissions from the lamp.Additionally, the VUV light passes through a set of bandpass filters, used to selectthe desired portion of the lamp emission spectrum and a second 1 mm diameter col-limator, close to the SiPM surface (Sec. 3.2.2). Prior to filters and collimator, thelight beam passes through a beam splitter, allowing to simultaneously illuminatethe VUV4 MPPC and a Newport 918D-UV-OD3 Photo-Diode (PD) [73], used tomonitor the xenon flash lamp light stability. The SiPM is mounted inside a secondRF shielding copper box (RF Shield #2 in Fig. 3.1) placed on a movable opticalarm which allows for remote positioning of the SiPM in the x-y plane. A liquid ni-44trogen controlled cold finger adjusts the temperature of the SiPM down to 163 K3.An additional UV-sensitive R9875P Hamamatsu PMT [70] is also mounted on thex-y stage and used during PDE measurements to calibrate the absolute light fluxat the location of the SiPM. The SiPM and PMT can be interchanged remotely.A CAEN DT5730B Digitizer [74] and a Maximum Integrated Data AcquisitionSystem (MIDAS)-based control system [75], are used for signal digitalization andconstitute the Data AcQuisition System (DAQ) of the current setup. The SiPMsignal is amplified by two MAR6-SM+ amplifiers in series [76]. The acquisitiontrigger module, the PD controller, the filters controller, the x-y stage controller, thePMT and the SiPM power supply are all placed outside the dark box.3.2.2 Light Filtering SchemeA set of 4 narrow bandpass filters with transmission nominally centered at180 nm selects the desired portion of the lamp emission spectrum and attenuatesthe xenon flash lamp light intensity. Two of the filters are 25180FNB from eSourceOPTICS [72] and two are 180-NB-1D from Pelham Research Optical LLC [77].The typical peak transmission of these filters at 180 nm is on the order of 20%.In order to establish the transmitted wavelength distribution, each filter was char-acterized using a VUV spectrometer (Resonance TR-SES-200 [78]). The filteredspectrum is shown in Fig. 3.2. It has a mean wavelength of 189 nm and a FullWidth Half Maximum (FWHM) of 13 nm.3.2.3 Beam Position MappingThe VUV4 MPPC and the PMT, used for absolute light calibration, have dif-ferent Photosensitive Area (PA)s of 6× 6 mm2 and 50.24 mm2, respectively. Forthe PDE calculations it is usually necessary to normalize SiPM and PMT measure-ments by their photosensitive areas. This correction can be neglected if the crosssection of the impinging beam is smaller than the SiPM and PMT photosensitiveareas. To verify this condition, the collimated light beam was mapped with respectto the surface of both photon-sensors. Particular attention was devoted to the SiPMBeam map, since the SiPM represents the smaller of the two sensors. The beam3The temperature stability was found to be ±1 K.45Figure 3.1: Hardware setup used for the characterization of the HamamatsuVUV4 MPPC.map of the SiPM is shown in this section while the beam map of the PMT is in-troduced in Sec. 3.3.5. In both cases the beam map was achieved by moving theSiPM (or the PMT) in the x-y plane (Fig. 3.1) in increments of 0.5 mm, and bymeasuring (noise subtracted) the counting rates detected by the device at each po-sition. A typical beam-map for the SiPM is shown in Fig. 3.3. To size the diameterof the beam: dBEAM, at the SiPM and PMT location, the x and y projections of the46Figure 3.2: Filtered xenon flash lamp spectrum measured after application ofthe 4 VUV filters. The shoulder effect around 190 nm is due to thecombination of the original xenon flash lamp spectrum and the differentfilters transmissions.beam map are compared with a Monte-Carlo model (MC). Based on the collima-tor size and shape described in Sec. 3.2.1 and Fig. 3.1, the beam map should bethe convolution between a circular beam and a square SiPM whose response in theMC model is assumed uniform across its surface. Different x and y profiles werecreated by letting dBEAM float, and a likelihood method was used to determine thecombination that best fits the data, shown in Fig. 3.4. The best fit beam diameterat the SiPM (or PMT) location is 1.2 ± 0.2 mm. This result confirms that: (i) thebeam cross-section is smaller than the SiPM and PMT photon-sensitive areas andtherefore an area correction can be neglected during efficiency measurements, (ii)the SiPM response is uniform across its surface.3.2.4 Collected Data and Trigger ConfigurationsThe VUV4 MPPC characteristics, as a function of the temperature, were in-vestigated in the range 163 K ≤ T ≤ 233 K. The collected data can be dividedinto two types: dark data, where the SiPM was shielded from any light source,and xenon flash lamp data. For dark measurements (Sec. 3.3.2, Sec. 3.3.3 andSec. 3.3.4) the SiPM copper box (RF shield # 2 in Fig. 3.1) was closed, enabling47Figure 3.3: Position mapping of the VUV beam at the SiPM location. TheSiPM was moved in the x and y coordinates of Fig. 3.1 at increments of0.5 mm in each direction.data-collection at temperatures below 233 K. The DAQ system was set to triggeron individual SiPM pulses with a DAQ threshold above the noise. For each trig-ger, the DAQ saves the event with a total sample window of 20 µs, split into 4 µsof pre-trigger and 16 µs of post-trigger samples. The long post-trigger window isnecessary in order to measure delayed correlated pulses, while the long pre-triggerwindow ensures that no tail from previous pulses persists. Dark data were col-lected at different temperatures and over voltages. For xenon flash lamp data (PDEmeasurements in Sec. 3.3.5), the DAQ was externally triggered by pulses from awaveform generator which also fired the xenon flash lamp. Furthermore, the SiPMRF shielding box was opened, allowing light to reach the SiPM. PDE measure-ments were performed at 233 K to prevent residual water vapour condensation.The external trigger had a frequency of 500 Hz.48Figure 3.4: Comparison between the measured beam map x-y projections(Blue) and the Monte Carlo model (Red) for the x-projection (Top) andy-projection (Bottom) of the beam map of Fig. 3.3. The beam diameterwas estimated to be 1.2±0.2 mm at the SiPM and PMT location, indi-cating that the beam cross-section is smaller than the SiPM and PMTphoton-sensitive surface area. The χ2 test for the two projections givesrespectively a χ2/NDF of 1.48 for the x projection and a χ2/NDF of1.24 for the y projection where NDF is the Number of Degree of Free-dom. The biggest deviation between the model and the measurementsis evident for points at the edge of the SiPM, where the relative errorof the measurement increases due to a worsening of the signal to noiseratio.493.3 Experimental Results3.3.1 Signal Pulse Fitting ProcedureThe collected dark data were analyzed at the pulse level in order to resolve in-dividual PE pulses. A ROOT-based [79] waveform analysis toolkit was developed,similar to the one reported in [80]. See Fig. 3.5.Figure 3.5: Schematic representation of the waveform analysis toolkit devel-oped for this study. See text for a detailed explanation.The implemented algorithm relies on a χ2 minimization to identify and fitSiPM pulses. The Single Avalanche Response Function (SARF) was parametrizedusing the following equation, which accounts for the presence of two time con-stants in the SiPM pulse shape [60]:V (t) = A×[1− kτS(e−t−t0τS+τR − e−t−t0τR)++kτL(e−t−t0τL+τR − e−t−t0τR)] (3.1)where: τR is the pulse rise time, A is the pulse area (proportional to the pulsecharge, see Sec. 3.3.2), t0 is the pulse time, τS and τL are the short and longpulse fall time constants, respectively. k is the relative contribution of the two falltime components in the SiPM pulse shape: 0 ≤ k ≤ 1. For each over voltage andtemperature the collected dark pulses were fitted in a multistage algorithm. First,a pulse-finding algorithm identifies and fits single avalanche pulses to extrapolatethe average SARF parameters (τR,τS,τL and k), according to Eq. 3.1. The SiPMpulse shape is then set by fixing these parameters to their estimated average values.Finally, a second fit iteration is performed with fixed pulse shape to improve theestimation of pulse time and area. For fits exceeding a certain threshold of reducedχ2, test pulses are added iteratively to the fit. The new pulse combination is kept50permanently if the reduced χ2 of the new fit improves significantly. Else, the testpulses are discarded. The last step of the algorithm improves the capability toidentify overlapping pulses (more details in [81]). As an example, we report inFig. 3.6 the charge distribution of first pulses following single PE primary pulses(also called trigger or prompt pulses) as a function of the time difference withrespect to their primary pulse recorded at T=163 K and for an over voltage of5.1±0.2 V.Figure 3.6: Charge distribution (normalized to the average charge of 1 PEpulses) of first pulses following single PE trigger pulses as a function ofthe time difference with respect to (wrt) their primary pulse for T=163 Kand for an over voltage of 5.1± 0.2 V. The grey scale represents thenumber of events in each bin on a logarithmic scale. The solid red lineshows a fit of the afterpulsing events and is used to measure the recoverytime of one cell, equal to 35±4 ns.3.3.2 Single PE Gain and Breakdown Voltage ExtrapolationSingle PE dark pulses were used to measure the single PE SiPM gain as afunction of the SiPM temperature. The single PE (amplified) pulse charge Q canbe defined as:Q≡(IDR214)×(A1 PE×10−9R)(3.2)51Figure 3.7: Measured single PE gain (Eq. 4.3) as a function of the over volt-age for different SiPM temperatures.where: IDR is the Input Dynamic Range of the digitizer (0.5 V), A1 PE is the av-erage area (Eq. 3.1) of the fitted digitizer signals for 1 PE pulses (measured inLSB× ns [74]), and R is the amplifier load resistance (R=50 Ω). Therefore, thesingle PE (un-amplified) gain G1 PE can be extracted from Q using the followingequation:G1 PE =QgAMP×qE(3.3)where gAMP is the gain of the amplifier (measured to be 142± 2)4 and qE is theelectron charge. In agreement with [82], the gain was found to increase linearlywith the bias voltage V with a measured gradient of (72.4± 3.7)× 104 1V . Fromthe single PE gain it is possible to extrapolate the single PE (un-amplified) chargedefined as Q1 PE ≡ qE × G1 PE. The single PE (un-amplified) charge, as a functionof the bias voltage, was then linearly fitted as Q1 PE =CD× (V −VBD), in order toextract: (i) the single SiPM cell capacitanceCD and (ii) the Breakdown VoltageVBDdefined as the bias voltage at which the SiPM single PE gain (or charge) is zero.4The amplifier gain was computed by applying a step voltage to a precision capacitor in orderto inject a known charge into the SiPM amplifier input (i.e. QIN). The output charge was thencomputed from the digitized amplifier output waveform (i.e. QOUT). The amplifier gain follows asthe ratio between the final integrated charge and the input known charge as gAMP =QOUTQIN.52The breakdown voltage is found to linearly depend on the SiPM temperature with ameasured gradient of 50±2 mVK . At 163 K it is measured to beVBD = 44.9±0.1 V.The average cell capacitance, extrapolated from the fit, is CD = 116±6 fF with noobserved temperature dependence in the analyzed temperature range. Moreover,the total SiPM capacitance was measured using a capacitance meter (Wayne Kerr6440B [83]), with an extracted single cell capacitance of CD = 104± 10 fF. Thegain measurements are shown in Fig. 3.7 as a function of the over voltage fordifferent SiPM temperatures.3.3.3 Prompt Pulse Charge DistributionThe pulse-charge distribution was studied using dark data and prompt pulses5with the SiPM set at different over voltages and temperatures. The single (andmulti) PE charge response of prompt pulses follows the shape of a Gaussian dis-tribution, where the width of the distribution corresponds to the charge resolutioncombination of the electronic noise and SiPM gain fluctuations. However, we haveobserved that all the charge peaks show a shoulder-like component to the right ofthe expected Gaussian charge distribution. This feature is observed to be highlydependent on over voltage, as shown in Fig. 3.8 for T = 233 K and 163 K. Theshape of the shoulder and its dependence on over voltage were further investigated.We observed that the shape of the pulses which are contributing to the shoulder isconsistent with that of single PE with a higher integrated charge. Based on theseobservations, this feature could arise from fast (<4 ns) correlated avalanches (af-terpulse) which do not get resolved from their parent primary pulse by the DAQsystem. This effect could also be explained by a discrepancy in gain betweenmicro-cells in the device.3.3.4 Noise AnalysisDark Noise (DN) and Correlated Avalanche noise (CA) are among the cru-cial parameters that characterize SiPMs. We refer the reader to Chapter 2 for adetailed explanation of the different sources of noise in SiPMs. The DN rate of theHamamatsu VUV4 MPPC as a function of the applied over voltage for different5We define prompt pulse as the first SiPM pulse in each waveform recorded by the DAQ53Figure 3.8: Charge distribution for prompt pulses obtained using dark datafor different SiPM temperatures and over voltages (Top: T=233 K. Bot-tom: T=163 K). All the charge peaks show a shoulder-like componentto the right of the expected Gaussian charge distribution. This featureappears to be highly dependent on the over voltage.SiPM temperatures, is presented in Sec. 3.3.4.2. The subset of the CAs constitutedby afterpulses and Delayed CrossTalk events (DeCT) is named Correlated DelayedAvalanches (CDAs). In nEXO the maximum charge integration time after the trig-ger pulse will be 1 µs. The number of CAs and CDAs per primary pulse in this timewindow as a function of the applied over voltage for different SiPM temperatures,is reported in Sec. 3.3.4.1 and Sec. 3.3.4.2, respectively. Direct CrossTalk (DiCT)is discussed in Sec. 3.3.4.3. It is worth recalling that the SiPM noise was studiedusing dark data, taken with the SiPM shielded from any light source (Sec. 3.2.4).543.3.4.1 Number of Correlated Avalanches per PulseIn order to reach the nEXO design performance, the relative fluctuation of themean number of CAs per primary pulse must be below 0.4, within a time windowof 1 µs after the primary pulse. A higher value would result in worsened energyresolution. The average number of CAs per pulse is measured by directly con-Figure 3.9: Histogram of the baseline subtracted integral of collected darkwaveform for an over voltage setting of 5.1± 0.2 V and a temperatureof 163 K. Each waveform recorded by the DAQ is integrated in therange [0-5]µs. The trigger pulse is at 4µs and no pulses are present inthe pre-trigger region ([0-4]µs). The edge next to the 1 PE Gaussianpeak is a combination of shoulder-like events (as reported in Fig. 3.8)and waveform with after-pulses.structing a histogram of the baseline subtracted integral of collected dark waveformin the range [0−5] µs and normalizing it to the average charge of 1 PE pulses, asdiscussed in [1] (An example is reported in Fig. 3.9). In the absence of correlatednoise, the mean of this histogram should be exactly 1. However, each avalanche hasa non-zero probability of being accompanied by correlated avalanches causing themean of the waveform integral histogram to be larger than unity. The excess fromunity can be then used to measure (in unit of PE) the average number of CAs perpulse in the 1 µs interval after the trigger pulse: 〈Λ〉. The 〈Λ〉 number is reported inFig. 3.10, for different SiPM temperatures and over voltages. At low over voltages55over voltage [V]0 1 2 3 4 5 6 7 8s [PE]µnumber of CAs in 100.20.40.60.811.21.41.61.82Temperature:233 [K]213 [K]193 [K]178 [K]163 [K]FBK-LF #1FBK-LF #2Figure 3.10: Number of Correlated Avalanches (CAs) per primary pulsewithin a time window of 1 µs after the trigger pulse as a function of theapplied over voltage for different SiPM temperatures. FBK-LF #1 and#2 are instead the number of CAs per pulse, always in a time windowof 1 µs after the trigger pulse for two FBK-LF SiPMs.〈Λ〉 doesn’t show an evident temperature dependence; a minor deviation is, how-ever, observed at higher over voltages. Similar trends are reported for other SiPMsby other investigations [84]. For comparison, in Fig. 3.10 we have also reportedthe average number of CAs for two FBK VUV HD 1 SiPM (called FBK-LF #1 andFBK-LF #2 in figure due to their fabrication technology, as shown in Chapter 2),characterized in [1]. The Hamamatsu VUV4 has a considerably lower 〈Λ〉 thanFBK-LF. For reference, at T=163 K and at 3.1±0.2 V of over voltage we measure〈Λ〉 = 0.161±0.005 for the Hamamatsu VUV46, while the FBK LF #1 and #2 atT = 163 K and 3.26 V and 3.17 V have a 〈Λ〉 equal to 0.39 and 0.33, respectively.Fig. 3.11 shows instead the Root Mean Square (RMS) (often called standard de-viation) of the number of correlated avalanches per primary pulse within a timewindow of 1 µs after the trigger pulse (i.e. σΛ), as a function of the applied overvoltage, for different SiPM temperatures. Differently from Fig. 3.10, in Fig. 3.11we couldn’t include the RMS error of the FBK LF data, since in [1] it was only63.1± 0.2 V is the closest measured points for which the requirement on relative fluctuation ofthe number of CAs in 1 µs is satisfied. At this over voltage and temperature the electronics noisewas measured to be 0.064 PE.56over voltage [V]0 1 2 3 4 5 6 7 8s [PE]µRMS in 100.511.522.5Temperature:233 [K]213 [K]193 [K]178 [K]163 [K]Figure 3.11: Root Mean Square Error (RMS) of the number of CorrelatedAvalanches (CAs) per primary pulse within a time window of 1 µsafter the trigger pulse as a function of the applied over voltage fordifferent SiPM temperatures.reported the mean number of correlated avalanches in 1 µs, without any additionalinformation of the data RMS error. The high values in Fig. 3.11 show as there is asignificant amount of fluctuations in the number of correlated avalanches betweendifferent events. For instance at 163 K and at 3.1±0.2 V of over voltage the meannumber of correlated avalanche is 〈Λ〉 = 0.161± 0.005, while its RMS error is0.46±0.01. Fig. 3.12 reports the relative fluctuation of the number of CAs in 1 µsat 163 K, useful for nEXO operation, defined asRatio≡ σΛ1+ 〈Λ〉 (3.4)In order to meet the nEXO requirements (Sec. 3.1), the Hamamatsu VUV4 canbe operated at T=163 K up to about 3.2 V of over voltage keeping the relativefluctuation of the number of CAs in 1 µs smaller than 0.4. For reference at 3.1±0.2 V of over voltage we measure a relative fluctuation of the mean number of CAsin 1 µs equal to 0.39±0.01.57Over Voltage [V]1 2 3 4 5 6 7 8Ratio [#]00.20.40.60.81Figure 3.12: Relative fluctuation of the number of CAs in 1 µs measured at163 K and derived with Eq. 3.4 from the data of Fig. 3.10 and Fig. 3.11.3.3.4.2 Dark Noise Rate and Number of Correlated Delayed Avalanches perPulseDN and CDAs events can be distinguished by studying the time distribution ofevents relative to the primary pulse using a method, described in [85], that requiresthe charge of the primary pulse to be a single PE equivalent. The observed pulserate R(t) is then computed as a function of the time difference t from the primarypulse (t = 0) as:R(t) = RDN(t)+RCDA(t) (3.5)where RDN is the rate of dark noise pulses and RCDA is the rate of the CDAs perpulse. An example of the measured time distribution for a given over voltage andfor two different temperatures is reported in Fig. 3.13. The DN rate can then beestimated from Fig. 3.13, performing a weighted mean of the asymptotic rate atlong times7. The measured DN rates, for different SiPM temperatures, are shownin Fig. 3.14 as a function of the over voltage. For the same temperature and OVsetting reported in Sec. 3.3.4.1 (163 K, 3.1±0.2 V of OV), the DN rate is measuredto be 0.137± 0.002 Hz/mm2, which satisfies nEXO requirements (Sec. 3.1). By7Each point in the mean was weighted with its error derived as reported in [85].58Figure 3.13: Observed pulse rate R(t) normalized by the SiPM photon sensi-tive area as a function of the time difference with respect to (wrt) theprimary pulse for a temperature of 163 K (5.1± 0.2 V of over volt-age) (Blue) and 233 K (5.7±0.2 V of over voltage) (Red). At 233 K,to avoid ADC dead time corrections due to the high self trigger DNrate, the time differences were computed only between pulses insidethe same DAQ window (maximum time difference: 16µs)applying Eq. 3.5 to the observed pulse rate (e.g. Fig. 3.13), it is possible to computethe expected number of CDAs per pulse in a fixed time window of length ∆t afterthe trigger pulse as:NCDA(∆t) =∫ ∆t0(R(t)−RDN(t))dt (3.6)where RDN is the measured DN rate as reported in Fig. 3.14. The measured averagenumber of CDAs per pulse in the 1 µs window after the trigger pulse, for differentSiPM temperatures and over voltages is reported in Fig. 3.15. For 163 K and 3.1±0.2 V of OV, the average number of CDAs per pulse in 1 µs is 0.178± 0.003.Finally, it is worth noting that the number of CDAs, extrapolated in this section,cannot be compared directly with the number of CAs (Sec. 3.3.4.1). The number ofCDAs is in fact derived, accordingly to [85], considering only the time differencesof delayed events with respect to their primary pulse while the number of CAsaccounts instead also for their different charge.59Figure 3.14: Dark Noise (DN) rate normalized by the SiPM photon sensi-tive area as a function of the applied over voltage for different SiPMtemperatures.3.3.4.3 Number of Additional Prompt AvalanchesBased on the measured dark noise rate reported in Sec. 3.3.4.2, and assumingPoisson statistics, the probability of having two dark noise pulses occurring withinfew nano-seconds is negligible. Therefore, the collected dark data can be used toinvestigate Direct CrossTalk (DiCT). DiCT occurs when photons generated duringa triggered avalanche in one micro-cell promptly travel to the amplification regionof neighboring micro-cells, where they induce a secondary avalanche. This mech-anism happens over pico-seconds [64] and it mimics a multiple PE signal, thusbiasing the photon counting ability of the device. The charge distribution of theprompt pulses obtained from the dark data (Sec. 3.3.3) can be used to determinethe mean number of Additional Prompt Avalanche (APA)s, NAPA, due to DirectCrossTalk :NAPA =1NN∑i=1AiA1 PE−1 (3.7)where Ai is the charge of the prompt pulse i (Sec. 3.3.1), A1 PE is the averagecharge of 1 PE pulses and N is the number of prompt avalanches analyzed. TheNAPA number, in unit of PE, as a function of the over voltage and for different SiPM60Figure 3.15: Number of Correlated Delayed Avalanches (CDAs) per primarypulse within a time window of 1 µs after the trigger pulse as a functionof the applied over voltage for different SiPM temperatures.temperatures, is reported in Fig. 3.16. For 163 K and for 3.1 ± 0.2 V of OV wemeasure a mean number of additional prompt avalanches, due to direct CrossTalk,equal to 0.032±0.001. The small amount of NAPA can also be understood lookingat Fig. 3.6 and Fig. 3.9 where 3 PE events are greatly suppressed.Figure 3.16: Number of Additional Prompt Avalanches (APAs) as a functionof the over voltage for different SiPM temperatures.613.3.5 Photon Detection EfficiencyTo meet nEXO requirements, the SiPM PDE must be ≥ 15% for liquid xenonscintillation wavelengths (174.8± 10.2 nm [47]). In this chapter, the PDE wasmeasured using a filtered pulsed xenon flash lamp enabling measurements freefrom correlated avalanches [58]. As shown in Sec. 3.2.2, the mean wavelengthafter filtering is 189± 7 nm. The generated flash pulse has a width ∼ 1µs, whichprevents room temperature measurements, as the dark noise would overwhelm thelight signal. For this reason, PDE data were taken with the SiPM temperatureset at 233 K. The PDE was measured using an experimental technique similar tothe one described in [58]. The light flux was assessed using a calibrated PMT(Sec. 3.2.1) with no corrections applied for the different photosensitive areas of thetwo devices (Sec. 3.2.3). The average number of photons detected by the SiPM(µSiPMγ ) was measured by counting the number of lamp flashes in which no pulseswere detected (N0). Using Poisson statistics µSiPMγ can be expressed as:µSiPMγ =− ln(N0NTOT)−µDN (3.8)where NTOT is the total number of lamp flashes. This method is independent ofcorrelated avalanches and it requires only correcting for the average number ofdark noise pulses in the trigger window (µDN). The same analysis was applied tothe reference PMT (Hamamatsu R9875P, Sec. 3.2.1) in order to measure the av-erage number of photons detected by the PMT (µPMTγ ) and then extrapolate, usingthe PMT Quantum Efficiency (QE) and Collection Efficiency (CE), the effectivenumber of photons produced by the pulsed xenon flash lamp at the SiPM and PMTsurface: Nγ . The PMT QE expresses the probability of photon-electron emissionwhen a single photon strikes the PMT photocathode [86]. The QE reported byHamamatsu for this phototube is 16.5±2.1 %. The PMT CE expresses the proba-bility that the generated photon-electron will land on the effective area of the firstPMT dynode and start the amplification process [86]. The CE of this phototubewas determined by Hamamatsu to be 71% without any estimate of the uncertainty.The PMT Beam map is reported in Fig. 3.17. Conservatively, in agreement withthe discussion done in Sec. 3.2.3 and with [1], we assume a 10 % error for theCE of this PMT (i.e. 71± 10 %) to account for the non-uniformity of the photon62collection at the photo-cathode. The number of incident photons Nγ on the PMTx [mm]0 1 2 3 4 5 6 7 8 9 10y [mm]024681012Intensity [a.u.]05001000150020002500Figure 3.17: Position mapping of the VUV beam at the PMT location. ThePMT was moved in the x and y coordinates of Fig. 3.1 at incrementsof 0.5 mm in each direction.surface can then be obtained as:Nγ =(µPMTγCE×QE)(3.9)The SiPM PDE is in turn obtained as:PDESiPM =(µSiPMγNγ)(3.10)The measured PDE as a function of the over voltage is shown in Fig. 3.18 for twodifferent VUV4 devices labelled VUV4 #1 and VUV4 #2. VUV4 #2 is the de-vice for which DN, CAs, CDAs and APAs are reported in the previous sectionsof this chapter. The measured saturation PDE for VUV4 #2 and VUV4 #1 are14.8± 2.8% and 12.2± 2.3%, respectively. Both values are well below the 24 %saturation PDE advertised by Hamamatsu [87]. For comparison, we measured thePDE of one FBK LF (FBK LF # 3 in Fig. 3.18), for which the saturation PDE was63measured to be 22.8±4.3%, in agreement with [1] (FBK-LF #1 and #2 in Fig. 3.18,see Sec. 3.3.4.1). It is important to mention that different sources of systematic un-certainty were considered and investigated for this measurement. The PMT gainstability was found to be a negligible source of uncertainty. The stability of thelight flux, monitored with a photo-diode (Sec. 3.2.1), was also found to have anegligible effect, with fluctuations within 1 %. The dominant source of systematicuncertainty is therefore the uncertainty on the PMT CE. We conclude this sectionby interpreting the results of the PDE measurement in the context of the nEXOexperiment. There are three main differences between the experimental conditionof this study and the nEXO environment: (i) wavelength, (ii) angle of incidence ofthe light, and (iii) temperature. Firstly, as shown in Sec. 3.2.2, the filtered wave-length distribution is about 10 nanometers higher than liquid xenon scintillation. In[87] Hamamatsu reports little wavelength dependence in this range. Secondly, asshown in Sec. 3.2.3, the angular distribution of photons at the SiPM location in theTRIUMF setup is normal to the SiPM surface. This is not the case for nEXO, forwhich preliminary GEANT4 optical simulations [88] show an average deviationfrom a normal distribution at the SiPM surface. The photon detection efficiencyis likely to be lower at higher incidence angles due to increased reflectivity [58].Finally, as explained in Sec. 3.2, the VUV4 PDE is measured at 233 K instead ofliquid xenon temperature, which may affect the total PDE [89, 90]. Measurementsof SiPM reflectivity to VUV light as a function of photon incident angle and wave-length are being planned with new setups properly customized to perform PDEmeasurements down to 163 K, as the one introduced in Chapter 4 of this thesis.These custom setups will allow us to measure the VUV4 PDE in conditions closerto those in nEXO. A lower systematic uncertainty on the VUV4 PDE will be alsoachieved substituting the calibrated Hamamatsu PMT with a calibrated NIST pho-todiode, as it will be shown in Chapter 4, due to the smaller systematic uncertaintyon the provided responsivity [91] if compared with the PMT CE.3.3.5.1 Analysis of the reflectivity of the Hamamatsu VUV4 MPPC andFBK LF SiPMAs shown in Fig. 3.18, the PDE of the Hamamatsu VUV4 MPPC is lowerif compared with the one of the FBK LF SiPM. A possible explanation could64over voltage [V]0 1 2 3 4 5 6 7 8photon detection efficiency00.050.10.150.20.25Hamamatsu VUV4 #1Hamamatsu VUV4 #2FBK-LF #1FBK-LF #2FBK-LF #3Figure 3.18: Photon Detection Efficiency (PDE) as a function of the overvoltage for two Hamamatsu VUV4 MPPCs and three FBK-LF SiPMs.The Hamamatsu MPPC used throughout this chapter is the VUV4 #2.The FBK-LF #3 is a new FBK LF SiPM measured, for comparison, inthe setup reported in this chapter. FBK-LF #1 and #2 are instead theFBK-LF PDE whose number of CAs is reported in Sec. 3.3.4.1 andFig. 3.10. The error, on each point, for all the five devices accounts forthe presence both to the statistical and the systematic uncertainty.be searched in the different surface reflectivity of the two SiPMs. To investi-gate this aspect, the nEXO collaboration in Ref. [92] studied the reflectivity ofthe two SiPMs as a function of the incident wavelength and angle, as shown inFig. 3.19 and Fig. 3.20. In particular in Ref. [92] five samples were investigated: aFBK-VUV-HD1-LF (FBK-LF) SiPM; a FBK-VUV-HD1-STD (FBK-STD) SiPM;a FBK silicon wafer and two Hamamatsu VUV4 MPPCs. The FBK SiPMs havethe same dimension (10 mm× 10 mm), a pixel size of 30 µm and a fill factor of∼ 73%. The FBK silicon wafer is a 6-in silicon wafer deposited by a layer of SiO2with a thickness of approximately 1.5 µm. This silicon wafer is identical to the oneused during SiPM manufacturing and diced into 20 mm×20 mm pieces. The twoHamamatsu VUV4 MPPCs have instead a dimensions of 6 mm× 6 mm and a pixelsize of 50 µm and 75 µm, respectively. The 50 µm version is the one characterisedin the previous sections of this chapter. As shown in Fig. 3.19 and Fig. 3.20, thelower efficiency of the Hamamatsu VUV4 MPPC cannot be attributed to its reflec-65Figure 3.19: Specular reflectance as a function of the Angle of Incidence(AOI) for five samples measured at 175 nm. The wavelength is labeledon each plot, and samples are indicated by different colors. Solid linesrepresent light beams with s-polarization, while dashed lines indicatep-polarization. From Ref. [92].tivity at 175 nm or 193 nm. If compared with the FBK LF SiPM, the HamamatsuVUV4 has in fact a lower surface reflectivity and this results in a higher amountof light transmitted throw the SiO2 coating layer at the top of the SiPM. Addition-ally, the FBK samples show oscillations in their specular reflectivity that are notobserved for VUV4 MPPCs. This result is caused by the interference of the inci-dent light in the thin SiO2 layer deposited on the surface of the FBK samples. Thethickness of the thin SiO2 layer is approximately 1.5 µm, as measured by FBK.The FBK-Si-Wafer sample has a higher specular reflectance than that of the othertwo FBK SiPMs, due to the microstructures on the surface of SiPMs, such as tracesand quenching resistors that can reduce the specular reflectance. The HamamatsuVUV4 instead doesn’t show oscillation most likely due to the thinner SiO2 layerdeposited at the top of it. Unfortunately, no information of the MPPC structurewere provided by Hamamatsu.Overall, as already noticed, the reflectivity of Hamamatsu VUV4 MPPC islower if compared with the one of the FBK SiPM. The lower PDE of the Hama-matsu VUV4 MPPC is therefore probably due to absorption of the incident lightin the not depleted region close to the surface between the SiO2 layer and the66Figure 3.20: Specular reflectance as a function of the Angle of Incidence(AOI) for five samples measured at 193 nm. The wavelength is labeledon each plot, and samples are indicated by different colors. Solid linesrepresent light beams with s-polarization, while dashed lines indicatep-polarization. From Ref. [92].avalanche region rather than due to light directly reflected from the silicon surface.The attenuation length of VUV photons in Silicon is in fact extremely sensitive tothe location of the avalanche region that can produce noticeable differences in thefinal PDE, as shown for example in Chapter 5 and in Ref. [93].83.4 ConclusionsThis chapter described measurements performed at TRIUMF to characterizethe properties of VUV sensitive SiPMs at cryogenic temperatures. In particular,this chapter focused on the Hamamatsu VUV4 MPPC, identified as a possibleoption for the nEXO experiment. The results of the characterization are sum-marized in Table 3.1. For a device temperature of 163 K, the VUV4 dark noise8The higher PDE measured by Hamamatsu could be also related to the different technique usedby Hamamatsu to evaluate the VUV4 PDE. According to an internal meeting with Hamamatsu, thePDE reported in [87] was not assessed by pulse counting, but reading out instead the MPPC currentunder illumination. However, as shown in [94], the MPPC current is affected by CA noise and it istherefore easier to overestimate the PDE if the CA noise contribution is not accounted properly.67Quantity Value UnitDark noise rate 0.137±0.002 Hz/mm2Number of CAs 0.161±0.005 PERelative fluctuation of the mean number of CAs 0.39±0.01 -Number of APAs 0.032±0.001 PENumber of CDAs 0.178±0.003 -PDE VUV4 #2 13.4±2.6 % -PDE VUV4 #1 11±2 % -Table 3.1: Summary of the results derived for the characterization of theHamamatsu VUV4 MPPC useful for nEXO operation. The first five mea-surements are reported for a temperature of 163 K and at 3.1±0.2 V ofOver Voltage (OV). The Photon Detection Efficiency (PDE) was mea-sured for two Hamamatsu VUV4 devices (labelled as VUV4 #2 andVUV4 #1) at T = 233 K, for a mean wavelength of 189± 7 nm and atan over voltage of 3.6±0.2 V and 3.5±0.2 V, respectively.rate is 0.137± 0.002 Hz/mm2 at 3.1± 0.2 V of over voltage, a level comfortablylower than what required for nEXO (<50 Hz/mm2). At the same over voltage set-ting and temperature, we measure: (i) a number of additional prompt avalanchesequal to 0.032±0.001; (ii) a number of correlated delayed avalanches per pulse inthe 1µs following the trigger pulse of 0.178± 0.003, (iii) a number of correlatedavalanches per pulse and a relative fluctuation of the mean number of CAs per pulsein the same time window equal to 0.161±0.005 and 0.39±0.01, respectively. TheDark characteristics of the Hamamatsu VUV4 MPPC are therefore consistent withthe nEXO requirements up to ∼ 3.2 V of over voltage. Finally, the PDE of theHamamatsu VUV4 was measured for two different devices (labelled as VUV4 #2and VUV4 #1) at T = 233 K. At 3.6± 0.2 V and 3.5± 0.2 V of over voltagewe measure, for a mean wavelength of 189± 7 nm, a PDE of 13.4± 2.6 % and11± 2 % for the two devices, corresponding to a saturation PDE of 14.8± 2.8 %and 12.2± 2.3 %, respectively. Both values are well below the 24 % saturationPDE advertised by Hamamatsu [87]. More generally, the VUV4 #1 at 3.5 V ofover voltage is below the nEXO PDE requirement. The VUV4 #2 instead yieldsa PDE that is marginally close to meeting the nEXO specifications. This suggests68that, with modest improvements, the Hamamatsu VUV4 MPPCs could be consid-ered as an alternative to the FBK-LF SiPMs for the design of the nEXO detector.69Chapter 4Characterization of theFBK VUV HD 3 for nEXO4.1 IntroductionIn the previous chapter of this work we reported the characterization of theHamamatsu VUV4 MPPC as possible candidate for the nEXO experiment. Inthis chapter we report the characterization of the newest generation of FBK de-vices: FBK VUV HD 3 Vacuum Ultra-Violet (VUV) sensitive SiPMs. Followingthe same procedure introduced in Chapter 3, various SiPM features such as: darknoise, gain, correlated avalanches and direct CrossTalk were measured at 163 Kand compared not only with the Hamamatsu VUV4 MPPC characteristics, butalso with the previous generation of FBK devices: FBK VUV HD 1, presentedin [1]. Table 4.1 summarises the characteristics, useful for nEXO operation, ofthe two previously characterised devices. According to the nEXO SiPMs spec-ification introduced in Chapter 2 (Sec. 2.4.2), the FBK VUV HD 1 meets thenEXO Photon Detection Efficiency (PDE) requirement at 174.8± 10.2 nm, whilethe Hamamatsu VUV4 MPPC only marginally meets the nEXO PDE requirements(Fig. 3.18). Both devices meet instead the nEXO Dark and Correlated Avalanche(CA) noise requirements at 163 K in however a different over voltage range. Moreprecisely, the Hamamatsu VUV4 MPPC and FBK VUV HD 1 can be operated upto 3.5 V and 2.5 V of over voltage, respectively while keeping the relative fluctu-70Quantity Value UnitDark Noise Rate VUV4 0.137±0.002 Hz/mm2Relative fluctuation of the mean number of CAs (VUV4) 0.39±0.01 -PDE VUV4 11.9±1.6 % -Dark Noise Rate LF 0.19±0.06 Hz/mm2Relative fluctuation of the mean number of CAs (LF) 0.44±0.05 -PDE LF 19.8±2.6 % -Table 4.1: Summary of the results derived from Chapter 3 and [1] for thecharacterization of the Hamamatsu VUV4 MPPC and FBK VUV HD 1Low Field (LF) SiPM. The Hamamatsu VUV4 dark noise rate and num-ber of Correlated Avalanches (CAs) per pulse (in the 1µs following thetrigger pulse) are reported for a temperature of 163 K and at 3.1±0.2 Vof over voltage. The FBK LF dark noise rate is reported for a tempera-ture of 163 K and at 3.58 V of over voltage. The FBK LF relative fluc-tuation of the mean number of CAs (in the 1µs following the triggerpulse) is extrapolated, using Poisson statistics, from the mean numberof CAs for a temperature of 163 K and at 3.2 V of over voltage. TheHamamatsu VUV4 PDE was measured at 233 K for an over voltage of3.55± 0.1 V, while the FBK VUV HD 1 (LF) PDE was measured at163 K for an over voltage of 3.2±0.1 V.ation of the mean number of CAs in the 1µs after the trigger pulse smaller than0.4. The smaller operational over voltage and junction capacitance [59] of theFBK VUV HD 1, if compared with the ones of the Hamamatsu VUV4 MPPC,could be a potential issue for the nEXO light detection subsystem, due to the lim-ited operational gain achievable with these SiPMs.From an electronics point of view, a higher over voltage is in fact desirable,since this automatically means higher gain and better signal-to-noise ratio.The aim of this chapter is to assess the performance of a new generation ofFBK devices (FBK VUV HD 3) developed for application in liquid xenon. Ad-ditionally, we will also introduce a new technique (based on the time distributionbetween pulses [85]) to measure the SiPM PDE, that not only is free from cor-related avalanche noise corrections, but also it allows to reduce significantly thesystematic uncertainly on the measured PDE, especially in the VUV wavelength71range. At the end of this chapter we will also estimate the contribution of theHamamatsu VUV4 MPPC and FBK VUV HD 3 SiPM to the overall nEXO energyresolution using the model introduced in Chapter 2 (Sec. 2.4.3). The cell geome-try and size of the FBK VUV HD 3 are comparable with the ones of its previousgeneration (FBK VUV HD 1). An image of the FBK VUV HD 3 SiPM is reportedin Fig. 4.1. The total number of pixel is 25500 with a pitch size of 34µm and a fillfactor of 0.8 giving a sensitive area that is comparable with the one of the Hama-matsu VUV4 MPPC and equal to ∼ 36 mm2. The novelty of the FBK VUV HD 3Figure 4.1: Image of a FBK VUV HD 3 SiPM.SiPM, if compared with its previous generation, is a new triple-doping technologydeveloped by FBK for the Darkside-20k experiment and used for the fabricationof the sensor [18]. As it will be shown in this chapter, this new technology signifi-cantly suppresses the after-pulsing probability allowing to increase the operationalover voltage of these devices of 1 V, if compared with its previous generation whilekeeping the requirement on the relative fluctuation of the mean number of CAs tobe smaller than 0.4. The absolute PDE of this device could not be finalized in thiswork due to an ongoing study of the light beam profile in the new commissionedsetup. The confinement of the beam inside the photosensor area is in fact necessaryto precisely measure the sensor efficiency. If the PDE of the FBK VUV HD 3 willbe the same of its previous generation, it will allow to consider this device, with its72improved correlated avalanche noise contribution, as an excellent candidate for thenEXO light detection subsystem.4.2 Experimental Details4.2.1 Hardware SetupA new setup called Vacuum Emission Reflectivity Absorption (VERA) wasdeveloped at TRIUMF to characterize the response of SiPMs at VUV wavelengths.A schematic representation of the setup is reported in Fig. 4.2. VERA consistsFigure 4.2: Hardware setup used for the characterization of theFBK VUV HD 3 SiPM.73of a vacuum chamber (Fig. 4.3 a)) coupled with a vacuum VM200 Resonancemonochromator [78]. The entire chamber is coated with a MH2200 Alion Sci-ence vacuum compatible antireflective paint [95] whose reflectivity was certifiedto be < 1% in the range 250-2500 nm. Light from a Resonance Lyman-Alpha DClamp [78] is separated by the monochromator and directed alternatively towarda Photo-Diode (AXUV100G [96]), used to calibrate the absolute light flux, or aSiPM under test (Fig. 4.4). Both devices are placed on a movable arm which allowsfor remote positioning of the devices under the light beam (Fig. 4.3 b)). Differentlyfrom the setup introduced in Chapter 3, the movable arm allows only to performa beam mapping along the direction marked as x in Fig. 4.2. The AXUV100G(a) Vacuum Chamber (b) Cold FingerFigure 4.3: Vacuum Emission Reflectivity Absorption (VERA) setup at TRI-UMF.Photo-Diode was calibrated against a NIST calibrated Photo-Diode (XUV-100C)that was placed on the movable arm, in replacement of the SiPM under test, for acalibration measurement (Fig. 4.4). A liquid nitrogen controlled cold finger adjuststhe device temperature down to 163 K.For efficiency measurements the light from the Resonance Lyman-Alpha source74(a) FBK VUV HD 3 efficiencymeasurement(b) Photo-Diode CalibrationmeasurementFigure 4.4: Configuration for efficiency and calibration measurements in theVERA Setup.passes through a filter wheel, used to suppress multiple orders of the vacuummonochromator and a splitter Gold coated Parabolic Mirror. The mirror allowsto simultaneously illuminate the SiPM (or the Photo-Diode) under test and a Ref-erence UV sensitive Hamamatsu Photonics PMT (R8486), used to monitor thelight stability. The gold coating was chosen due to its flat reflectivity in a broadwavelength range. Its reflectivity in the VUV wavelength range is however fairlypoor and it is partially compensated by the high lamp flux. Before reaching the de-vices location, light passes also through a motorized IRIS (Uniblitz AI25 [97]) anda 2 mm diameter collimator coupled with a Acktar Hexa-Black collimation tube[98], as shown in Fig. 4.5, with a certified 99.9% absorbance in the wavelengthrange 200-5000 nm. Particular attention was devoted on the choice of the IRISblades and on the collimator design to avoid fluorescence from materials locatedin the light path. The motorized IRIS is used to optimize the light flux for dif-ferent wavelengths and to change the beam width accordingly to the device under75Figure 4.5: Particular of the motorized IRIS assembly inside the vacuumchamber. The IRIS also incorporates a shutter useful to shield the sen-sor from the lamp light (at the monochromator 0-order) and to recordbackground (dark) measurements.test. Moreover, it also incorporates a shutter useful to shield the sensor from thelamp light at the monochromator 0-order, and to record background (dark) mea-surements.A CAEN DT5730B Digitizer Module [74] and a MIDAS-Labview based con-trol system [75] are used for signal digitalization and for the management of theslow control hardware of the setup. Overall they constitute the VERA Data Ac-quisition System (DAQ). For pulse counting measurements the SiPM signal is am-plified by a two stage amplifier (MAR6-SM+ [76] and OPA695 [99]) while forbeam mapping and IV measurements the DC SiPM current is measured with aKeithley 6487 picoammeter [100]. The Photo-Diode current is instead measured76with a Keysight B2985 low noise picoammeter [101]. The reference PMT used tomonitor the light stability is biased by a C13654-01 Hamamatsu socket assembly.The output voltage from the Hamamatsu socket is digitized by a Texas InstrumentsADS1248 24 bit ADC [102], and it is read by a Nanopi.4.3 Experimental Results4.3.1 Lamp SpectrumDifferently from the light filtering scheme introduced in Chapter 3, prelimi-nary studies of the FBK VUV HD 3 PDE, reported in Sec. 4.4, were done using aResonance Lyman-Alpha light source coupled with a Resonance VM200 vacuummonochromator, as introduced in Sec. 4.2.1. The VM200 allows to precisely selectthe wavelength and its resolution with a Labview-based control software and a setof input and output slits. In Fig. 4.6 it is reported the lamp spectrum recorded bythe Reference PMT as a function of the monochromator slits width. For reference,monochromator input and output slit had always the same width. The main lamppeak is at 160 nm [103, 104]. This peak is used as calibration point for the VM200monochromator along with its second order at 320 nm. The wavelength resolutiongenerally achievable with a monochromator depends from several characteristics ofthe monochromator itself: grating, focal length and slit width. Higher groove grat-ing, longer focal length and narrow slit widths allow to achieve better resolution inwavelength. The drawback is the rather poor light intensity since light is more dis-persed inside the monochromator. To calibrate the absolute light flux for efficiencymeasurements (Sec. 4.4) we used a re-calibrated Photo-Diode (AXUV100G). Bydesign Photo-Diodes have no internal gain, therefore the Photo-Diode photon-current measured for rather low photon fluxes (∼ MHz) is fairly small (∼ fA).The VM200 monochromator has a short focal length (200 mm) and it is equippedwith a grating with relatively low number of lines per mm: 1200 G/mm1. Thefinal wavelength resolution is therefore lower if compared with the one of othercommercially available monochromators, but its higher light throughput allows to1Gratings are usually designated by their groove density, the number of grooves per unit length,usually expressed in grooves per millimeter: G/mm.77Wavelength [nm]120 130 140 150 160 170 180Voltage [V]00.511.5 Slit width:1.5 mm1 mm - Voltage X 2.50.5 mm - Voltage X 19Figure 4.6: Lamp Spectrum of the Lyman-Alpha Resonance light source(Lamp temperature set point: 423 K) recorded by the reference PMT(Bias Voltage: 1050 V) as a function of the VM200 monochromator slitwidth. Input and output slit had the same width. Smaller slit widthresults in higher wavelength accuracy (the oscillations in the lamp spec-trum can be resolved), but lower photon flux.achieve a better S/N if used in conjunction with a Photo-Diode. Moreover the LXescintillation spectrum is fairly broad 174.8± 10.2 nm [47], therefore a resolutionof few nm is acceptable to characterize devices in this wavelength range.4.3.2 Beam Mapping StrategyAs introduced in Sec. 4.2.1, the movable arm allows for remote positioningof the devices under the light beam. Differently from the beam mapping schemereported in Chapter 3, the VERA setup doesn’t allow to perform 2D beam mappingof the device under test. This can be a serious issue, since the Photo-Diode andthe SiPM under test have different Photosensitive Areas (PA)s of 1× 1 cm2 and36 mm2, respectively. The light beam can therefore not be completely containedon the smaller of the two devices (SiPM) bringing to an underestimation of the totalmeasured PDE. To address this issue a CCD camera (ARTCAM-2020UV-USB3)was purchased and it will temporarily substitute the cold finger to map, in the nearfuture, the beam size as function of wavelength and IRIS aperture. This will allow78to correctly measure the light flux, and therefore the PDE, at 175 nm using thetechnique introduced in Sec. 4.4. For this reason, in Sec. 4.4 we will only presenta relative measurement of the SiPM efficiency without proving a normalization forthe photon flux at 175 nm.4.3.3 Collected Data and Trigger ConfigurationsThe SiPMs characteristics were investigated at 163 K. The collected datafollow the same scheme presented in Chapter 3 and they can be divided into twotypes: dark data and DC light lamp data. For both data-sets the DAQ system wasset to trigger on individual SiPM pulses with a DAQ threshold above the noise.For each trigger, the DAQ saves the event with a total sample window of 10 µs,split into 2 µs of pre-trigger and 8 µs of post-trigger samples. The data wereanalyzed at the pulse level with the same ROOT-based [79] waveform analysistoolkit introduced in Chapter 3 with the only difference of the Single AvalancheResponse Function (SARF) used to parametrize the FBK VUV HD 3 pulse shape.For the FBK VUV HD 3 SiPM the SARF was represented as the superimpositionof two exponentially modified Gaussian distributions with the same variance, butwith two exponential time constants as follows [105]V (t) = A×[1− k2τS(Exp[σ22τS2 −t− t0τS]×Erfc[ σ√2τS− t− t0√2σ])++k2τL(Exp[σ22τL2 −t− t0τL]×Erfc[ σ√2τL− t− t0√2σ])] (4.1)where: t0 is the pulse time, σ is the square root of the variance of the Gaussiancomponent, τS and τL are the two exponential decay constants and 0≤ k≤ 1 is therelative contribution of the two fall time components in the SiPM pulse shape. Ais the pulse area (proportional to the pulse charge).4.3.4 Single PE Gain and Breakdown Voltage ExtrapolationSingle Photo-electron Equivalent (PE) dark pulses at 163 K from two differentFBK devices (FBK VUV HD 3 #1 and FBK VUV HD 3 #2) were used to measurethe single PE charge as a function of the SiPM over voltage, as shown in Fig. 4.7.79In the same figure we also reported the single PE charge of the Hamamatsu VUV4MPPC and FBK VUV HD 1 measured in Chapter 3 and [59], respectively. Thesingle PE (amplified) pulse charge Q was defined as:Q≡(IDR214)×(A1 PE×10−9R)(4.2)where: IDR is the Input Dynamic Range of the digitizer (0.5 V), A1 PE is the av-erage area (Eq. 4.1) of the fitted digitizer signals for 1 PE pulses (measured inLSB× ns [74]), and R is the amplifier load resistance (R=50 Ω). Therefore, thesingle PE (un-amplified) gain (G1 PE) can be extracted from Q using the followingequation:G1 PE =QgAMP×qE(4.3)where gAMP is the gain of the amplifier (measured to be 141± 3) and qE is theelectron charge. The amplifier was calibrated using the same scheme already intro-duced in Chapter 3 (Sec. 3.3.2). The single PE (un-amplified) charge, as a functionover voltage [V]0 1 2 3 4 5 6 7 8single PE charge00.10.20.30.40.50.60.70.80.9112−10×FBK VUV HD 3 #1FBK VUV HD 3 #2Hamamatsu VUV4FBK VUV HD 1 213 [K] Figure 4.7: Measured single PE charge as a function of the over voltage forseveral devices tested for the nEXO experiment. The measurements ofthe FBK VUV HD 3 and Hamamatsu VUV4 were done at 163 K, whilethe one of the FBK VUV HD 1 was extrapolated from [59] and reportedfor a temperature of 213 K.80of the bias voltage, was then linearly fitted as Q1 PE =CD× (V −VBD), in order toextract: (i) the SiPM single cell capacitanceCD and (ii) the Breakdown VoltageVBDdefined as the bias voltage at which the SiPM single PE gain (or charge) is zero.Table 4.2 summarises the breakdown voltage at 163 K and the capacitance of thedevices reported in Fig. 4.7. The capacitance of the FBK VUV HD 3 is compatiblewith one of the FBK VUV HD 1. The cell structure for the two generations ofFBK devices is in fact almost identical (Sec. 4.1). The Hamamatsu VUV4 has asingle cell pitch bigger if compared with the one of FBK devices (50µm vs 35µm,respectively) resulting in a larger SPAD capacitance.Device Capacitance [fF] Breakdown [V]Hamamatsu VUV4 116±6 44.8±0.11FBK VUV HD 1 [213 K] 86±5 30.6±0.14FBK VUV HD 3 #1 100±5 27.4±0.15FBK VUV HD 3 #2 96±5 27.7±0.17Table 4.2: Summary of the capacitance and breakdown voltage for severalphoton-sensors tested for nEXO. The FBK VUV HD 3 and Hama-matsu VUV4 measurements were done at 163 K, while the one of theFBK VUV HD 1 was derived from [59] and reported for a temperatureof 213 K.4.3.5 Noise AnalysisIn this section we report the results of the dark characterization at 163 K forthe two FBK VUV HD 3 devices (FBK VUV HD 3 #1 and FBK VUV HD 3 #2)already introduced in the previous section. In particular, the FBK VUV HD 3characteristics were compared against: (i) the nEXO requirements, (ii) the Hama-matsu VUV4 MPCC and FBK VUV HD 1 SiPM, reported in Chapter 3 and in [1],respectively. More precisely, the FBK VUV HD 3 Dark Noise rate (DN), as a func-tion of the over voltage, is presented in Sec. 4.3.5.2. The FBK VUV HD 3 num-ber of Correlated Avalanches (CAs) and Correlated Delayed Avalanches (CDAs)per primary pulse in 1 µs after the trigger pulse is reported in Sec. 4.3.5.1 and81Sec. 4.3.5.2, respectively2. Direct CrossTalk (DiCT) is discussed in Sec. 4.3.5.3. Itis worth recalling that the SiPM noise was studied using dark data, taken with theSiPM shielded from any light source (Sec. 4.3.3). All the measurements reportedin the next sections were performed at 163 K.4.3.5.1 Number of Correlated Avalanches per PulseIn order to reach the nEXO design performance, the relative fluctuation ofthe mean number of CAs, within a time window of 1 µs after the primary pulse,needs to be < 0.4. The average number of CAs per primary pulse is measured bydirectly constructing a histogram of the baseline subtracted integral of collecteddark waveform in the range [0−3] µs (the trigger pulse is at 2 µs) and normalizingit to the average charge of 1 PE pulses, as discussed in Chapter 3. The number ofcorrelated avalanches is then computed as〈Λ〉= 1NN∑i=1AT-wiA1 PE−1 (4.4)where AT-wi is the Total charge of the waveform-i (baseline subtracted) integratedup to 1 µs after the trigger pulse, A1 PE is the average charge of 1 PE pulses and Nis the number of waveform analyzed. The 〈Λ〉 number, in unit of PE, as a functionof the over voltage, is reported in Fig. 4.8. For comparison, in the same figure wealso reported the number of CAs for the other two SiPMs tested for nEXO. TheFBK VUV HD 3 has a significantly smaller number of CAs if compared with itsprevious generation (FBK VUV HD 1). As it will be shown in Sec. 4.3.5.2 andSec. 4.3.5.3, the significant improvement of the new generation of FBK devicesis mainly due to the reduction of after pulse thanks to the new triple doping tech-nology developed by FBK, rather than the reduction of the optical CrossTalk, thatinstead is essentially the same of the previous generation. Overall the correlatedavalanche noise characteristics of the FBK VUV HD 3 are comparable with the oneof the Hamamatsu VUV4 MPPC. Fig. 4.9 reports instead the Root Mean SquareError (RMS) of the number of CAs per primary pulse within a time window of2We refer the reader to Chapter 2 for a detailed explanation of the different sources of noise inSiPMs.82over voltage [V]0 1 2 3 4 5 6 7 8s [PE]µnumber of CAs in 100.20.40.60.811.21.41.61.82FBK VUV HD 3 #1FBK VUV HD 3 #2Hamamatsu VUV4FBK VUV HD 1 #1FBK VUV HD 1 #2Figure 4.8: Number of Correlated Avalanches (CAs) per primary pulse mea-sured at 163 K within a time window of 1 µs after the trigger pulse asa function of the applied over voltage for several photon-sensors testedfor nEXO.1 µs after the trigger pulse as a function of the applied over voltage (i.e. σΛ). Dif-ferently from Fig. 4.8, the FBK VUV HD 1 data could not be included in Fig. 4.9since in [1], it was only reported the mean number of correlated avalanches in 1µs, without any additional information of its RMS error. As shown in Fig. 4.9and in Fig. 4.8, the RMS error and the mean number of correlated avalanchesof the FBK VUV HD 3 and Hamamatsu VUV4 MPPC are compatible: the twoSiPMs have therefore similar noise performances. Additionally both devices showa high RMS error that results in a significant fluctuation in the number of correlatedavalanches between different events. Fig. 4.10 reports the relative fluctuation of themean number of CAs in 1 µs at 163 K, useful for nEXO operation, for the threedevices of Fig. 4.9. The relative fluctuation was defined as introduced in Eq. 3.4and here reported for clarityRatio≡ σΛ1+ 〈Λ〉In order to meet the nEXO requirements (Sec. 2.4.2), the FBK VUV HD 3 can beoperated at T=163 K up to about 3.2 V of over voltage while keeping the relative83over voltage [V]0 1 2 3 4 5 6 7 8s [PE]µRMS in 100.511.522.5FBK VUV HD 3 #1FBK VUV HD 3 #2Hamamatsu VUV4Figure 4.9: Root Mean Square Error (RMS) of the number of CorrelatedAvalanches (CAs) per primary pulse measured at 163 K within a timewindow of 1 µs after the trigger pulse as a function of the applied overvoltage for several photon-sensors tested for nEXO.fluctuation of the mean number of CAs in 1 µs smaller than 0.4. The triple dopingtechnology allows therefore to increase of 1 V the operational over voltage of thesedevices. This automatically means, accordingly to Fig. 4.7, a higher single PEcharge and gain with better S/N ratio.4.3.5.2 Dark Noise Rate and Number of Correlated Delayed Avalanches perPulseDark Noise (DN) and Correlated Delayed Avalanches (CDA)s events can bedistinguished by studying the time distribution of events relative to the primarypulse using the method introduced in Sec. 3.3.4.2 of Chapter 3. An example of theFBK VUV HD 3 charge distribution (for the FBK VUV HD 3 #1) as a functionof the time difference with respect to the primary pulse is reported in Fig. 4.11 foran over voltage of 5.64± 0.17 V, at 163 K. If compared with the charge distribu-tion of the Hamamatsu VUV4 MPPC (Fig. 3.6) measured at the same temperatureand roughly over voltage, the FBK VUV HD 3 has a significantly higher amountof multiple PE events due to direct CrossTalk between pixels. A study of theFBK VUV HD 3 Direct CrossTalk (DiCT) contribution is reported in Sec. 4.3.5.3.84Over Voltage [V]1 2 3 4 5 6 7Ratio [#]00.20.40.60.81FBK VUV HD 3 #1FBK VUV HD 3 #2Hamamatsu VUV4Figure 4.10: Relative fluctuation of the number of CAs in 1 µs measured at163 K and derived with Eq. 3.4 from the data of Fig. 4.8 and Fig. 4.9.Fig. 4.11 can then be used to extrapolate the pulse rate R(t) as a function of thetime difference with respect to the primary pulse using Eq. 3.5, as reported inSec. 3.3.4.2. The result is reported in Fig. 4.12. In the same figure we also re-ported the observed pulse rate for the highest over voltage dataset measured at163 K for the Hamamatsu VUV4 MPPC. Fig. 4.12 clearly shows as the Hama-matsu device has a significantly higher amount of correlated avalanches if com-pared with the FBK VUV HD 3, especially at short times after the trigger pulse(≤ 100 ns) where the time distribution is dominated by after pulse events. Thehigh Hamamatsu VUV4 afterpulse rate was already reported in Sec. 3.3.3 whileanalysing its prompt pulse charge distribution. In that case we noticed shoulder-like events in the Hamamatsu VUV4 charge distribution that we attributed to fastcorrelated avalanches which do not get resolved from their parent primary pulse bythe DAQ (≤ 4 ns).The afterpulse rate of the FBK and Hamamatsu devices can be better com-pared analysing the total Number of Correlated Delayed Avalanches (CDA) in 1 µswith respect to the trigger pulse, as a function of the over voltage, using Eq. 3.6 ofSec. 3.3.4.2, as shown in Fig. 4.13. The number of CDA of the FBK VUV HD 3is greatly reduced not only if compared with its previous generation, but also ifcompared with the Hamamatsu VUV4 MPPC resulting therefore in a smaller num-85time difference wrt the primary pulse [ns]1 10210 310 410 510 610 710 810 910 1010Pulse Area [LSB x ns]020040060080010001200310×number of events050100150200250Figure 4.11: FBK VUV HD 3 #1 charge distribution of first pulses followingsingle PE trigger pulses as a function of the time difference with re-spect to (wrt) their primary pulse for T=163 K and for an over voltageof 5.64± 0.17 V. The grey scale represents the number of events ineach bin on a logarithmic scale. The solid red line shows a fit of theafterpulsing events and is used to measure the recovery time of onecell, equal to 195±10 ns.ber of after pulse events in the same acquisition window (1 µs after the trigger).As already introduced in Sec. 4.3.5.1, this is a consequence of the triple dopingtechnology developed by FBK for the Darkside-20k experiment and used in thisnew generation of FBK devices. From Fig. 4.12 it is possible to extrapolate theDark Noise Rate at 163 K, as a function of the over voltage, performing a weightedmean of the asymptotic rates at long times, as reported in Fig. 4.14. For a devicetemperature of 163 K all the SiPMs tested (including the FBK VUV HD 3) meetthe nEXO requirement of <50 Hz/mm2 (Sec. 2.4.2) with values comfortably lowerthan the required one.4.3.5.3 Number of Additional Prompt AvalanchesDirect CrossTalk (DiCT) can be investigated with the same technique usedin Sec. 3.3.4.3 by studying the charge distribution of prompt pulses obtained fromdark data. More precisely, using Eq. 3.7 it is possible to measure the number ofAdditional Prompt Avalanches (APA) as a function of the over voltage at 163 K,as shown in Fig. 4.15. The number of APA of the FBK VUV HD 3 is significantly86time difference wrt the primary pulse [ns]1 10 210 310 410 510 610 710 810 910 1010]2pulse rate [Hz/mm2−101−10110210310410510610 Over voltage:2.64 [V]3.64 [V]4.64 [V]5.64 [V]6.64 [V]7.12 [V] - VUV4Figure 4.12: Observed dark pulse rate R(t) of the FBK VUV HD 3 #1 SiPMas a function of the time difference with respect to (wrt) the primarypulse for a temperature of 163 K and for different over voltages. Forcomparison, in the same figure we also reported the pulse rate forthe highest over voltage point measured in Chapter 3 for the Hama-matsu VUV4 MPPC (7.12±0.16 V).higher if compared with the one of the Hamamatsu VUV4 MPPC, as already no-ticed in Sec. 4.3.5.2. Additionally, the new generation of FBK devices has almostidentical performances of its previous generation (FBK VUV HD 1). From thiswe can conclude as the reduced number of correlated avalanches (Sec. 4.3.5.1) ismainly due to the reduced after pulse (Sec. 4.3.5.2) rather than the reduced Directoptical CrossTalk, as anticipated in Sec. 4.3.5.1.4.4 A new DC technique to measure the SiPM PhotonDetection EfficiencyTo meet the nEXO requirements, the SiPM PDE must be ≥ 15% for liquidxenon scintillation wavelengths (174.8±10.2 nm [47]), as shown in Sec. 2.4.2. InChapter 3 the Hamamatsu VUV4 PDE was measured using a filtered pulsed xenonflash lamp and a technique that was based on Poisson statistics. More precisely, theaverage number of photons detected by the SiPM was firstly measured by countingthe number of lamp flashes in which no photons were detected (corrected for the87over voltage [V]2 3 4 5 6 7 8sµnumber of CDAs in 1 00.20.40.60.81FBK VUV HD 3 #1FBK VUV HD 3 #2Hamamatsu VUV4FBK VUV HD 1Figure 4.13: Number of Correlated Delayed Avalanches (CDAs) per primarypulse measured at 163 K within a time window of 1 µs after the trig-ger pulse as a function of the applied over voltage for several photon-sensor tested for nEXO.SiPM dark noise rate), and then normalized for the average number of photons de-tected by a calibrated Hamamatsu PMT. This technique cannot be applied with DClamps (like the Lyman-Alpha Resonance light source), since the probability to haveno photons in the acquisition window is negligible if compared with the probabil-ity to have one or multi-photon events in the same acquisition window. Moreover,the high photon flux that is associated with DC light sources may produce delayedcorrelated avalanches that trigger the DAQ artificially increasing therefore the finalSiPM PDE. Different techniques are available in literature to measure the SiPMPDE with DC lamps. These techniques relay on measuring the SiPM current andthen correct it for the correlated avalanche noise contribution as shown, for ex-ample, in [94]. These corrections, however, are often model dependent, since itis complicated to resolve analytically higher orders of correlated avalanche noise(e.g. afterpulse of DiCT and/or afterpulse of DeCT). In this section we introduce adifferent technique that is free from correlated avalanche noise and that can be usedto measure the SiPM efficiency with DC light sources. The main characteristic isto estimate the SiPM photon induced avalanche rate at the SiPM location using thetime distribution between pulses, in analogy with what was done in Sec. 3.3.4.288over voltage [V]2 3 4 5 6 7 8]2dark noise [Hz/mm1−101FBK VUV HD 3 #1FBK VUV HD 3 #2Hamamatsu VUV4FBK VUV HD 1Figure 4.14: Dark Noise rate measured at 163 K and normalized by the SiPMphoton sensitive area as a function of the applied over voltage for sev-eral photon-sensor tested for nEXO.and Sec. 4.3.5.2 to measure the dark noise rate of the Hamamatsu VUV4 MPPCand FBK VUV HD 3 SiPM, respectively. More precisely, since photon inducedavalanches are uncorrelated events (like dark noise events), it is possible to distin-guish them from dark noise and correlated delayed avalanches by studying the timedistribution of all the events relative to the primary pulse. The total observed pulserate R(t) can then be computed as a function of the time difference with respect tothe primary pulse using Eq. 3.5 including an additional contribution due to photoninduced avalanches as follows:R(t) = RDN(t)+R0(t)+RCDA(t) (4.5)where: R0(t) is the contribution due to the photon induced avalanches detected bythe SiPM; RDN(t) is the SiPM dark noise measured in Sec. 4.3.5.2; and RCDA(t) isthe correlated delayed avalanche rate. The FBK VUV HD 3 pulse rate R(t), as afunction of the time difference with respect to the primary pulse, for different overvoltages under 175 nm illumination is reported in Fig. 4.16. It is clear comparingFig. 4.16 with Fig. 4.12 as the pulse rate at 163 K is significantly higher underillumination due to the photon induced contribution to the total pulse rate. The89over voltage [V]2 3 4 5 6 7 8mean number of APA [PE]00.10.20.30.40.50.60.70.80.9 FBK VUV HD 3 #1FBK VUV HD 3 #2Hamamatsu VUV4FBK VUV HD 1Figure 4.15: Number of Additional Prompt Avalanches (APA)s measured at163 K as a function of the over voltage for several photon-sensor testedfor nEXO.uncorrelated pulse rate (RDN(t)+R0(t)) can then be measured, as a function of theover voltage, from Fig. 4.16 performing a weighted mean of the asymptotic rateat long times3. Subtracting from this last quantity the dark noise rate measured inSec. 4.3.5.2 with the same technique (but without illumination), gives the photoninduced avalanches rate (R0(t)) detected by the SiPM, as shown in Fig. 4.17. TheSiPM PDE can then be obtained dividing R0(t) by the photon flux Φ0 measuredwith a calibrated detector at the SiPM location as:PDE =R0Φ0(4.6)Fig. 3.18 in Chapter 3 and Fig. 4.17 differ only for the missing normalization Φ0for the FBK VUV HD 3 data (Sec. 4.3.2) that is independent from the SiPM overvoltage. The photon induced pulse rate of Fig. 4.17 and the SiPM PDE of Fig. 3.18have the same trend as a function of the applied over voltage: both curves saturateat high over voltages due to the saturation of the electron avalanche triggeringprobability, as it will be discussed in more details in Chapter 5. We stress as thetechnique introduced in this section is free from correlated avalanche noise, since3Each point in the mean was weighted with its error derived as reported in [85].90time difference wrt the primary pulse [ns]1 10 210 310]2pulse rate [Hz/mm410510Over voltage:2.64 [V]3.64 [V]4.64 [V]5.64 [V]6.64 [V]Figure 4.16: Observed pulse rate R(t) of the FBK VUV HD 3 #1 SiPM as afunction of the time difference with respect to (wrt) the primary pulsefor a temperature of 163 K under 175 nm light illumination.their contribution to the total pulse rate can be discriminated while constructing therate plot, as the one shown for example in Fig. 4.16.4.4.1 Calibration of the photon flux with a NIST Photo-Diode asreferenceAs introduced in Sec. 4.3.2, the PDE of the FBK VUV HD 3 could not befinalized due to the ongoing study of the beam shape that will be mapped in a closefuture with a linear CCD. For this reason, in the previous section we didn’t providea normalization (Φ0) for the data of Fig. 4.17. As introduced in Sec. 4.2.1, forthe measurement of the FBK VUV HD 3 efficiency we plan to use a re-calibratedphoto-diode in order to calibrate the absolute light flux Φ0, as follows:Φ0 =(I− IDN)λRhc(4.7)where: I and IDN are the Photo-Diode currents with and without illumination, re-spectively; R is the Photo-Diode responsivity at the wavelength λ ; h is the Planckconstant and c is the speed of light. This is a radical difference if compared withwhat was done in Chapter 3 where we used a calibrated PMT to measure the abso-91over voltage [V]2 3 4 5 6 7 8photon pulse rate [Hz]140150160170180190200210220310×Figure 4.17: Observed photon induced pulse rate R0(t) extrapolated fromFig. 4.16 for the FBK VUV HD 3 #1 SiPM as a function of the overvoltage, for a temperature of 163 K, under 175 nm light illumination.lute light flux at the SiPM location. The choice to abandon PMTs is in fact drivenby the low information available on their collection efficiency. Additionally, NISTPhoto-Diodes come with a small uncertainty on their responsivity (Fig. 4.18) andthis will allow to reduce significantly the systematic error on the final measuredPDE. The drawback to use Photo-Diodes is the small current (∼ fA) measured forrather low photon fluxes (∼MHz). Eq. 4.5, in fact, assumes the capability to keepthe SiPM in pulse counting mode: it therefore assumes that the fitting procedure in-troduced in Sec. 4.3.3 can be successfully applied on the SiPM pulses recorded bythe DAQ under illumination. In order to do so, it is necessary to adjust the light flux(done with the motorized IRIS introduced in Sec. 4.2.1) to have, at the same time,the SiPM in pulse-counting mode and the S/N of the Photo-Diode high enoughto measure the 175 nm light of the DC lamp. For this reason, to minimize thenoise induced on the Photo-Diode by other sources, not only we used shielded lownoise triax cable (Keithley 7078-TRX-1), but also we measured the Photo-Diodecurrent with a Keysight B2985 low noise picoammeter that is one of the commer-cially available instruments with the lowest RMS current noise (RMS noise withopen input of∼ 140 aA). Without implementing these noise suppression strategies,Photo-Diode measurements would be in fact dominated by the noise induced by:92Wavelength [nm]150 200 250 300 350 400 450 500Responsivity [A/W]1−10 Figure 4.18: Responsivity of the NIST calibrated Photo-Diode as a functionof the wavelength.the picoammeter itself, the cabling and other instruments rather than the photoncurrent measured by the Photo-Diode.4.4.2 Temperature dependence of the Photo-Diode currentIn Sec. 4.4.1 we provided a technique to obtain a measurement of the pho-ton flux at the SiPM location using a calibrated NIST diode. In this section wewill study the temperature dependence of the Photo-Diode current under identi-cal photon fluxes. Fig. 4.19 and Table 4.3 show typical currents measured by thePhoto-Diode for different wavelengths with and without illumination, as a func-tion of the temperature. The Photo-Diode photon current, reported in Fig. 4.19,was computed asI0FDiode−T = I0Diode−T×V0PMT−TV0PMT-300(4.8)where: I0Diode−T and I0FDiode−T refer to the Photo-Diode current, corrected for the darkcurrent, measured at the temperature T before and after re-scaling. The quantityI0Diode-T, for example, was computed asI0Diode-T = IDiode-T− IDDiode-T (4.9)93where: IDDiode-T is the Photo-Diode dark current measured at the temperature T , re-ported in Table 4.3, and IDiode-T is the current measured by the Photo-Diode underillumination at the same temperature. V0PMT−T and V0PMT-300 refer instead to theTemperature [K] Current [A]300 (36.5±7.2)×10−15223 (3.5±3.7)×10−15163 (3.0±3.3)×10−15Table 4.3: Average dark current of the Photo-Diode as a function of the tem-perature.voltage measured by the reference PMT when the Photo-Diode had a temperatureof T and 300 K, respectively. V0PMT−T is reported in Fig. 4.20. The rationale for theWavelength [nm]150 160 170 180 190 200Diode Photon Current [A]14−1013−10Diode Temperature:300 [K]223 [K]163 [K] Figure 4.19: Photo-Diode photon current measured, as a function of thewavelength, for several Photo-Diode temperatures.ratio in Eq. 4.8 is the correction of the Photo-Diode currents for light fluctuationsindependent from the Photo-Diode itself, but due instead to the DC lamp. Thereference PMT was in fact used to monitor the light flux between different Photo-Diode measurements, as introduced in Sec. 4.2.1. The studies of the temperaturedependence of the Photo-Diode current, reported in Fig. 4.19, are crucial to obtaina reliable PDE measurement at cryogenic temperatures. Vacuum systems can in94Wavelength [nm]150 160 170 180 190 200Voltage [V]1−10Diode Temperature:300 [K]223 [K]163 [K] Figure 4.20: Voltage recorded with the reference PMT during the Photo-Diode measurements reported in Fig. 4.19.fact suffer from residual moisture condensation. According to [106], the AXUVPhoto-Diode series used for this measurement (AXUV100G) should have a weaktemperature dependence quantifiable in a change of its responsivity of 0.03% perdegree Kelvin4. The authors however acknowledge in their publication possibleresidual contamination on the diode surface due to some anomalous drops in thediode responsivity at cryogenic temperatures. More generally, any drop in thediode responsivity, in particular in the 150-170 nm range, suggests the possibilityof moisture condensation since water strongly absorbs in this wavelength range,as shown in [107]. In order to prevent the possibility of moisture condensationduring PDE measurements, a number of procedural techniques were implemented.First of all, in the VERA setup we only used ultra high vacuum materials. Thechamber was evacuated by a turbomolecular pump and the baseline pressure be-fore each measurement was typically around ∼ 1×10−7mBar. Additionally, afterany exposure to air the chamber was heated for 48 h at temperatures > 150 C. Thiswas done thanks to heating strips wrapped around the vacuum chamber with thesystem under vacuum (Fig. 4.3 a)). This allowed to force the desorption of water4Moisture condensation can only happen on the Photo-Diode or on the SiPM that are cooled at163 K, not on the reference PMT that instead is located on a separate flange of the VERA setup andit is not cooled.95molecules from walls and other assemblies in the vacuum chamber and to there-fore reduce the content of contaminants in the setup. Finally, a Residual Gas Ana-lyzer (RGA) (SRS 100) was also installed on one of the flanges and the amount ofwater measured by the instrument after 48 h of baking was always below its sensi-tivity. All these precautions allowed to obtain the Photo-Diode currents measuredin Fig. 4.19 that show a temperature dependence smaller of the ones reported in[106] with currents measured, at different temperatures, always compatible withinthe error at each wavelength.4.5 Estimation of the nEXO energy resolutionThe nEXO experiment is designed to optimize the characteristics of the lightand charge channels to provide the best possible energy resolution for a LXe TPCwith a final design goal of 1% energy resolution (σ/Q) for the 0νββ decay of136Xe (Q-value at 2458.07± 0.31 keV [9]). In Chapter 2 we shown as the firstgeneration of FBK devices (FBK VUV HD 1) satisfies the requirement on theoverall nEXO energy resolution, at an over voltage roughly between 2 and 3 V.In this section we will predict the nEXO energy resolution, as a function of theSiPM over voltage, using the characteristics of the two SiPMs fully characterisedin this work: the Hamamatsu VUV4 MPPC and the FBK VUV HD 3 SiPM. Thestarting point is the model of the nEXO energy resolution with Eq. 2.53, derived inSec. 2.4.3, and here reported for clarityσn〈n〉 =√((1−εp)npεp+εpnpσ2Λ(εp(1+〈Λ〉))2)+((1−εq)nqεq+σ2q,noiseε2q)〈n〉Table 4.4 summarises the meaning and the values of the parameters used in thisequation.As already anticipated in Sec. 2.4.3, Eq. 2.53 differs from the one used in [1].The main difference is the estimation of the correlated avalanche noise contributionto the overall energy resolution. In [1] CAs are in fact treated as Poisson processes.96The overall energy resolution therefore was proportional to√〈Λ〉1+ 〈Λ〉 (4.10)This approximation is justified at low over voltages (when 〈Λ〉 < 1), but tendsto artificially improve the energy resolution at high over voltages. In the modelderived in Sec. 2.4.3 the resolution is instead proportional toσΛ1+ 〈Λ〉 (4.11)therefore it worsens at high over voltages since σΛ increases faster than 〈Λ〉. Fig. 4.21compares the two estimators, as a function of the over voltage, for the two SiPMstested in this work. The two estimators are comparable at low over voltages: < 4 V.Over Voltage [V]1 2 3 4 5 6 7 8Ratio [#]00.20.40.60.81Hamamatsu VUV4FBK VUV HD 3Hamamatsu VUV4 POISSONFBK VUV HD 3 POISSONFigure 4.21: Comparison of two estimators used to account for the CA noisecontribution in the derivation of the nEXO energy resolution for thetwo SiPMs tested in this work. The estimator labelled as POISSONwas derived from [1] and was defined, assuming Poisson statistics as√〈Λ〉1+〈Λ〉 . The other one, introduced in this work, is defined asσΛ1+〈Λ〉 .At higher over voltages instead the new estimator accounts for the increased fluctu-ation in the number of correlated avalanches while the previous one was artificiallydecreasing. Fig 4.22 reports the predicted nEXO energy resolution, using the new97Symbol Meaning Valuenp [γ] Number of photons 90946CE [#] Photon Collection Eff. 20−33%PDE [#] Photon Detection Eff. Fig. 3.18〈Λ〉 [PE] Mean number of CA Fig. 4.8σΛ [PE] Fluctuation in number of CA Fig. 4.9nq [e−] Number of electrons 122900εq [#] Charge Collection Eff. 97%σq,noise [e−] Noise in the charge ch. 1100n [#] Total number of quanta 2.14×105Table 4.4: Summary of the parameters of Eq. 2.53. np and nq represent thenumber of photons and electrons produced by the 0νββ decay of 136Xe(Q-value at 2458.07± 0.31 keV). CE and PDE represent the detectorphoton Collection Efficiency (CE) and the SiPM Photon Detection Effi-ciency (PDE). Their product defines the overall light detection efficiencyof the experiment i.e. εp = CE× PDE. The SiPMs Photon DetectionEfficiency, Correlated Avalanche (CA) noise (〈Λ〉) and fluctuation in thenumber of CA (σΛ) are reported in Fig. 3.18, Fig. 4.8 and Fig. 4.9 for thetwo devices tested in this work: Hamamatsu VUV4 and FBK VUV HD 3.εq and σ2q,noise represent the charge collection efficiency and the noise inthe charge channel. n is the total number of quanta of either type (lightand charge) produced by the original energy deposition. We refer thereader to Sec. 2.4.3 for a detailed explanation of the values reported inthis table.estimator for the SiPM CA noise, including the contribution of the light and chargechannels using the data of Table 4.4 and a 20% light Collection Efficiency (CE) forthe experiment. This last number is a conservative value and it was derived fromlight transport simulation of the nEXO detector using conservative parameters forthe reflectivity of the detector components, as shown in Fig. 2.18 of Chapter 2.The three main parameters that drive the energy resolution of Fig. 4.22 in the lightchannel are: the SiPMs Photon Detection Efficiency (PDE), the SiPM mean num-ber of Correlated Avalanche (CA) per pulse (〈Λ〉) and its fluctuation (σΛ). The lasttwo quantities, used for the construction of Fig 4.22, are reported in Fig. 4.8 andFig. 4.9 for the two SiPMs tested. The efficiency of the Hamamatsu VUV4 MPPC98is reported in Fig. 3.18. The efficiency of the FBK VUV HD 3 SiPM could notbe finalised in this work due to an ongoing study of the beam size in the VERAsetup (Sec. 4.4). In Fig 4.22 we therefore assumed that the new generation ofFBK devices had the same efficiency of its previous generation: FBK VUV HD 1,reported in Fig. 3.18 of Chapter 3. Conservatively we also assumed that the effi-ciency of the FBK VUV HD 3 was equal to the lower of the three measurementsreported in Fig. 3.18. The error bars account for the systematic errors in the mea-surements of the SiPMs PDE, as shown in Fig. 3.18. The most dominant featureOver Voltage [V]0 1 2 3 4 5 6Energy Resolution [%]0.70.80.911.11.21.31.4Hamamatsu VUV4FBK VUV HD 3Figure 4.22: nEXO predicted energy resolution as a function of the SiPMover voltage for the two SiPMs tested in this work. Both curves includethe contribution of the charge channel and use the values reported inTable 4.4. The overall detector collection efficiency was set to 20%.of the two curves is the existence of a minimum, as already noticed in Sec. 2.4.2while analysing the energy resolution of the FBK VUV HD 1 SiPM. Furthermore,the minimum does not coincide with the largest operational over voltage, which ingeneral results in a worse energy resolution due to the increase of the SiPM cor-related noise. Fig. 4.22 therefore shows that, if the PDE of the FBK VUV HD 3will be the same of its previous generation, it will allow to consider this deviceas an excellent candidate to the FBK VUV HD 1 for the nEXO light detectionsubsystem, since it satisfies the requirement on the nEXO energy resolution to besmaller (or equal) to 1%. Additionally, the requirement on the energy resolution99is satisfied up to 4 V of over voltage, differently from the previous generation ofFBK devices that was limited up to 3 V of over voltage. The Hamamatsu VUV4is instead close to meet this requirement, but its lower efficiency doesn’t allow toreach a value of 1% with a detector light collection efficiency of 20%. However, anincrease of the overall detector light collection efficiency to 33% (value that cur-rently is considered as the new baseline by the nEXO collaboration), would pushboth devices to a significant higher energy resolution giving a value close to 0.8%for the FBK VUV HD 3 and comfortably lower than 1% (0.9%) for the HamamatsuVUV4 MPPC, as shown in Fig. 4.23. Overall Fig. 4.22 and Fig 4.23 show as bothOver Voltage [V]0 1 2 3 4 5 6Energy Resolution [%]0.70.80.911.11.21.31.4Hamamatsu VUV4FBK VUV HD 3Figure 4.23: nEXO predicted energy resolution as a function of the SiPMover voltage for the two SiPMs tested in this work. Both curves includethe contribution of the charge channel and use the values reported inTable 4.4. The overall detector collection efficiency was set to 33%.SiPMs, depending on the final detector light collection efficiency, meet or are closeto meet the 1 % nEXO energy resolution requirement. An additional study by thenEXO collaboration is ongoing to finalize light transport simulations of the TPCthat will guide, in the next years, the final choice of the SiPM candidate for thenEXO experiment.1004.6 ConclusionsThis chapter describes measurements performed at TRIUMF to character-ize the properties of a new VUV sensitive SiPM at cryogenic temperatures forthe nEXO experiment. In particular we characterized a new generation of FBKSiPM named FBK VUV HD 3 and compared it against the old generation ofFBK devices: FBK VUV HD 1, and the Hamamatsu VUV4 MPPC. The resultsof this characterization are summarized in Table 4.5. For a device temperature ofQuantity Value UnitDark noise rate 0.278±0.001 Hz/mm2Number of CAs 0.211±0.004 PERelative fluctuation of the mean number of CAs 0.444±0.009 -Number of APAs 0.184±0.003 PENumber of CDAs 0.025±0.001 -Table 4.5: Summary of the results derived in this chapter for the characteri-zation of the FBK VUV HD 3 SiPM. The measurements are reported fora temperature of 163 K and at 3.42±0.11 V of Over Voltage. CA standsfor Correlated Avalanche. APA stands for Additional Prompt Avalanchesand CDA stands for Correlated Delayed Avalanches.163 K, the FBK VUV HD 3 dark noise rate is 0.278± 0.001 Hz/mm2 at 3.42±0.11 V of over voltage, a level comfortably lower than what required for nEXO(< 50 Hz/mm2). At the same over voltage setting and temperature, we measure:a number of additional prompt avalanches equal to 0.184±0.003 PE, a number ofcorrelated avalanches per pulse and a relative fluctuation of the mean number ofCAs in the 1µs following the trigger pulse of 0.211±0.004 PE and 0.444±0.009,respectively. Additionally, we measure a number of correlated delayed avalanchesper pulse in the same time window of 0.025± 0.001, also consistent with nEXOrequirements. This last quantity is significantly lower of the ones extrapolated forthe Hamamatsu VUV4 MPPC and FBK VUV HD 1 SiPM, reported in Table 3.1and in [1], respectively. The novelty of the FBK VUV HD 3 SiPM is in fact anew triple-doping technology developed by FBK for the Darkside-20k experimentand used for the fabrication of the sensor. This new technology significantly sup-presses the after-pulsing probability of this SiPM reducing therefore the number101of CDAs and CAs. This allows to increase the operational over voltage of thesedevices of almost 1 V if compared with its previous generation. Overall the darkcharacteristics of the FBK VUV HD 3 are consistent with the nEXO requirement.The efficiency of the FBK VUV HD 3 SiPM could not be finalized in this workdue to an ongoing study of the light beam confinement. However, we presenteda new technique, based on the time distribution between pulses, that not only isfree from correlated avalanche noise corrections, but also it allows to reduce sig-nificantly the systematic uncertainly on the measured PDE, especially in the VUVwavelength range. It will be used in the near future to measure the efficiency of theFBK VUV HD 3 SiPM. Finally, at the end of this chapter, we used the data derivedfrom the characterization of the FBK VUV HD 3 SiPM and Hamamatsu VUV4MPPC to estimate the nEXO energy resolution, as a function of the SiPM overvoltage including the contribution of the light and charge channel. More preciselyassuming: (i) an efficiency for the FBK VUV HD 3 equal the one of its previousgeneration, (ii) a detector light collection efficiency of at least 20%, we obtained apredicted energy resolution for the FBK VUV HD 3 SiPMs compatible with the 1%requirement set by the nEXO experiment. We can therefore conclude that, if thePDE of this device will be the same of its previous generation, the FBK VUV HD 3SiPM could be considered as an excellent alternative to the FBK VUV HD 1 SiPMfor the nEXO light detection subsystem. The Hamamatsu VUV4 MPPC instead,due to its lower efficiency (Chapter 3), doesn’t satisfy the nEXO energy resolutionrequirement. This suggests that with modest improvements in its PDE, or with anoverall higher baseline value for the light collection efficiency of the nEXO detec-tor, the Hamamatsu VUV4 MPPC could be considered as a possible alternative toFBK SiPMs for the nEXO experiment.102Chapter 5A new detector for particlephysics and beyond5.1 IntroductionIn the previous chapters of this work we characterized several SiPM photon-sensors for nEXO. In particular, we studied their contribution to the nEXO en-ergy resolution focusing on the two main parameters that drive this quantity inthe nEXO light detection subsystem: photon detection efficiency and correlatedavalanche noise. Chapters 3 and 4, in particular, show as the current generationof SiPMs is limited for the following reasons: (i) high correlated avalanche noise,(ii) low photon detection efficiency for vacuum ultraviolet wavelengths. Addi-tionally, as shown in Fig. 5.1 the current generation of SiPM is affected by lowtiming resolution (> 100 ps) [109, 110]. While the first two quantities are stronglyrelated to the photo-detector characteristics, the timing resolution of a large lowbackground cryogenic experiment, such nEXO, is limited not only by the timingjitter of the photo-detectors, but also from the slow electronics that is necessaryto use in order to obtain, over the entire detector, a manageable power consump-tion [65]. As shown in Chapter 2, for example, the current nEXO baseline de-sign does not require a time resolution better than 100 ns. A detector with fastertiming, at the ns level for example, would be however extremely beneficial forXe-based cryogenic experiments, since it would allow not only to separate singlet103Figure 5.1: Measured Single Photon Timing Resolution (SPTR) with a420 nm PiLas picosecond laser (42 ps FWHM intrinsic pulse width)for several SiPMs. The SPTR in nowadays devices is around 100 ps to140 ps FWHM for a SiPM size around 3×3 mm2. From Ref. [108].and triplet lifetimes in xenon, useful for background discrimination (Sec. 2.3), butalso to discriminate, from a timing prospective, the Cherenkov photons of the twoelectrons produced in the 0νββ decay that constitute a unique signature of thisdecay. The second part of this thesis wants to explore from a theoretical prospec-tive Geiger mode properties of SiPMs. This study will be in fact crucial for thedevelopment, in the near future, of a new type of SiPM technology to dramati-cally improve energy and timing resolution of the next generation of noble liquiddetectors. More precisely, we propose to develop a 3D integrated Back-side il-luminated SiPM (3D B-SiPM) where every SPAD is individually connected to aQuenching Circuit and a Time-to-Digital Converter [111, 112]. This new tech-nology would not only yield unprecedented light detection efficiency, but it wouldalso be suitable to build detectors with 4pi light coverage and (∼ ps) timing res-olution. Differently from the current generation of front-side illuminated SiPMs,where the incoming photons are converted into charge carriers in a shallow deple-tion region close to the surface [59], in B-SiPMs the back-side of the detector iswhat faces the incoming photons, with the depletion region extending for almost104the full thickness of the silicon substrate. Some advantages of this configurationare: 1) lower delayed correlated avalanches if compared with analog devices (after-pulsing reduction [81]); 2) early digitization by individual readout of each SPADopens the door to in situ signal processing, limiting required data bandwidth andlowering power consumption; 3) damaged/noisy SPADs can be disabled, whichcan’t be done with analog SiPM (otherwise compromising single photon countingability) [113]; 4) shorter electronics transmission lines minimizing therefore thetotal timing jitter: a 10 ps single photon timing resolution is achievable. In ad-dition, the back side photon-entrance window of the 3D B-SiPM is suitable to betreated with standard anti-reflective coatings technology (e.g. CCD, [114, 115])that shows extremely low reflection in the expected scintillation spectrum of liquidxenon and argon (174.8± 10.2 nm [47] and 126.8± 7.8 nm [116], respectively).The expected low silicon surface reflectivity [92], among other characteristics, willbe in fact the key component to achieve a high detector energy resolution thanks tothe almost 100% photon detection efficiency that the 3D B-SiPM technology canoffer.In order to start this development, in this chapter and in the next one we re-port new theoretical models to better understand Geiger mode properties of SiPM.This study in fact will be crucial to optimize the electric field of the 3D B-SiPMthat drives not only the device avalanche triggering probability, but also its noiseperformance. Disadvantage of the back-side configuration is in fact the potentiallyhigher dark noise rate due to the extended depleted region [117–119]. The maintheoretical study of Geiger mode devices properties goes back to 1972 with thework done by R. J. McIntyre [120] and by P. P. Webb [121] that is at the basisof modern semiconductor simulators. Up to now, there were not analytical mod-els that could be used to link the micro-physics of the device, responsible for theavalanche formation, with the measured wavelength and voltage dependence ofthe SiPM photon detection efficiency. Moreover, it was missing a connection be-tween the Shockley-Read-Hall thermal rate, considered to be the source of noise inGeiger mode device, and the measured voltage and temperature dependence of theSiPM dark noise rate. In the last two chapters of this work we will try to provide aphysics explanation of these two mechanisms.More precisely, in this chapter we will introduce a new model to explain the105wavelength and voltage dependence of the SiPM photon detection efficiency. Wewill also show how to infer from this model useful design parameters. Finally, inChapter 6, we will provide an extension of the model presented in this chapter topredict the voltage and temperature dependence of several nuisance processes inSiPMs, named: dark noise rate, correlate delayed avalanche and direct CrossTalk.These models were tested against the measurements reported in the previous chap-ters of this work and against new set of data specifically collected for this study.5.2 Characterization of SiPM Avalanche TriggeringProbabilitiesThanks to the rapid evolution of signal processing and light source technolo-gies, the field of light detection has significantly advanced over the last 10 years[122]1. Sensors capable of detecting single photons are crucial not only in particlephysics, but also in a wide range of scientific and commercial applications. SiPMsare an emerging and very promising technology that addresses the challenge ofsensing, timing and quantifying low-light signals down to the single-photon level.A key parameter of SiPMs is their Photon Detection Efficiency (PDE), which is de-fined as the probability for a single photon of wavelength λ to produce a detectablecurrent pulse when the SiPM is operated at a reverse bias voltage V . Experimen-tally, this quantity can be measured as the ratio between the number of photonsproducing detectable pulses and the total number of photons impinging onto theSiPM surface, usually measured with a reference detector [54]. In previous studiesthe PDE was parameterized as [123]PDE = FF ·QE(λ ) ·TP(V,λ ) (5.1)where FF is the Fill Factor, i.e. the ratio of the sensitive to total area of the device;QE(λ ) is the quantum efficiency, i.e. the probability for an impinging photon tocreate a primary electron-hole pair in the active volume; TP(V,λ ) is the avalanchetriggering probability, i.e. the probability for the generated electron-hole pair toinitiate a Geiger-mode avalanche inside the depletion layer. The main drawback of1This chapter was published as a standalone publication in [59]. Its content was adapted to fit thethesis structure.106Eq. 5.1 is the lack of formal separation between the different physical processes thatdefine the total PDE. Absorption and avalanche triggering probabilities are in factcorrelated, since the latter probability depends on where the photon is absorbed. In-ternal and optical quantum efficiency are also not formally separated in Eq. 5.1 andthe lack of an analytical expression for TP(V,λ ) brings to the need to introduce foreach SiPM a different data-driven parametrization of their PDE (e.g. [58, 123]). Inthis chapter we propose a new formulation of the SiPM PDE that accounts for theposition of photon-absorption and allows to infer key insight on the electric fieldstructure within SiPMs. This new parametrization predicts the PDE as a functionof the reverse bias voltage and wavelength, corresponding to attenuation lengths insilicon between a few nanometers and several tens of micrometers, specifically ac-counting for the transition from electron-driven avalanches (close to the surface), tohole-driven avalanches (deeper inside the silicon) in p-on-n SiPMs. The model hasbeen successfully applied to characterize the response of three SiPMs: two Hama-matsu Multi-Pixel Photon Counter (MPPC)s and one Fondazione-Bruno-Kessler(FBK) SiPM, and it can be extended to any other SiPM including n-on-p devices.5.2.1 Parametrization of the SiPM PDE5.2.1.1 Model for Single Photon Avalanche DiodesSiPMs are arrays of SPADs separated by guard rings and other structures,such as trenches to suppress optical CrossTalk [124]. The field at the edge ofeach SPAD is expected to be distorted by the proximity of the isolation structures[125]. Nevertheless, the small fraction of the SPAD area affected by edge effectsand the uniformity of the electric field in the SPAD depletion layer allows to treatthe parametrization of the SiPM PDE as a one-dimensional problem [126]. Thisapproximation may not apply to ultra-high-density SiPMs with very small SPADs[125]. Each SiPM SPAD is a reversely biased p-n junction, operated above break-down. In this configuration, a photo-generated carrier (electron or hole) enteringthe depletion layer may trigger an avalanche [127]. Not every carrier, however, willinduce one. Carriers can travel undisturbed or lose energy by interacting with thelattice, recombining before the junction reaches breakdown [128]. Additionally,107electrons (holes) may be lost if they diffuse to the silicon surface (into the siliconsubstrate).It is therefore possible to associate a finite probability of triggering an avalancheto each carrier depending on the SPAD reverse bias voltage V and on the positionx in which the carrier enters or is generated in the depletion layer: Pe(x,V ) orPh(x,V ) [120]. Fig. 5.2 shows the electric field of a typical p-n junction for a p-on-n SiPM simulated with the Lumerical DEVICE simulation package [129]. Theelectric field has a maximum at the p-on-n transition labeled xPN . The depletionlayer starts at dP (on the P+ side) and ends at dW (on the N side), defining the totaljunction width of W ≡ (dW − dP). Fig. 5.2 also shows the combined avalanchetriggering probability PP(x,V ) that an electron-hole pair will trigger an avalanchewithin the depleted regionPP(x,V )≡(Pe(x,V )+Ph(x,V )−Pe(x,V ) ·Ph(x,V ))This probability is electron-driven at x = dP and hole-driven at x = dW , yieldingPP(dP,V ) = Pe(dP,V ) and PP(dW ,V ) = Ph(dW ,V ), respectively [127]. The prob-ability is smaller on the N side due to the significantly lower impact-ionization-coefficient for holes compared to electrons [130]. Carriers created outside of thedepleted region may contribute to the total PDE reaching the depletion layer bydrifting or diffusing and subsequently triggering an avalanche. In this case, theprobability that a carrier reaches the depleted region depends on its lifetime, on thecarrier mobility and on the original position of photo-generation [128, 131].5.2.1.2 Modelling photon absorption and carrier transportThe probability that a single photon of wavelength λ is absorbed between xand x+dx as a function of the photon attenuation length µ(λ ) is:dPAbs(x) =1µexp(− xµ)dx (5.2)The photon absorption results in the generation of one or more electron-hole pairs[132]. Depending on the photon attenuation length and on the location and exten-108Figure 5.2: p-on-n SPAD simulated with Lumerical DEVICE. The SPAD hasan asymmetric constant doping concentration of NP+ = 7.5 ·1016 cm−3and NN = 2.5 ·1016 cm−3. The breakdown voltage for this configurationis VBD = 36.3 V. Top: Combined electron-hole Avalanche TriggeringProbability (ATP): PP(x,V ), within the depletion layer for a bias voltageof 40 V. Bottom: Carrier (electron-hole) concentration and electric fieldprofile. dP and dW mark the edges of the depletion layer. Additionally,xPN is the position of maximum electric field, while dP∗ and dW ∗ are theedges of the effective photon collection region. Different factors likecarrier mobility and recombination time contribute to defining the exactlocation of dP∗ and dW ∗ .sion of the microcell depletion layer, the avalanche process can be reduced to oneof these three independent mechanisms [133]:1. The photon is absorbed in the quasi-neutral upper layer (x ∈ [0,dP]). Thephoto-generated electron diffuses (or drifts) to the depleted region trigger-ing an avalanche with probability Ptr-e(x) · Pe(dP,V ), where Ptr-e(x) is the109probability for the electron produced at x to reach the upper depletion layerboundary dP.2. The photon is absorbed in the depleted layer (x ∈ [dP,dW ]). The photo-generated electron-hole pair triggers an avalanche with probability PP(x,V ).3. The photon is absorbed in the quasi-neutral lower layer (x ≥ dW ). Thephoto-generated hole diffuses (or drifts) to the depleted region triggeringan avalanche with probability Ptr-h(x) ·Ph(dW ,V ), where Ptr-h(x) is the prob-ability for the hole produced at x to reach the lower depletion layer boundarydW .The second process is the dominant mechanism for the avalanche breakdown[134]. Nevertheless, the drift and diffusion of minority carriers from the neutralregions contribute to the total PDE, but produce significant delays in the avalanchegeneration, as shown experimentally in [135] and numerically in [126]. The datareported in this chapter are not directly sensitive to time delays in the avalanchegeneration (Sec. 5.2.2). Diffusing or drifting electrons (holes), in particular, havethe same probability to create avalanches once they enter the depletion layer, re-gardless of their original creation depth, i.e. Pe(dP,V )(Ph(dW ,V )). We can there-fore simplify the transport of the photo-generated carriers in the depleted regionby introducing two effective depth parameters: dP∗ and dW ∗ , such that electrons(holes) photo-generated between dP∗ and dP (dW and dW ∗) always reach the deple-tion layer boundaries at dP (dW ) (Fig. 5.2). With this simplification the electron andhole transport probabilities Ptr-e(x) and Ptr-h(x) become step functions as follows:Ptr-e(x) = 1 if x ∈ [dP∗ ,dP]0 else (5.3)Ptr-h(x) = 1 if x ∈ [dW ,dW ∗ ]0 else (5.4)1105.2.1.3 Modelling the probability of triggering avalanches within thejunctionThe SiPM PDE for a wavelength λ can be obtained by combining the prob-ability of photon absorption (Eq. 5.2) with the simplified transport probabilities(Eq. 5.3 and Eq. 5.4) and with the combined electron-hole avalanche triggeringprobability PP(x,V ) as:PDEλ = ε0 ·∫ dW∗dP∗1µexp(− xµ)·PP(x,V ) dx (5.5)where ε0 is the optical quantum efficiency, i.e. the probability that a photon istransmitted in the silicon. This quantity depends on the SPAD fill factor (Sec. 5.2)and reflectivity [58]. The integral quantity represents instead the internal quantumefficiency , i.e. the probability that a photon is absorbed in the sensitive volume ofthe detector and triggers a self-sustained avalanche process.The main drawback of Eq. 5.5 is that it cannot be expressed using only mea-surable quantities. The combined electron-hole avalanche triggering probabilityPP(x,V ), for example, can be calculated numerically by solving a differential equa-tion that depends on the generally unknown SPAD electric field [120]. Therefore,an expression of Eq. 5.5, suitable for SiPM characterization, requires a secondapproximation in addition to the effective model of the quasi-neutral regions in-troduced in Sec. 5.2.1.2. Precisely, the avalanche triggering probability PP(x,V ) issimplified with a step function considering its asymptotic values at the microcelldepletion layer boundaries such that2PP(x)∼Pe(dP) if x ∈ [dP∗ ,xPN ]Ph(dW ) if x ∈ [xPN ,dW ∗ ] (5.6)With Eq. 5.6, Eq. 5.5 can be integrated exactly obtaining:PDEλ = PDEMAX ·(Pe(dP) · f ∗e +Ph(dW ) · (1− f ∗e ))(5.7)2From here on to keep the notation simple, we will drop the voltage dependence of these quanti-ties.111wherePDEMAX ≡ ε0 exp(− dP∗µ)(1− exp(−W∗µ))(5.8)with W ∗ ≡(dW ∗ − dP∗), the length of the effective region in which an absorbedphoton can initialize an avalanche process3. PDEMAX represents the saturationPDE for a wavelength λ and it is defined as the product of three quantities: (i)the optical efficiency (Sec. 5.2.1.3), (ii) the probability that a photon is transmittedthrough the upper quasi neutral layer, and (iii) the probability that a photon isabsorbed within the effective depletion zone W ∗. The fractionf ∗e ≡1− exp(− (xPN−dP∗ )µ)1− exp(− W ∗µ) ∈ [0,1] (5.9)represents the fraction of electron-driven avalanches for a wavelength λ . It de-pends on(xPN − dP∗): the length of the region in which avalanches are triggeredby an electron. Considering the weak voltage dependence around the breakdownof(xPN − dP∗)and W ∗ [131], PDEMAX and f∗e will be considered as voltage-independent quantities. An experimental validation of this approximation will beproposed in Sec. 5.2.2. It is worth noting that Eq. 5.5 neglects the multi-carrierproduction per single photon by assuming a quantum yield of 1. This processthat happens in the UV-B, UV-C and Vacuum Ultraviolet (VUV) wavelength range(< 320 nm [132]) may affect the total internal quantum efficiency and a separatework is needed to study PDEλ in this wavelength range.5.2.1.4 Inferring the electron-hole avalanche triggering probabilitiesThe evaluation of Pe(dP) and Ph(dW ) in Eq. 5.7 is a complicated numericalproblem [120]. Inspection of Eq. 5.7 shows an elegant way to find Pe(dP) experi-mentally, without the need to know the microcell electric field. In particular, if theattenuation length for a given wavelength is such that f ∗e ∼ 1 (i.e. short attenuation3W ∗ ≥W due to the extended junction boundaries (Sec. 5.2.1.2).112length), then Eq. 5.7 reduces toPDEλ ∼ PDEMAX ·Pe(dP) (5.10)In this case, PDEλ simply reduces to Pe(dP) since PDEMAX is assumed to be volt-age independent (Sec. 5.2.1.3). The condition f ∗e ∼ 1 for a p-on-n microcell is wellverified at UV wavelengths due to short attenuation lengths [136]. More generally,the condition f ∗e ∼ 1 could be also verified for longer wavelengths depending of thejunction structure. We propose an approximate empirical expression to overcomethe difficulty to fit the PDE of UV wavelengths as a function of the reverse biasvoltage V . Following an approach similar to the one developed in [137] (see alsoSec. 5.2.1.5), Pe(dP) can be expressed asPe(dP) =[1−(ke ·V · exp(− ke2/√V))−2](5.11)where ke and ke2 are two voltage-independent parameters. The problem in evaluat-ing Ph(dW ) can be solved by introducing a parameter k that represents an effectiveratio of the impact-ionization-coefficients [120]. In this way Ph(dW ) can be derivedfrom Pe(dP) as followsPh(dW ) =[1−(1−Pe(dP))k](5.12)This equation allows to express Eq. 5.7 in term of Pe(dP) and k only4.5.2.1.5 Evaluation of the ionization integral and Eq. 5.11The ionization integral δ (i.e. the average number of ionization per carrierpair) can be computed as [138]δ =〈∫ xidPαe(E)dx+∫ dWxiαh(E)dx〉(5.13)4It is worth recalling what was stated in Sec. 5.2.1.3 that, even if in the UV-B, UV-C and VUVwavelength range photon avalanches are electron driven in p-on-n SiPMs, the multi-carrier produc-tion per single photon may artificially increase the internal junction efficiency. Eq. 5.7 assumes aquantum yield of 1, therefore Eq. 5.10, that is derived from it, can only be used in the UV-A rangewhen this mechanism is not yet relevant [132].113where αe(E) and αh(E) are the ionization coefficients of an electron and a hole,respectively, which have originated from an ionization which occurred at xi, andthe average is on i. E is the electric field module.5 Since αe(E) >> αh(E) theprevious equation can be simplified as [138]δ ∼ C ·∫ dWdPαe(E)dx (5.14)where C is a constant near unity. The major contribution to the integrand ofEq. 5.14 occurs at fields close to the maximum electric field EMAX [138], there-fore Eq. 5.14 can be simplified asδ ∼ C ·αe(EMAX) ·W (5.15)where W = (dW − dP) is the junction width. According to [131], αe(E) can beparameterized asαe(E) = A ·E · exp(− BE)(5.16)where A and B are two model dependent parameters [139]. Substituting Eq. 5.16in Eq. 5.15, δ becomesδ ∼ C ·A ·EMAX · exp(− BEMAX)·W (5.17)The maximum electric field as a function of the reverse bias voltage V is [62]EMAX = EMAX0(1+VVi)(1−p)∼ EMAX0(VVi)(1−p)(5.18)where EMAX0 is the zero-bias maximum electric field, Vi is the built in potentialand p∈ [0,1] is the ideality factor [131]. The depletion layer width is given by [62]W =W0(1+VVi)p∼W0(VVi)p(5.19)5The ionization coefficients represent the number of electron-hole pairs generated per unit dis-tance and and they are strong function of the electric field114where W0 is the depletion layer width at zero-bias. The additional simplificationin Eq. 5.18 and Eq. 5.19 holds since, after breakdown, VVi >> 1. Finally, if wecombine Eq. 5.18 and Eq. 5.19 with Eq. 5.17, we can write δ asδ ∼ ke ·V · exp( −ke2V (1−p))(5.20)where ke and ke2 are two parameters that absorb all the constants. The choice ofp has no strong influence on the model behaviour. In this work we used p = 12 .Pe(dP) follows then as [138]Pe(dP) = 1−δ−2 (5.21)or explicitlyPe(dP) =[1−(ke ·V · exp(− ke2/√V))−2](5.22)that matches Eq. 5.11.5.2.1.6 Data analysis procedureThe procedure to characterize the SiPM PDE for p-on-n junction structuresand for different wavelengths is:• Measure Pe(dP) by fitting the SiPM PDE as a function of the reverse biasvoltage using short wavelengths (e.g. UV-A) and Eq. 5.10 (combined withEq. 5.11). This sets the three voltage-independent fitting parameters: ke, ke2,and PDEMAX.• Fit the SiPM PDE as a function of the reverse bias voltage for the otheravailable wavelengths with Eq. 5.7 and a unique χ2 minimization. Eq. 5.7has four fitting parameters(xPN −dP∗), k, W ∗ and PDEMAX. The first threeparameters are (approximately) wavelength and voltage independent, whilePDEMAX is a voltage-independent, but wavelength-dependent parameter.1155.2.2 Model validationIn this section we will apply the model introduced in Sec. 5.2.1.3 to charac-terize the voltage and wavelength dependence of the PDE of three SiPMs with thesame junction structure (p-on-n). The first SiPM is a Hamamatsu H2017 MPPCwhose characterization was reported in [94] (Sec. 5.2.2.1). The PDE of this MPPCwas studied in the range [400−640] nm at a temperature of 23.6 ◦C using a pulsefrequency method (corrected for the SiPM correlated avalanche noise [64]) and acalibrated photodiode as reference to calibrate the absolute light flux. The othertwo SiPMs are: (i) a Hamamatsu VUV4 MPPC (S/N: S13370-6152), and (ii) aFBK Low Field (LF) SiPM (Sec. 5.2.2.2). The last two SiPMs were already testedFigure 5.3: Single Photo-electron Equivalent (PE) charge as a function of theover voltage (difference between the reverse bias voltage and the break-down voltage) for the three tested devices.in Chapter 3 at 175 nm as possible candidates for the nEXO experiment. Themodel introduced in this chapter cannot be applied directly in the VUV wave-length range due to the higher quantum yield of VUV photons (Sec. 5.2.1.3). Thetwo SiPMs were therefore tested specifically for this work in a different wavelengthrange using the following wavelengths: 378 nm, 444 nm and 782 nm. The threewavelengths were obtained with a Hamamatsu Photonics laser controller C10196operated at 500 Hz with PLP-10 laser heads. The experimental technique used tomeasure the SiPMs PDE is reported in Chapter 3. Precisely, the average number116of photons detected by the SiPM (µSiPMλ ) was first measured by counting the num-ber of laser flashes in which no SiPM pulses were detected (N0). Using Poissonstatistics, µSiPMλ can then be expressed as:µSiPMλ =− ln(N0NTOT)−µDN (5.23)where NTOT is the total number of laser flashes. This method is independent ofcorrelated avalanches [58] and it requires only correcting for the average numberof dark noise pulses in the trigger window (µDN) [54]. The absolute PDE can thenbe obtained dividing µSiPMλ for the effective number of photons produced by thepulsed laser at the SiPM location (Nλ ), assessed with a reference detector, as:PDEλ =(µSiPMλNλ)(5.24)The PDE of the Hamamatsu VUV4 MPPC and the FBK LF SiPM were measuredat −40 ◦C and −60 ◦C to prevent dark noise overwhelming the light signal. Thedependence of the attenuation length on the temperature in Eq. 5.9 and Eq. 5.8 forthe three SiPMs was accounted considering the temperature coefficients reportedin [136].In addition, for each SiPM the single Photo-electron Equivalent (PE) charge(Q1 PE) was also extrapolated from the single PE gain, as discussed in [54]. Q1 PEwas then linearly fitted as a function of the bias voltage as Q1 PE =CD× (V −VBD)in order to extract for each SiPM: (i) the single cell capacitance CD, (ii) the Break-down Voltage VBD defined as the bias voltage at which the SiPM single PE charge(or gain) is zero. The results are shown in Fig. 5.3 as a function of the over voltage6.The extrapolated capacitance and breakdown voltages are reported in Table 5.1 andTable 5.2. The well tested linear dependence in Fig. 5.3 gives an experimental ver-ification of the weak voltage dependence of(xPN−dP∗)andW ∗ close to the break-down voltage (Sec. 5.2.1.3) showing as the changing of the single SPAD junctioncapacitance (and therefore the changing of the single SPAD junction width) can be6The over voltage is defined as the difference between the reverse bias voltage and the breakdownvoltage VBD.117neglected and PDEMAX (Eq. 5.8) and f∗e (Eq. 5.9) can be considered as voltage-independent quantities close to the breakdown.Finally, it is worth noting that the shortest wavelength measured in the nextsections is 378 nm whose quantum yield is 1, in agreement with the discussion ofSec. 5.2.1.3.Figure 5.4: Absolute PDE as a function of the over voltage for the Hama-matsu H2017 MPPC for wavelengths in the range [400−640] nm. Thecomplete data-set accounts for a wavelength scan with a resolution of∼ 5 nm (here displayed every 50 nm). The solid lines represent fits per-formed with Eq. 5.10 for the 400 nm data, and the combined fit withEq. 5.7 for the other wavelengths.5.2.2.1 Analysis of the Hamamatsu H2017 MPPCThe absolute PDE of the Hamamatsu H2017 as a function of the over voltageis reported for different wavelengths in Fig. 5.4. The solid lines represent fits per-formed with Eq. 5.10 and Eq. 5.7. First, the 400 nm data (µ(400 nm) ∼ 0.1 µm)were fitted with Eq. 5.10 (combined with Eq. 5.11) to constrain Pe(dP), as de-scribed in Sec. 5.2.1.4. The other wavelengths were then fitted using Eq. 5.7, withthe Pe(dP) constrained by the 400 nm fit, and(xPN − dP∗), k, W ∗ and PDEMAXas free parameters. The measured effective value for kH2017 = 0.25± 0.06. Thewidth of the e-triggered avalanche layer is 1.8±0.1 µm and the effective junction118Type(xPN−dP∗)[µm] W ∗ [µm] CD [fF]H2017 [94] 1.8±0.1 4.1±0.4 163±1VUV4 [54] 0.8±0.2 3.9±0.8 116±6LF [1] 0.145±0.01 2.2±0.1 83±5Table 5.1: Comparison of the fit parameters derived for the three tested de-vices (1/2).(xPN − dP∗)represents the length of the region in whichavalanches are triggered by an electron. W ∗ is the length of the effectiveregion in which an absorbed photon can initialize an avalanche process.CD is the single cell capacitance extrapolated from the single PE gain.Type VBD [V] W [µm] kH2017 [94] 52.2±0.1 1.54±0.01 0.25±0.06VUV4 [54] 48.3±0.1 1.01±0.05 0.07±0.06LF [1] 30.6±0.1 0.92±0.06 0.05±0.01Table 5.2: Comparison of the fit parameters derived for the three tested de-vices (2/2). VBD is the breakdown voltage. W is the physical junctionwidth derived using: (i) the pixel size, (ii) the fill factor provided byeach manufacturer and (iii) CD (e.g. [135]). k is an effective ratio of theimpact-ionization-coefficients as reported in [120].width is W ∗ = 4.1±0.4 µm. This last quantity can be compared with the physicaljunction width W = 1.54±0.01 µm derived as shown in [135] from the single cellcapacitance CD (Sec. 5.2.2). W∗ is bigger than W in agreement with the effect ofcarrier drift and diffusion described in Sec. 5.2.1.3. Additionally, PDEMAX and f∗e(this last quantity extrapolated using Eq. 5.9) are reported in Fig. 5.5 as a func-tion of the wavelength. f ∗e represents the fraction of electron driven avalanches(Sec. 5.2.1.3). It decreases with increasing wavelength which reflects the fact thatlonger wavelengths are absorbed deeper in the microcell (closer to the N side) and aconsiderable contribution to the total PDE thus comes from hole-driven avalanches.5.2.2.2 Analysis of the Hamamatsu VUV4 MPPC and FBK LF SiPMThe same analysis as for the H2017 SiPM was applied for the HamamatsuVUV4 MPPC and the FBK LF SiPM. In this case we were only interested in rel-119Figure 5.5: Fraction of Electron Driven Avalanches (EDA) ( f ∗e , derived us-ing Eq. 5.9 and the fit results reported in Table 5.1 and Table 5.2) andsaturation PDE (PDEMAX) plotted as a function of the wavelength forthe H2017 Hamamatsu MPPC. Due to the slower saturation of the holeprobability (Ph(dW )) compared to the electron one (Pe(dP)) (see alsoFig. 5.7), the error on the saturation PDE increases with increasingwavelength. For comparison, in this figure is also reported the PDEat the highest over voltage of Fig. 5.4.ative changes of the PDE for different wavelengths, therefore the absolute lightfluxes were not calibrated. In Fig. 5.6 we report the average number of photonsdetected for these two SiPMs (µSiPMλ , Eq. 5.23) as a function of the over voltage.The solid and dashed lines represent fits performed with Eq. 5.10 for the 378 nmdata (µ(378 nm) ∼ 0.03 µm). The other two wavelengths were fitted together us-ing Eq. 5.7 and the four free parameters introduced in Sec. 5.2.1.6. The effec-tive k values derived from the fit for the FBK LF and the Hamamatsu VUV4 arekLF = 0.05±0.01 and kVUV4 = 0.07±0.06, respectively7. For the FBK LF (Hama-matsu VUV4) the width of the e-triggered avalanche layer is 0.145± 0.01 µm7The uncertainty on the parameter k is related to the slow saturation of the hole probability com-pared with the electron one. See Fig. 5.7. The current generation of SiPMs suffers from correlatedavalanche noise that increases with the over voltage as shown in Chapters 3 and 4, therefore SiPMscan be operated only up to few volts of over voltage [64]. The progresses on reducing correlatedavalanche noise are however encouraging (e.g. [84]) and the next generations of SiPMs should fea-ture a reduced correlated avalanche noise that will allow the operation of these devices at higher overvoltages, constraining the error on k and therefore the uncertainty on Ph(dW ).120Figure 5.6: Average number of photons detected by the Hamamatsu VUV4MPPC and the FBK LF SiPM (µSiPMλ , Eq. 5.23) as a function of theover voltage for not calibrated light fluxes. The solid and dashed linesrepresent the fits performed with Eq. 5.10 for the 378 nm data and thecombined fit with Eq. 5.7 for the other two wavelengths.(0.8±0.2 µm) and the effective junction width is 2.2±0.1 µm (3.9±0.8 µm). Theeffective junction of the Hamamatsu VUV4 is less symmetric than the one of theHamamatsu H2017. Instead the FBK LF has a smaller electron dominated thick-ness suggesting a stronger doping asymmetry. Additionally, the physical junctionwidth of the Hamamatsu VUV4 (FBK LF) is 1.01± 0.05 µm (0.92± 0.06 µm).Both these lengths are smaller than the corresponding effective ones and againcompatible with the model described in Sec. 5.2.1.3. In Table 5.1 and Table 5.2 wereport a summary of the fit parameters for the three SiPMs. An additional compari-son between the three devices can be drawn analyzing their electron/hole avalanchetriggering probabilities: Pe(dP) and Ph(dW ), as reported in Fig. 5.7. The Pe(dP) ofthe three SiPMs saturates faster then the corresponding Ph(dW ). This aspect is re-lated to higher impact-ionization-coefficient of electrons compared to holes [127].Additionally, Fig. 5.7 shows that the two Hamamatsu devices have almost the sameelectron avalanche triggering probabilities, while those of the FBK LF are notice-ably different. Pe(dP) (Ph(dW )) at fixed over voltage is always larger (smaller) forthe FBK LF than for the Hamamatsu MPPCs, indicating that the FBK LF is more121Figure 5.7: Electron and hole Avalanche Triggering Probability (ATP):Pe(dP) and Ph(dW ), for the three SiPMs analyzed in this chapter. Foreach Pe(dP) are also reported the data of Fig. 5.4 and Fig. 5.6 used toobtain the corresponding curve. Each Ph(dW ) is derived using Eq. 5.12.The dashed regions represent the uncertainty on the hole probabilitiesPh(dW ) due to the uncertainty on the effective k-values of Table 5.1 andTable 5.2.sensitive to UV wavelengths since, for these wavelengths, the avalanche mecha-nism is driven by electrons (Sec. 5.2.1.4). The lower sensitivity of the HamamatsuVUV4 MPPC in the VUV range was in fact measured in Chapter 3. The reportedsaturation PDE of the Hamamatsu VUV4 MPPC and the FBK LF SiPM at an av-erage wavelength of 189±7 nm are 14.8±2.8 % and 22.8±4.3 %, respectively8.It is worth noting, however, that we cannot conclude that the higher efficiency ofthe FBK LF is exclusively due to a more optimised internal structure (i.e. higheravalanche triggering probability). Surface reflectivity, as well as junction depth,can also play an important role in defining the total PDE, as shown by Eq. 5.8.5.2.3 Design considerations for the next generation of SiPMsThe model presented in this chapter can be used to extrapolate useful designparameters to build new generations of SiPMs. The avalanche triggering prob-8The Hamamatsu VUV4 MPPC and the FBK LF SiPM were designed to cover the same spectralrange.122abilities can in fact be linked to the device micro-physics using the constant kapproximation introduced in Sec. 5.2.1.4.In Sec. 5.2.1.5 we defined the average number of ionization per carrier pairas δ ∼ ∫ dWdp αe(x) dx. This quantity can be experimentally extrapolated from theavalanche triggering probabilities as follows [120]e(1−k)δ =Pe(dP)1−Pe(dP)[(1−Pe(dP))k1− (1−Pe(dP))k](5.25)since Pe(dP) and k can be derived from the fitting procedure presented in the pre-vious sections of this chapter. Additionally, not only δ , but also the parameter kis linked to the device micro-physics, since it represents an effective ratio of theionization coefficient. In Ref. [120] it was defined ask =αh(E)αe(E)(5.26)where E is the electric field. Therefore δ and k represent two different parametersto inspect the junction characteristics. While the first one is sensitive to the junctionelectric field module and width, the second one depends mainly from the electricfield module. k, in particular, increases with the electric field [120], therefore aFigure 5.8: Number of ionization carriers produced along the carrier path de-rived using Eq. 5.25 for the three devices tested in this chapter.123lower k is related, on average, to a lower electric field in the junction.Fig. 5.8 reports the average number of ionization per carrier pair for the threetested devices extrapolated using Eq. 5.25. The FBK LF has the highest δ . Fromthis follows that even if the junction of the FBK LF has a smaller capacitance(Table 5.1) and field (lower k, Table 5.2) if compared with the ones of the othertwo SiPMs tested, its junction has a more efficient electric field structure since, onaverage, a carrier produces more-electron hole pair during the avalanche formation.Therefore, a lower peak field associated with a wider junction is more efficientduring the avalanche formation. The superior structure of the FBK LF SiPM isalso visible in Fig. 5.7 that shows as the FBK LF electron avalanche triggeringprobability saturates faster with over voltage if compared with the one of the othertwo SiPMs.Figure 5.8 coupled with the extraction of the k and δ parameters proposes away to optimize new generations of p-on-n SiPMs: reduce the field and increasethe junction width is in fact the key to achieve a faster saturation of the electronavalanche triggering probability and therefore a higher ionization efficiency. Thisconfiguration can be achieved with p-i-n junction structures rather than simple p-nstructures, as shown in [108].The k and δ parameters can be precisely estimated when performing semi-conductor simulations, as shown in Fig. 5.2, since the electric field in the junctionis known. Reduce k or, in other words, optimize the electric field in the junctionin order to obtain a high δ , will therefore be the key to design new generations ofmore efficient p-on-n SiPMs.5.3 ConclusionsIn this chapter we have presented a new analytical model to describe the SiPMPDE as a function of the reverse bias voltage. The new model was used to explainthe wavelength dependence of the SiPM PDE, attributed to a combination of elec-tron and hole avalanche triggering probabilities. In particular, we have shown thatthe photo-generated carrier drift and diffusion in the microcell quasi neutral layerscan be treated like an effective re-sizing of the microcell depletion layer bound-aries, therefore increasing the effective photon collection region. The model was124applied to analyze the response of three p-on-n SiPMs and can naturally be ex-tended to any SiPM, including n-on-p devices. In particular, it shows like a lowand wide electric field in the junction is crucial to achieve a faster saturation of theelectron probability and a higher ionization efficiency. This aspect will be the keyto optimize the electric field in the next generation of SiPMs.125Chapter 6Nuisance Processes in p-on-nSiPMs6.1 IntroductionIn the previous chapter of this thesis we presented a new model to describethe SiPM Photon Detection Efficiency (PDE) as function of the reverse bias volt-age and wavelength. To develop new generation of SiPMs, it is not only crucial tohave a better understanding of their avalanche triggering probabilities (Chapter 5),but it is also important to reduce significantly their nuisance processes named: darknoise, after pulse and CrossTalk. In this chapter we will introduce a new theoreticalframework based on the model introduced in Chapter 5, that allows to explain thevoltage and temperature dependence of all the nuisance processes in SiPM. Thenew model has been successfully applied to characterize two p-on-n SiPMs: anHamamatsu VUV4 Multi-Pixel Photon Counter (MPPC), already studied in Chap-ter 3, and one Fondazione-Bruno-Kessler (FBK) SiPM (FBK VUV HD 1 (LF)),and it can be extended to other SiPMs, including n-on-p devices.6.2 Nuisance Processes in SiPMDark and correlated avalanche noise are among the crucial parameters thatcharacterize SiPMs. Dark Noise (DN) pulses are charge signals generated by the126formation of electron-hole pairs due to thermionic or field enhanced processes, asintroduced in Chapter 1. The dark current produced by a p-n junction under reversebias can be considered, as first approximation, due to three independent mecha-nisms: (i) Shockley-Read-Hall recombination via traps, (ii) diffusion, (iii) bandto band tunneling. The total current is then given by the sum of each of thesemechanisms increased by avalanche multiplication. Different models are availablein literature to study p-n junction under reverse bias up to the breakdown volt-age [62, 140, 141], but no models are available to explain the relationship betweenthe source of the current (the three independent mechanisms listed above) and thepulse rate measured when a Geiger mode device is biased above the breakdownvoltage. The complication arises from the fact the probability a cell is dischargedi.e. a pulse is produced, depends on the avalanche triggering probability that is afunction of the position in which the e-h pair is originally created in the p-n junc-tion depleted region. A model to explain the Geiger mode DN pulse rate, as afunction of the applied over voltage, is presented in Sec. 6.3. Additionally, in thesame section, we will also show how to infer the Silicon bandgap from dark noisedata.Geiger mode devices don’t only suffer from dark noise, but also from Cor-related Avalanches (CA). As introduced in Chapter 1, CAs are due to at leasttwo mechanisms: the production of secondary photons during the avalanche inthe gain amplification stage detected in nearby cells, and the trapping and sub-sequent release of charge carriers produced in avalanches. The latter process isusually referred to as afterpulsing, while the former is usually called CrossTalk.CrossTalk photons produce nearly simultaneous avalanches to the primary one (Di-rect CrossTalk (DiCT)) or delayed by several ns (Delayed CrossTalk (DeCT)) [64].In general, the subset of the CAs constituted by afterpulses and delayed CrossTalkevents is named Correlated Delayed Avalanches (CDAs). The probability a cellis discharged and therefore creates a CDA depends, for both mechanisms, on theavalanche triggering probability that is a function of the position where the carrieris originally produced in the depleted region (for after pulsing events) or where thephoton is absorbed (for CrossTalk events). A detailed explanation of the voltagedependence of these nuisance processes in SiPMs will be presented in Sec. 6.4.1276.3 A model to explain the SiPM Dark Noise RateThe first step to develop a model to explain the voltage and temperature depen-dence of the SiPM Dark Noise (DN) rate consists in introducing the three mecha-nisms that are responsible for its formation: diffusion, Shockley-Read-Hall recom-bination via traps and band to band tunneling. Fig. 6.1 represents a visualization ofa symmetric p-on-n junction under reverse bias. The notation used in this chapter isthe same introduced in Chapter 5. The depletion region starts at dP (on the P+ side)Figure 6.1: Model of the symmetric p-on-n junction used in this chapter.and ends at dW (on the N side), defining the total junction width ofW ≡ (dW −dP).W0 represents the depleted region width at zero-bias. The electric field has a maxi-mum at the p-on-n transition labeled as xPN .6.3.1 Diffusive contributionThe diffusive carrier rate can be derived using the ideal diode current densityequation as [131]Rdiff =Jsqe(eqeVkBT −1) (6.1)where: Js is the reverse saturation current density; kB is the Boltzmann constant;T the temperature and qe is the elementary electron charge. The reverse biasvoltage V is taken to be negative. Using Eq. 6.1, and introducing a parameterβ ∈ [0,1][141], it is possible to derive the p-n junction electron and hole diffusivecarrier rates as followsRn-diff(dp) = βRdiff (6.2)128Rp-diff(dw) = (1−β )Rdiff (6.3)where each contribution is computed at the respective junction boundary, accord-ingly to Fig. 6.1.6.3.2 Band to Band TunnelingBand to band tunneling describes transitions of electrons which tunnel di-rectly from the valence band to the conduction band [62]. Its contribution to thetotal carrier rate can be accounted as a Dirac Delta function at the position of themaximum electric field xPN asRbbt(x) =Jbbtqeδ (x− xPN) (6.4)Jbbt is defined asJbbt = cbbtV[FmF0] 32e−F0Fm (6.5)where: Fm is the maximum electric field at x= xPN ; δ (x) is the Dirac delta function;F0 is a constant which has a value of 1.9×107 V/cm at room temperature, and cbbtis a fit parameter that is assumed to be temperature independent.6.3.3 Recombination via trapsThe recombination via traps carrier rate accounts for the rate at which elec-trons and holes are captured from the conduction or valence band, respectively. Inparticular, its contribution to the total carrier rate contains not only the conventionalShockley-Read-Hall mechanism, but also an additional term due to tunneling viatraps. It can be written as [62]Rtrap(x) = (1+Γ(x))Rsrh(x) (6.6)where Γ(x) is a field dependent quantity and it accounts for the effects of tunneling.It is given byΓ(x) = 2√3pi|F |FΓexp( FFΓ)2(6.7)129where: F is the local electric field. FΓ is a constant that depends on the effectivecarrier mass (m∗) [142] and temperature T as followsFΓ =√24m∗(kBT )3qeh2pi(6.8)Rsrh(x) is the Shockley-Read-Hall rate given by [131]Rsrh(x) =pn−n2ieτp(n+n1)+ τn(p+ p1)(6.9)where: p and n are the hole and electron densities; τp and τn are their lifetimes;n1 ∼ nie exp(−(ET −Ei)/kBT ) and p1 ∼ nie exp((ET −Ei)/kBT ) where nie is theintrinsic carrier concentration given by [143]n2ie = NcNv exp[−EgkBT](6.10)with Eg Silicon band gap and Nc and Nv effective densities of states in the conduc-tion and valance band, respectively. ET represents the trap energy in the band-gapand Ei is the intrinsic Fermi level. In reverse bias condition n ∼ p ∼ 0, thereforeRsrh(x) is almost constant within the depletion layer boundaries. If we assume towork with a symmetric junction approximation, Rsrh(x) can be assumed constantexcept within a distance of W0/2 from the depletion layer boundaries [144], suchthatRsrh(x)∼−csrh if x ∈ [dP+W02 ,dW − W02 ]0 otherwise(6.11)where csrh is derived from Eq. 6.9 and it is defined as1csrh ≡nie2τc cosh [(ET −Ei)/kBT ](6.12)The negative sign in Eq. 6.11 implies a negative recombination rate; hence a gen-eration of electron–hole pairs within the reverse-biased space charge region. If we1In Eq. 6.12 we substituted the electron and hole lifetimes with a single lifetime τc such thatτc ≡ (τp = τn).130assume mid-gap traps (i.e. ET = Ei), Eq. 6.11 becomesRsrh ∼−csrh ∝−e−Eg2kBT (6.13)This dependence of the Shockley-Read-Hall rate will be tested in Sec. 6.3.7. UsingEq. 6.11, Eq. 6.6 becomesRtrap(x)∼−(1+Γ(x))csrh if x ∈ [dP+W02 ,dW − W02 ]0 otherwise(6.14)6.3.4 SiPM Dark Noise RateThe SiPM dark noise rate (RDN), when the device is reverse biased abovethe breakdown voltage, can be obtained summing the thee independent carrierrates introduced in the previous sections and weighting them for the correspondingavalanche triggering probability. More precisely, in Chapter 5 we showed how it ispossible to associate to each carrier (electron or hole) a finite probability of trigger-ing an avalanche depending on the SiPM reverse bias voltageV and on the positionx in which the carrier enters or is generated in the depletion layer i.e. Pe(x, |V |) orPh(x, |V |) [120].The contribution to the total dark noise pulse rate due to the diffusive carrierrates can then be obtained weighting Rn-diff(dp) and Rp-diff(dw)with the correspond-ing boundary avalanche triggering probability i.e. Pe(dP, |V |) or Ph(dW , |V |), wherePe(dP, |V |) (Ph(dW , |V |)) represents the probability an electron (hole) that enters inthe depletion layer at x= dP (x= dW ) triggers an avalanche.The contributions to the total dark noise pulse rate due instead to the recom-bination via traps and tunneling carrier rates (i.e. Rtrap(x) and Rbbt(x)) depend in-stead on the position where the electron-hole pair (for the recombination via trapsrate) or the electron (for the band to band tunneling rate) is originally created inthe depletion layer. The corresponding dark noise pulse rate is therefore obtainedweighting each carrier rate for its avalanche triggering probability i.e. PP(x, |V |) or131Pe(x, |V |), respectively. PP(x, |V |) was defined in Chapter 5 as [59]PP(x, |V |)≡(Pe(x, |V |)+Ph(x, |V |)−Pe(x, |V |) ·Ph(x, |V |))It represents the probability an electron-hole pair, generated at the position x inthe depleted region, triggers an avalanche within a p-n junction reverse biased ata voltage V 2. The SiPM dark noise pulse rate after breakdown can be writtensumming the three pulse rates contributions just introduced as followsRDN =∫ dWdPRtrap(x)PP(x) dx+Rbbt(x)Pe(xPN)+Rn-diffPe(dP)+Rp-diffPh(dW )(6.15)where the first integral extends up to the depletion layer boundaries, and the band-to-band tunneling term is accounted as a Dirac Delta function at the position ofthe maximum electric field (xPN , Sec. 6.3.2). The diffusive contributions are neg-ligible if compared with the generation and band to band tunneling term in Silicon[131], especially under reverse bias condition, therefore the third and fourth termsin Eq. 6.15 can be safely neglected. The latest generation of SiPMs also stronglyreduced the band to band contribution to the total dark noise rate whose naturecan now be probed only at cryogenic temperatures [145]. In the range of temper-atures analysed in Sec. 6.3.7, this term results in fact still subdominant respect tothe generation via traps term therefore in what follows it will also be neglected.Eq. 6.15 can be additionally simplified with the model introduced in Chap-ter 5. In this way PP(x) can be written asPP(x)∼Pe(dP) if x ∈ [dP,xPN ]Ph(dW ) if x ∈ [xPN ,dW ]Eq. 6.15 therefore reduces toRDN ∼ Pe(dP)∫ xPNdPRtrap(x) dx+Ph(dW )∫ dWxPNRtrap(x) dx (6.16)2From here on to keep the notation simple, we will drop the voltage dependence of the avalanchetriggering probability, in agreement with the notation used in Chapter 5.132The first integral in Eq. 6.16 can be computed using Eq. 6.14. In this way this termreduces to∫ xPNdPRtrap(x) dx=−∫ xPNdP+W02(1+Γ(x))csrh dx==−csrh(fDN(W −W0))− csrh∫ xPNdP+W02Γ(x) dx(6.17)where (xPN− (dP+W02))≡(fDN(W −W0))(6.18)with fDN ∈ [0,1]. In the same way the second integral in Eq. 6.16 follows as∫ dWxPNRtrap(x) dx=−∫ dW−W02xPN(1+Γ(x))csrh dx==−csrh((1− fDN)(W −W0))− csrh∫ dW−W02xPNΓ(x) dx(6.19)where ((dW −W02)− xPN)≡((1− fDN)(W −W0))(6.20)Eq. 6.16 then becomesRDN ={− csrhPe(dP)[(fDN(W −W0))+∫ xPNdP+W02Γ(x) dx]+− csrhPh(dW )[((1− fDN)(W −W0))+∫ dW−W02xPNΓ(x) dx]} (6.21)The term multiplied by Pe(dP) (Ph(dW )) in Eq. 6.21 represents the contribution tothe total dark noise rate due to avalanches initialised by an electron (hole). Elec-trons or holes avalanches therefore give to the total dark noise rate two contribu-tions due to: (i) Shockley-Read-Hall thermal-only recombination; (ii) Shockley-Read-Hall thermal-trap assisted recombination.1336.3.5 Evaluation of the field enhanced recombination integralTo obtain a practical expression for RDN , in what follows we will assumeto work with a symmetric step junction for the extraction of the electric field:(Na = Nd) ≡ N where Na and Nd are the acceptor and donor concentration of thep-n-junction, respectively. In other words, we will approximate the real junctionelectric field with the one obtained symmetrizing the junction i.e. substituting itselectric field with the symmetric one obtained from a junction with same widthW .The electric field in the junction can then be written asF(x) = Fm(1−2 |x− xPN |W)(6.22)where Fm is the module of the maximum electric field at x= xPN . The first integralin Eq. 6.21 then becomes∫ xPNdP+W02Γ(x) dx==√3piWFΓ2|Fm|[exp( FFΓ)2]xPNdP+W02==√3piWFΓ2|Fm|[exp(FmFΓ)2− exp(FmFΓ(1− 2WfDN(W −W0)))2](6.23)and the second integral in Eq. 6.21 becomes∫ dW−W02xPNΓ(x) dx==−√3piWFΓ2|Fm|[exp( FFΓ)2]dW−W02xPN==−√3piWFΓ2|Fm|[− exp(FmFΓ)2+ exp(FmFΓ(1− 2W(1− fDN)(W −W0)))2](6.24)6.3.6 Fitting equation for the dark noise rateUsing Eq. 6.23 and Eq. 6.24, Eq. 6.21 becomes134RDN ={− csrhPe(dP)[(fDN(W −W0))+√3piWFΓ2|Fm|[exp(FmFΓ)2− exp(FmFΓ(1− 2WfDN(W −W0)))2]]+− csrhPh(dW )[((1− fDN)(W −W0))++√3piWFΓ2|Fm|[exp(FmFΓ)2− exp(FmFΓ(1− 2W(1− fDN)(W −W0)))2]]}(6.25)6.3.6.1 Analysis of dependencies of Eq. 6.25Despite the complexity, Eq. 6.25 can be simplified and reduced to only threeindependent parameters using the symmetric junction approximation introducedin Sec. 6.3.5 for the electric field. The avalanche triggering probabilities Pe(dP)and Ph(dW ) are in fact assumed known and fixed since they can be derived withthe method introduced in Chapter 5. FΓ is a constant. fDN represents the frac-tion of the junction width in which avalanches are initialized by an electron. It isa fit parameter and, by definition, it is constrained to be fDN ∈ [0,1]. The otherunknown quantities in Eq. 6.25 are: the Shockley-Read-Hall rate (csrh), the maxi-mum electric field (Fm) and the junction width (W ). csrh is a quantity that is voltageindependent, but temperature dependent, while Fm and W are assumed to be tem-perature independent, but voltage dependent quantities. Fm and W are however notindependent. The maximum electric field can in fact be written as [62]Fm = Fm0× (1−VVint)1−p (6.26)where: Fm0 is the maximum electric field at zero bias, Vint is the built-in potentialand p a parameter that depends on the junction type. In Sec. 6.3.5 we assumed towork with a symmetric step junction, therefore p = 12 . The value of Vint doesn’thave a strong influence on the model behaviour and it will be assumed equal to0.7 V. Fm0 can be extrapolated from the junction length at zero bias W0, as fol-135lows [62]Fm0 ≡Vint(1− p)×W0(6.27)The total junction length W ≡ (dW −dP) is then equal toW =√2ε0εr(Vint −V )qe[Na+NdNaNd](6.28)where ε0 and εr are the vacuum and relative Silicon dielectric constants. Assuminga symmetric step junction and defining W0 asW0 ≡√4ε0εrVintqeN(6.29)W can be written asW =W0√1− VVint(6.30)Finally,(W −W0)in Eq. 6.25 can be written as(W −W0)=W0[(1− VVint) 12 −1](6.31)As summary, Eq. 6.25 can be reduced to three fitting parameters: the Shockley-Read-Hall rate (csrh), the fraction of the junction width in which avalanches areinitialized by an electron ( fDN), and the junction width at zero bias (W0).6.3.7 Comparison of analytical dark noise calculations withmeasurementsIn this section we will apply the model just introduced to characterize thevoltage and temperature dependence of the dark noise rate of two SiPMs: a Hama-matsu VUV4 MPPC (S/N: S13370-6152) and (ii) a FBK VUV HD 1 (FBK LF)SiPM. The dark noise data of the Hamamatsu VUV4 MPPC were presented inChapter 3. We refer the reader to this chapter for a detailed description of thesetup used for their measurements and for the data taking procedure. Addition-ally, for this study, we measured the temperature dependence of the dark noise rate136of a FBK VUV HD 1 SiPM using the same electronics and techniques presentedin Chapter 3. For both devices (Hamamatsu VUV4 MPPC and FBK VUV HD 1SiPM) the avalanche triggering probabilities in Eq. 6.25 were considered as fixedquantities since they were derived, in Chapter 5, for the same two devices at 233 Kand at 213 K, respectively. Additionally, in what follows, we will treat the voltagedependencies of the avalanche triggering probabilities as temperature independentquantities. In this way, for example, the electron avalanche triggering probabilityfor the Hamamatsu VUV4 MPPC at a temperature T (PTe (dP)) could be derivedfrom the one measured at 233 K (P233 Ke (dp)) by only applying a translation tothe bias voltage (V ) due to the difference between the breakdown voltage at thetemperature T (V TBD) and the one at 233 K (V233 KBD ), as followsPTe (dp, |V |) = P233 Ke(dp; |V |+(|V |233 KBD −|V |TBD))(6.32)This approximation is justified due to the limited range of temperatures analysedfor the two devices (70 K for Hamamatsu VUV4 MPPC and 50 K for the FBK VUV HD 1).The avalanche triggering probabilities in fact depend on the ionization coefficientsin Silicon that are expected to have a weak variation in ∼ 100 K as shown, for ex-ample, in [146]. The fits done with Eq. 6.25 for the Hamamatsu VUV4 MPPC darknoise data are reported in Fig. 6.2. The fit parameter csrh is reported in Fig. 6.3.Note as the five data-set in Fig. 6.2 were fitted with a unique χ2 minimizationperformed with MINUIT [79]. According to the discussion of Sec. 6.3.6.1, theparameters W0 and fDN are in fact in common for the different temperatures, sincethey are assumed to be temperature and voltage independent parameters. csrh is in-stead a temperature dependent, but voltage independent parameter. In Fig. 6.3 wealso tested the dependence of the parameter csrh against the theoretical behaviourreported in Eq. 6.13. The temperature dependence of the Silicon band-gap in thefitting procedure was accounted as [147]:Eg(T ) = Eg(0)−αT 2T +β(6.33)with α = 4.73×10−4 eVK and β = 636 K. At 0 K Eg(0) = 1.166 eV. The exponen-tial behavior of Eq. 6.13 is well reproduced by the data. The fit gives a value of137voltage [V]46 48 50 52 54 56]2dark noise [Hz/m510610710810910 Temperature:233 [K]213 [K]193 [K]178 [K]163 [K]Figure 6.2: Dark Noise Rate as a function of the over voltage for differentSiPM temperatures for the Hamamatsu VUV4 MPPC. The solid linesrepresent fits performed with Eq. 6.25.Eg(0) = (1.30±0.01) eV. This value is in slight tension if compared with the the-oretical one. At the end of this section possible sources of systematic uncertaintythat could affect the bandgap extraction will be listed. For the other two parameters1/T [1/K]0.004 0.0045 0.005 0.0055 0.006 0.0065]3SRH [Hz/m610710810910101011101210131014101510Figure 6.3: Shockley-Read-Hall recombination rate (csrh) as a function of1/T for the Hamamatsu VUV4 MPPC. The parameter csrh was derivedby the fits of the dark noise data using Eq. 6.25. The solid line representsa fit with Eq. 6.13.W0 = (2.21±0.01)×10−7 m, while fDN = (1.7±0.2)×10−3. fDN represents the138fraction of the junction width in which avalanches are initialized by an electronand since fDN ∼ 0 we can conclude that in p-on-n SiPMs DN avalanches are holedriven. A more in depth analysis of Eq. 6.25 also shows as the Shockley-Read-Hall thermal-only rate is subdominant if compared with the Shockley-Read-Halltrap-assisted rate, as also shown in Fig. 6.4. This is interesting since it showsVoltage [V]44 46 48 50 52 54 56]2Dark Noise Rate [Hz/m3−102−101−10110210310410510610710810910233 [K] SRH Enh.233 [K] SRH163 [K] SRH Enh.163 [K] SRH Figure 6.4: Shockley-Read-Hall thermal and trap-assisted (enhanced) rate asa function of the over voltage for the Hamamatsu VUV4 MPPC at 233 Kand 163 K. The two contributions were derived from the fitting per-formed with Eq. 6.25.as, in p-on-n SiPMs, avalanches are initialized by holes (that additionally have alower probability to trigger an avalanche if compared with electrons [59]), and aredue to Shockley-Read-Hall trap-assisted mechanisms. Eq. 6.25 therefore showsas suppressing the field in Geiger mode devices not only reduces the band to bandtunneling contribution, here already negligible, but also the trap-assisted Shockley-Read-Hall contribution that drives the total dark noise rate in the current generationof SiPMs devices. Following the same procedure just introduced for the Hama-matsu VUV4 MPPC, the dark noise data of the FBK VUV HD 1 (FBK LF) andthe corresponding fits are reported in Fig. 6.5. As the previous fit, fDN convergesto 0, while W0 = (2.3± 0.2)× 10−7 m. We can therefore conclude that also forthe FBK VUV HD 1 the dark noise rate is given by avalanches initialized by holesand due to trap-assisted Shockley-Read-Hall recombination. The parameter csrh139voltage [V]31 32 33 34 35 36 37 38 39 40]2dark noise [Hz/m8109101010 Temperature:263 [K]253 [K]243 [K]233 [K]223 [K]213 [K]Figure 6.5: Dark Noise Rate as a function of the over voltage for differentSiPM temperatures for the FBK VUV HD 1. The solid lines representfits performed with Eq. 6.25.1/T [1/K]0.0036 0.0038 0.004 0.0042 0.0044 0.0046 0.0048 0.005]3SRH [Hz/m121013101410151016101710Figure 6.6: Shockley-Read-Hall recombination rate (csrh) as a function of1/T for the FBK VUV HD 1 SiPM. The parameter csrh was derived bythe fits of the dark noise data using Eq. 6.25. The solid line represents afit with Eq. 6.13.for these fits is reported in Fig. 6.6. The exponential behaviour also in this caseis well reproduced. Eg(0) converges to 1.01± 0.05 eV that is compatible in 3σwith the expected value. Table 6.1 summarises the common fit parameters derivedfor the two SiPMs tested in this section. In the table we additionally reported theχ2 \NDF (NDF is the Number of Degrees of Freedom) for the two global fittings.140Quantity Hamamatsu VUV4 MPPC FBK VUV HD 1 SiPMfDN [#] (1.7±0.2)×10−3 Compatible with 0W0 [m] (2.21±0.01)×10−7 (2.3±0.2)×10−7Eg(0) [eV] (1.30±0.01) 1.01±0.05χ2 \NDF 0.83 1.02Table 6.1: Summary of the parameters derived from the fitting of the darknoise data. Additionally, we reported the reduced χ2 of the global fitwith NDF Number of Degrees of Freedom.The good χ2 \NDF shows as the model reproduces well the data. In each globalfitting two sources of systematic errors were considered: (i) the error on the SiPMtemperature, (ii) the error on the breakdown voltage. The sensors temperature wasmeasured with 4 RTDs placed close to the position of the sensors and in good ther-mal contact with them (Chapter 3). The RTDs stability was found to be better than0.05 K. Therefore the temperature was considered fixed in the global fitting rou-tine of the dark noise data. However we cannot exclude a small shift between theaverage temperature measured by the 4 RTDs (used in the fitting) and the real sen-sor temperature. The absolute temperature was considered fixed also in the fittingof Fig. 6.6 and Fig. 6.3 used to extrapolate the silicon bandgap. The uncertaintyin the absolute SiPM temperature could affect the Silicon bandgap determinationsince this quantity is extremely sensitive to the absolute values of the temperaturesused in the fittings. Overall the temperature is not expected to be the biggest sourceof systematic uncertainty. The highest uncertainty comes in fact from the break-down voltage extrapolation. This quantity is extrapolated, for each SiPM, fromgain measurements and it is used to shift the zero of the probability (Eq. 6.32) ateach temperature. For each translation we considered an error compatible with thestatistical uncertainty of the breakdown voltage equal to 0.2 V. We therefore floatedthe quantity (|V |233 KBD − |V |TBD) in Eq. 6.32 considering tight boundaries of about0.2 V around the shifted value due to this uncertainty.1416.4 A model to explain Correlated Avalanches in SiPMsIn the previous section we introduced a model to explain the voltage and tem-perature dependence of the SiPM Dark Noise rate. In this section we will showhow the avalanche triggering probabilities introduced in Chapter 5 and used in thedark noise model can also be used to infer the voltage and temperature dependenceof other two SiPMs nuisance processes: Direct CrossTalk and correlated delayedavalanche. More precisely, a model to explain the voltage dependence of the Di-rect CrossTalk is reported in Sec. 6.4.1, while a model to explain the voltage de-pendence of the number of correlated delayed avalanches is reported in Sec. 6.4.2.In what follows we will use the same notation introduced in Chapter 5 without in-troducing it explicitly. We refer therefore the reader to that chapter to have moredetails.6.4.1 Direct CrossTalk modelFor about half a century it has been known that avalanche processes in Siliconproduce light usually called optical CrossTalk (CT). The photons emitted during anavalanche are in the infrared wavelength range [148, 149]. To suppress CT photonsSiPMs incorporate trenches and other structures to surround each pixel that act asphoton-stopper. It is however still extremely challenging to completely suppressthe propagation of infrared light in Silicon due to the high attenuation length ofthese photons that can be several µm long [136]. DiCT (Direct CrossTalk) andFigure 6.7: Different types of Optical CrossTalk in SiPM. The relative ratiobetween the different contributions is heavily dependent on the structureof the micro-cell. Overall four types of internal CrossTalk can be iden-tified: Delayed CrossTalk (DeCT), Substrate CrossTalk (SuCT), DirectCrossTalk (DiCT) and Reflection CrossTalk (ReCT). See text for moredetails.142DeCT (Delayed CrossTalk) are the two mechanisms associated with the produc-tion of CT photons, see Fig. 6.7. DiCTs photons occur when photons generatedduring a triggered avalanche in one micro-cell promptly travel to the amplificationregion of neighboring micro-cells, where they induce a secondary avalanche. Thismechanism happens over a pico-second time scale [64] and it mimics a multiplePE signal. DeCT photons occur instead when photons generated during a triggeredavalanche travel deeper in the substrate. Some of them get lost in the substrate(Substrate CrossTalk), but some drift back to the avalanche region, due to the low-field in the Silicon bulk, where they can trigger a subsequent avalanche that canbe delayed of several ns from the parent one. Additionally photons can also bereflected back (Reflection CrossTalk), as shown in [150, 151]. The voltage depen-dence of the number of photons detected by a SiPM as DiCT events i.e. promptevents, can be written as3NDiCT = χ1× kC(V −VBD)qe[fCTPe(dP)+(1− fCT )Ph(dW )](6.34)where: χ1 is a voltage independent parameter that accounts for the probability aphoton is detected in the active volume of a pixel (W ∗, Chapter 5) in a time scalesuch that it appears as a prompt signal to the DAQ (miming therefore a multiplePE event)4. The quantity C(V−VBD)qe represents the total number of carriers producedduring an avalanche with C single SPAD capacitance and VBD breakdown voltage.Eq. 6.34 therefore assumes as the number of photons produced in an avalancheis proportional (k) to the total number of carriers. The parameter k is assumed tobe voltage independent and its temperature dependence is expected to be weak asshown by measurements of the optical CrossTalk at cryogenic temperatures [145].The quantity in square brackets follows directly from Eq. 5.7 in Chapter 5 and3Differently from Sec. 6.3.4, to simplify the discussion from now on the reverse bias voltage istaken to be positive.4Note as the parameter χ1 in Eq. 6.34, as well as the ratio between prompt and delayed CT pulses,strongly depends on the overall electronic used to discriminate multiple-PE events. A slow electronicwith a high integration time will in fact tend to show higher multiple-PE events if compared with afast electronics, like the one used for this work (described in Chapter 3), where it is possible toperform better pulse shape reconstruction. The parameter χ1 in Eq. 6.34 therefore assumes as thedivision between prompt and delayed CT events is dependent only on the electronic and not on theSiPM voltage or temperature.143represents the probability a photon is absorbed in the electron or hole side of theavalanche region i.e. on the side in which the probability to trigger an avalancheis given by Pe(dP) or Ph(dW ), respectively. fCT represents therefore the fractionof DiCT events whose avalanche is initialized by an electron. It can be deriveddirectly from f ∗e (Eq. 5.9) performing a Taylor expansion of the exponential. Theattenuation length of infrared photons (µ) is in fact large enough compared to theeffective photon collection region (W ∗) such thatfCT = f∗e (µ >>W∗)≡1− exp(− (xPN−dP∗ )µ)1− exp(− W ∗µ)∼ (xPN−dP∗)W ∗∈ [0,1]The parameter fCT , in agreement with the discussion of the SPAD capacitancereported in Chapter 5, is considered to be voltage and temperature independent.(xPN − dP∗) and W ∗ in fact increase slightly with voltage, due to the increase ofthe junction boundaries, but their ratio can be considered as a voltage independentquantity, as shown in [143].The parameters χ1 and k in Eq. 6.34 cannot be treated as independ parametersin the fitting procedure; therefore Eq. 6.34 will be written asNDiCT = η1(V −VBD)[fCTPe(dP)+(1− fCT )Ph(dW )](6.35)where the pre-factor η1 absorbs all the constants. Note as this equation treats assecond order processes multi-reflection mechanisms i.e. photons produced in onecell that by reflection or other mechanisms reach n-additional neighbor cells beforeto trigger an avalanches with n= 2,3, ... .6.4.1.1 Comparison of analytical DiCT calculation with measurementsIn this section we will apply the model just introduced to characterize thevoltage and temperature dependence of the DiCT optical CrossTalk for the twoSiPMs introduced in Sec. 6.3.7 and used for dark noise measurements. We referthe reader to that section for more details. The number of DiCT photons, in unitof Photo-electron Equivalent (PE), can be estimated with the method introduced inSec. 3.3.4.3 and here summarized. More precisely, the charge distribution of the144prompt pulses obtained from dark data can be used to determine the mean numberof Additional Prompt Avalanches (APA)s, NAPA, due to Direct CrossTalk as:NAPA =1NN∑i=1AiA1 PE−1where: Ai is the charge of the prompt pulse i, A1 PE is the average charge of 1PE pulses and N is the number of prompt avalanches analyzed. NAPA is equalto the average number of DiCT photons produced per avalanche detected by theDAQ (NDiCT, Eq. 6.35)5. The NAPA number in unit of PE, as a function of theover voltage and for different temperatures, is reported in Fig. 6.8 and Fig. 6.9for the Hamamatsu VUV4 MPPC and for the FBK VUV HD 1 SiPM, respec-tively. The solid lines in each figure represent fits done with Eq. 6.35. As alreadyintroduced in Sec. 6.3.7 for the dark noise fitting, the avalanche triggering prob-abilities in Eq. 6.35 were considered as fixed quantities, since they were derivedin Chapter 5 for the same two devices at 233 K and at 213 K, respectively. Thetemperature dependence of the avalanche triggering probabilities was accountedin the same way reported in Sec. 6.3.7. We therefore considered the voltage de-pendence of the avalanche triggering probabilities as a temperature independentquantity by applying a translation to the bias voltage V due to the change of thebreakdown voltage with temperature, as shown for example in Eq. 6.32 for theHamamatsu VUV4 MPPC. Additionally, for each SiPM, the five and six data-setsreported in Fig. 6.8 and Fig. 6.9 were fitted with a unique χ2 minimization per-formed with MINUIT [79]. As introduced in fact in Sec. 6.4.1, the parameter fCTis assumed to be a voltage and temperature independent parameter. Table 6.2 sum-marises the parameters derived from the fit and the ratio xPN−dP∗W ∗ extrapolated from5Note as, in principle, it could be possible to have a cascade of DiCT photons due to differentcell discharges that mimic multiple-PE signal in the DAQ. This process is not accounted in Eq. 6.35,that instead assumes that multiple-PE events are due to n photons produced by the discharge ofthe same cell. For example, a photon produced by the discharge of one cell triggers another cell,with a DiCT photon. In a ps time scale, the discharge of the second cell produces a DiCT photonsthat discharges a third cell. This cascade process gives overall a signal of charge equal to 3 PEthat appears as prompt to the DAQ. Unfortunately, it is not possible with the current generation ofSiPMs to do coincidence at the ps time scale to discriminate these types of events, therefore we willalways assume that multiple-PE events that appear as prompt are due to n photons originated by thedischarge of the original cell.145over voltage [V]0 2 4 6 8 10number of APA [PE]0.020.040.060.080.10.120.14Temperature:233 [K]213 [K]193 [K]178 [K]163 [K]Figure 6.8: Mean number of Additional Prompt Avalanches (APA) due to di-rect CrossTalk as a function of the over voltage for different SiPM tem-peratures for the Hamamatsu VUV4 MPPC. The solid lines representfits performed with Eq. 6.35.Chapter 5 (Table 5.1 and Table 5.2), accordingly to the discussion of Sec. 6.4.1.The fCT parameter of the Hamamatsu VUV4 MPPC agrees in less than 1σ withthe one derived in Chapter 5. The fCT parameter of the FBK VUV HD 1 is in-stead in slight tension with the one predicted by the data reported in Chapter 5.However, the quality of the fit (χ2/NDF) does not worsen significantly while con-straining this parameter to be equal to the one predicted in Chapter 5. The reasonis to be searched in the highly asymmetric junction of the FBK VUV HD 1 thatresults in a small electron dominated thickness i.e. (xPN −dP∗), that gives a lowernumber of electron driven avalanches (for DiCT mechanisms) if compared with theHamamatsu VUV4 MPPC. The value of the parameter η1 reported in Table 6.2 isinstead obtained averaging the η1 parameter derived by the fits performed at eachtemperature. The small error in the values of η1 shows as, independently of thedevice and temperature, each fit converges essentially to the same value. This vali-dates the assumption done in the derivation of the DiCT model in Sec. 6.4.1, wherewe inferred a weak temperature dependence of this parameter due to the small tem-perature dependence of other DiCT measurements [145]. The good quality of thefitting is shown by the χ2 \NDF, reported in Table 6.2. The sources of systematic146over voltage [V]0 2 4 6 8 10number of APA [PE]00.10.20.30.40.5 Temperature:263 [K]253 [K]243 [K]233 [K]223 [K]213 [K]Figure 6.9: Mean number of Additional Prompt Avalanches (APA) due todirect CrossTalk as a function of the over voltage for different SiPMtemperatures for the FBK VUV HD 1. The solid lines represent fitsperformed with Eq. 6.35.errors for the DiCT measurements and for the fitting routine are compatible withthe ones reported in Sec. 6.3.7 for the fitting of the dark noise data. We refer thereader to that section for more details.Overall from this analysis, we can conclude that, since fCT ∼ 0 and η1 isessentially temperature independent, DiCT mechanisms in p-on-n SiPMs have aweak temperature dependence and are initialized by holes. This last aspect agreeswith the dark noise discussion reported in Sec. 6.3.7 where we noticed as also darknoise avalanches, in p-on-SiPMs, were initialised by holes.6.4.2 Correlated Delayed Avalanche ModelCorrelated Delayed Avalanches (CDA)s arise at least from two processes: af-terpulses and delayed optical CrossTalk. A detailed explanation of the latter mech-anism is introduced in Sec. 6.4.1. The former process is instead due to the largenumber of carriers present in Geiger-mode discharges [152]. Some of them canin fact remain trapped in metastable traps during the avalanche formation. Theirsubsequent release may produce additional pulses called afterpulses, which con-tribute to the observed signal. The time distribution between pulses can be used to147Quantity Hamamatsu VUV4 MPPC FBK VUV HD 1 SiPMfCT [#] 0.13±0.02 0.009±0.006η1 [V−1] 0.039±0.001 0.340±0.006xPN−dP∗W ∗ [#] 0.2±0.1 0.065±0.006χ2 \NDF 1.6 1.9Table 6.2: Parameters extracted from the fit of the DiCT data usingEq. 6.35 for the two SiPMs tested: Hamamatsu VUV4 MPPC andFBK VUV HD 1 SiPM. fCT represents the fraction of avalanches initial-ized by an electron. η1 is a parameter that accounts for several propor-tionality factors (see text for more details). xPN−dP∗W ∗ represents the ratiobetween the length of the region in which avalanches are initialized by anelectron and the length of the effective photon collection region, definedin Chapter 5. Additionally, we reported the reduced χ2 of the global fitwith NDF Number of Degrees of Freedom.discriminate the two types of events. An example is reported in Fig. 6.10 for theFBK VUV HD 1 SiPM. Trigger pulses6 producing prompt CrossTalk are markedFigure 6.10: Distribution of FBK VUV HD 1 SiPM pulses as a function ofthe time after the microcell was triggered. See text for a detailed ex-planation [1].with blue dashed circle and are measured as pulses with multiple PE amplitudes(Sec. 6.4.1). Avalanches due instead to delayed CrossTalk have amplitudes equalto 1 PE and are marked with a purple circle. Trigger pulses can also suffer from6Trigger pulses are called prompt in Fig. 6.10.148afterpulses represented with an orange circle in Fig. 6.10. The amplitude of theafterpulse events depends on the SPAD recharging time. This last quantity can beestimated directly from Fig. 6.10 fitting the recovery curve of the 1 PE events asfollowsA= A1 PE×(1− e−t−t0τSPAD)(6.36)where: A1 PE is charge of 1 PE pulses, τSPAD is microcell recharging time and t = t0is the time of the prompt pulse. Afterpulse events can also suffer of CrossTalk,but with a lower probability if compared with the trigger pulses, since the cellthat produces the afterpulse event has a lower bias voltage due to its rechargingtime. The orange band structure in Fig. 6.10 is therefore repeated above the 1 PE(orange dashed circle) to represent this contribution. Pulses occurring with largerdelay from the primary pulse can originate from either afterpulsing, thermal orfield enhanced mechanisms (green circle). They can suffer of prompt CrossTalkand they are represented in Fig. 6.10 as green dashed circles. Pulses marked with adashed purple circle represent instead pulses who do not get resolved by the DAQ.Fig. 6.10 is constructed requiring: (i) the charge of the trigger pulse to be a singlePE equivalent, (ii) the time of the trigger pulse to be equal to the mean triggertime set by the DAQ pre and post-trigger acquisition settings. The first condition isnecessary to avoid that multiple-PE events artificially increase the probabilities ofthe different SiPM nuisance processes, as shown in [85]. The voltage dependenceof the number of CDAs due to afterpulses, as a function of the time difference trespect to their primary pulse can be written asNCDA(t) =C(V −VBD)qe×ASiPMk1NtrapsW ×e−tττ××[fCDAPe(dP,V −Ve f f (t))+(1− fCDA)Ph(dW ,V −Ve f f (t))] (6.37)where: ASiPMk1NtrapsW represents the trapping probability i.e. the probability asingle carrier is trapped. This quantity is assumed to be proportional (k1) to thetrap density Ntraps.7 W represents the junction width, therefore NtrapsW represents7For simplicity, in the text we assumed that each carrier trapped is also realised. This conditioncan be relaxed introducing an effective k1 that accounts for the probability that not only a carrier istrapped, but also it is realised. k1 is assumed to be a voltage independent parameter. It is however a149the total number of traps per m2. This number has a voltage dependence, since Wincreases slightly with voltage. In what follows we will parameterizeW as done inSec. 6.3.6.1 such thatW =W0√1+VVint(6.38)with W0 junction length at zero bias and Vint = 0.7 V. Vint doesn’t have a stronginfluence on the model behaviour, as already noticed in Sec. 6.3.6.1. ASiPM is theSiPM active area. The quantity e− tττ accounts for the exponential decay of the num-ber of afterpulse events with time i.e. the exponential realise of the trapped carrierswith time [153]. τ represents an afterpulsing time constant often called afterpuls-ing lifetime and it depends on the temperature as shown, for example, in Chapter 3.The quantity inside the square brackets of Eq. 6.37 represents instead the probabil-ity a carrier produces a self sustained avalanche. More precisely, the first (second)term of the sum in Eq. 6.37 represents the probability a single carrier triggers anavalanche with probability Pe(dP,V −Ve f f (t)) (Ph(dW ,V −Ve f f (t))). fCDA ∈ [0,1]represents the fraction of afterpulse events whose avalanche is initialized by anelectron. The effective voltage Ve f f (t) in the avalanche triggering probabilities ac-counts for the reduced avalanche probability due to the cell recharging time: τSPAD,such thatVe f f (t)≡V −((V −VBD)× (1− e−tτSPAD )+VBD)(6.39)with V bias voltage and t elapsed time from the primary pulse at which the trappedcharge is realised. Practically, as it will be shown in Sec. 6.4.2.1, its effect is negli-gible in p-on-n SiPMs. Finally, the first term in Eq. 6.37: C(V−VBD)qe , represents thetotal number of carriers produced during an avalanche that depends on the SPADcapacitance C and breakdown voltage VBD, as already introduced in Sec. 6.4.1.Some of the parameters in Eq. 6.37 cannot be treated as independent in the fittingtemperature dependent parameter, since the trapping probability, like the trapping lifetime τ [152],depends on the SiPM temperature.150procedure, therefore Eq. 6.37 can be simplified as followsNCDA(t) =η2× e−tτ (V −VBD)×√1+VVint××[fCDAPe(dP,V −Ve f f (t))+(1− fCDA)Ph(dW ,V −Ve f f (t))] (6.40)where the parameter η2 absorbs all the constant. This parameter is assumed to bevoltage independent, but temperature dependent, since the trapping probability canbe function of the temperature.6.4.2.1 Comparison of analytical CDA calculation with measurementsIn this section we will apply the model just introduced to characterize the volt-age and temperature dependence of the number of correlated delayed avalanchesfor the two SiPMs used for the dark noise rate and DiCT measurements reportedin Sec. 6.3.7 and Sec. 6.4.1.1, respectively. More precisely, dark noise and CDAsevents can be distinguished by studying the time distribution of dark events relativeto the primary pulse using the method introduced in Chapter 3 and in [85]. Thistechnique requires the charge of the primary pulse to be a single PE equivalent andallows to compute the observed pulse rate R(t), as a function of the time differencet from the primary pulse (t = 0) as followsR(t) = RDN(t)+RCDA(t)where RDN is the rate of dark noise pulses and RCDA is the rate of CDAs per pulse.An example of the measured time distribution for the Hamamatsu VUV4 MPPCat different over voltages, for a temperature of 233 K, is reported in Fig. 6.11. Werefer the reader to Chapter 3 to have a detailed explanation of the constructionof this figure. The DN rate can then be estimated from Fig. 6.11, performing aweighted mean of the asymptotic rates at long times i.e. between 103 and 104 nsfor 233 K. The number of CDAs in a fixed time window of length ∆t can be derivedasNCDA(∆t) =∫ ∆t0(R(t)−RDN(t))dt151time difference wrt the primary pulse [ns]1 10 210 310 410]2pulse rate [Hz/mm110210310410510610 Over voltage:1.66 [V]2.66 [V]3.66 [V]4.66 [V]5.66 [V]6.66 [V]7.66 [V]Figure 6.11: Observed pulse rate R(t) of the Hamamatsu VUV4 MPPC as afunction of the time difference with respect to (wrt) the primary pulsefor a temperature of 233 K.where RDN is the DN rate. Each pulse rate in Fig. 6.11 can then be integrated toobtain the number of CDAs per pulse as a function of the over voltage and timedifference respect to its primary pulse. More precisely, the number of CDAs at agiven time ti respect to the primary pulse can be obtained integrating the rate (Ri)at the time ti for a length equal to the corresponding bin width (∆ti) as followsNCDA(ti) =(Ri−RDN)×∆ti (6.41)The number of CDAs for different times ti for the Hamamatsu VUV4 MPPC ispresented in Fig. 6.12 as a function of the applied over voltage. The data-setswere fitted together with a unique χ2 minimization performed with MINUIT totest the theoretical behaviour predicted by Eq. 6.40. According to the discussionof Sec. 6.4.2, τ , η2 and fCDA are in fact voltage independent parameters. Thefirst dataset reported in Fig. 6.12 corresponds to 28.4 ns. Before this time, asshown in Fig. 6.11, the rate distribution at 233 K suffers from a combination ofpulse reconstruction inefficiency and afterpulses too small to get resolved by theDAQ from their primary pulse (Chapter 3). After 112.9 ns, the rate distribution isinstead dominated by dark noise events and the afterpulse rate is hidden from this152over voltage [V]0 1 2 3 4 5 6 7 8 9 10CDA Number [#]4−103−102−101−10 Time Delay:28.4 ns35.7 ns45.0 ns56.6 ns71.3 ns89.7 ns112.9 nsFigure 6.12: Number of Correlated Delayed Avalanches (CDA) per primarypulse (derived from Fig. 6.11) for the Hamamatsu VUV4 MPPC as afunction of the over voltage. The number of CDAs was plotted for dif-ferent times ti with respect to (wrt) the primary pulse at a temperatureof 233 K.other nuisance process. The fits in Fig. 6.12 result in an afterpulsing time constantτ for the Hamamatsu VUV4 at 233 K of 24±2 ns. In the fitting procedure τSPADwas fixed to 35 ns. The cell recovery time was in fact derived from the chargevs time to next pulse plot, as shown in Sec. 6.4.2. The η2 parameter, commonto all the fits, was found to be (0.0301± 0.0003) V−1 . The fCDA fit parameterinstead converges to 0. This fact is crucial, since it shows as after pulse events inp-on-n SiPMs, like Dark Noise and DiCT events, are hole driven processes. ThefCDA parameter was found to be compatible with 0 not only at 233 K, but alsoat the other temperatures tested for this study. Due to this experimental fact, thetranslation of the bias voltage due to cell recharging time i.e. V−Ve f f (t) in Eq. 6.40has a negligible effect, since to hole probability saturates slowly if compared withthe electron one, as shown in Chapter 5. From this follows that in p-on-n SiPMafterpulse events at different times respect to their primary pulses can be combinedand fitted together without the need to discriminate them from a timing prospective.More precisely, the total number of CDAs (NCDA) in a window of length ∆t can be153fitted as followsNCDA ∼∑iNCDA(ti) == η2× (V −VBD)×√1+VVint×[fCDAPe(dP)+(1− fCDA)Ph(dW )](6.42)where we dropped the Ve f f dependence in the avalanche triggering probabilities.Fig. 6.13 reports the total number of correlated delayed avalanches for the Hama-matsu VUV4 as a function of the applied over voltage, and for different tempera-tures. The NCDA number was derived integrating the corresponding rate plot untilits baseline, i.e. until the rate plot starts to be dominated by dark noise events,as shown in Fig. 6.11. The solid lines in Fig. 6.13 represent fits performed withEq. 6.42. The fCDA parameter was fitted as a common parameter for the five tem-over voltage [V]0 2 4 6 8 10number of CDA [#]00.20.40.60.811.2 Temperature:233 [K]213 [K]193 [K]178 [K]163 [K]Figure 6.13: Total number of Correlated Delayed Avalanches (CDA) per pri-mary pulse for the Hamamatsu VUV4 MPPC as a function of the overvoltage, for different temperatures. Solid lines represent fits performedwith Eq. 6.42.peratures and it was found to be compatible with zero, as already anticipated at thebeginning of this section. The reduced χ2 of the fit was found to be bigger than10. This last quantity is dominated by the disagreement of the fit with the data atthe two higher temperatures, removing in fact these 2 datasets from the common154fitting routing gives a reduced χ2 smaller than 3. The fit was therefore found toimprove with decreasing temperature. This aspect is thought to be related to theincreased afterpulse carrier lifetime with temperature. The efficiency of the pulsefinding algorithm, used for the construction of the rate plot, increases with decreas-ing temperature, since afterpulses are realised, on average, at longer times respectto the trigger pulse and they can then carry a higher charge. It is therefore easier forthe pulse-finding algorithm to identify correctly these pulses. Moreover, the lowerdark noise rate at cryogenic temperatures allows to better discriminate afterpulsesthat otherwise would be hidden by the SiPM dark noise rate.A similar analysis was also done for the FBK VUV HD 1 SiPM. Its pulse rate,at 233 K, for different over voltages is reported in 6.14. Fig. 6.15 instead reportstime difference wrt the primary pulse [ns]1 10 210 310 410]2pulse rate [Hz/mm210310410510610Over voltage:1.81 [V]2.81 [V]3.81 [V]4.81 [V]5.81 [V]Figure 6.14: Observed pulse rate R(t) of the FBK VUV HD 1 SiPM as afunction of the time difference with respect to (wrt) the primary pulsefor a temperature of 233 K.the total number of correlated delayed avalanche for this SiPM as a function of overvoltage and temperature with additionally the fit performed with Eq. 6.42. In agree-ment with the analysis of the Hamamatsu VUV4, also for the FBK VUV HD 1 theNCDA number was derived integrating the corresponding rate plot until its baseline,i.e. until the rate plot starts to be dominated by dark noise events. For this device,fCDA was found to be compatible with 0, as in the previous case, resulting there-fore in hole driven afterpulses also for this p-on-n SiPM. The reduced χ2 for these155over voltage [V]0 2 4 6 8 10number of CDA [#]00.10.20.30.40.5 Temperature:263 [K]253 [K]243 [K]233 [K]223 [K]213 [K]Figure 6.15: Total number of Correlated Delayed Avalanches (CDA) per pri-mary pulse for the FBK VUV HD 1 SiPM as a function of the overvoltage, for different temperatures. Solid lines represent fits performedwith Eq. 6.42.fits was found to be 2.35, resulting significantly improved respect to the one of theHamamatsu VUV4 MPPC, particularly at higher temperatures. A possible expla-nation of this trend, not mentioned before, is the low probability of DeCT of thisSiPM compared to the Hamamatsu VUV4 MPPC, as shown in Fig. 6.16. In thissection we in fact implicitly assumed that the rate plot was completely dominatedby afterpulse events. This is, on average, the case since this plot is constructedonly accounting on the time differences between pulses and not on their differentcharges. For example an event with higher integrated charge (i.e. a DiCT from anafterpulse event) would be accounted in the rate plot as a single entry at a certaintime t respect to the primary pulse neglecting its higher integrated charge. Therate plot therefore accounts for the effective pulse rate after the trigger pulse i.e.the afterpulse rate, without considering additional nuisance processes that couldbe related to it. This assumption may become weaker for SiPMs with a significantcontribution of DeCT events in their CDA rate because DeCT and afterpulse eventsare uncorrelated between each other and they both contribute to the rate plot. Thisis not the case for the FBK VUV HD 1, as shown in Fig. 6.16, for which the amountof DeCT is negligible respect to the afterpulse rate. The Hamamatsu VUV4 MPPC156time difference wrt the primary pulse [ns]1 10 210 310 410Pulse Area [LSB x ns]050100150200250300350400310×number of events020406080100120140Figure 6.16: FBK VUV HD 1 charge distribution of first pulses followingsingle PE trigger pulses as a function of the time difference with re-spect to (wrt) their primary pulse for 233 K and for an over voltage of4.81±0.13 V. The grey scale represents the number of events in eachbin on a logarithmic scale. The solid red line shows a fit of the after-pulsing events and is used to measure the recovery time of one cell,equal to 35±5 ns.instead, as shown in Fig. 3.6 of Chapter 3, has a component of DeCT that affectsthe time distribution at short times after the trigger pulse, i.e. < 100 ns. This canexplain the lower quality of the fits of the Hamamatsu VUV4, if compared withthe ones of the FBK VUV HD 1, since Eq. 6.42 was derived assuming to workwith afterpulse-only events. In principle DeCT events after the trigger pulse couldbe removed by a careful selection based on the pulse charges before to constructthe corresponding rate plot. DeCT events carry in fact 1 full PE charge, differentlyfrom afterpulse events. This discrimination however becomes less powerful if aDeCT event happens at a time t from the trigger pulse close to 2 or 3 times thesingle PE SPAD recovery time. In this case, not only DeCT events, but also after-pulse events carry essentially a full 1 PE charge, therefore the discrimination is noteffective and could cut afterpulse events rather than true DeCT events. Overall, inaddition to the sources of uncertainties just introduced for the CDA fittings, the twosources of systematic errors listed for the dark noise measurements, and reportedin Sec. 6.3.7, apply also to these fittings. We refer the reader to that section formore details. Table 6.3 summarises the fit results of this section.157Quantity Hamamatsu VUV4 MPPC FBK VUV HD 1 SiPMfCDA [#] Compatible with 0 Compatible with 0χ2 \NDF > 10 2.35Table 6.3: Parameters extracted from the fit of the afterpulse data usingEq. 6.42 for the two SiPM tested: Hamamatsu VUV4 MPPC andFBK VUV HD 1 SiPM. fCDA represents the fraction of after pulse eventsinitialized by an electron. Additionally, we reported the reduced χ2 ofthe global fits with NDF Number of Degrees of Freedom.Quantity Hamamatsu VUV4 MPPC FBK VUV HD 1 SiPMfDN [#] (1.7±0.2)×10−3 Compatible with 0fCT [#] 0.13±0.02 0.009±0.006fCDA [#] Compatible with 0 Compatible with 0xPN−dP∗W ∗ [#] 0.2±0.1 0.065±0.006Table 6.4: Summary of the f parameters derived in this chapter. Addition-ally, we also reported the value xPN−dP∗W ∗ derived in Chapter 5 for the twoSiPMs. It represents the ratio between the length of the region in whichavalanches are initialized by an electron and the length of the effectivephoton collection region.6.5 ConclusionsIn this chapter we have presented a new analytical framework to describeseveral nuisance processes in SiPM. The new models are based on the concept ofthe avalanche triggering probability, derived in Chapter 5, and they predict witha minimum set of floating parameters all the nuisance processes in SiPM named:direct CrossTalk, correlated delayed avalanches and dark noise rate. Table 6.4summarises the f parameters derived in this chapter. In the three cases f ∼ 0;therefore all the nuisance processes in p-on-n SiPM can be considered initialised byholes i.e. they have a voltage dependence that is compatible with the correspondingPh(dW ) probability derived in Chapter 5. This is probably a consequence of thehigher absorption volume of holes compared to electron in p-on-n SiPMs sincethe doping of the P side is, on average, higher if compared with the one of the N158side. Additionally, we have shown how the source of the dark noise rate in Geigermode devices cannot be completely reduced to thermal Shockley-Read-Hall rate,but it needs to account for a strong component of enhancement due to trap-assistedcontributions. The three models were applied to analyze the response of two p-on-nSiPMs and they can naturally be extended to any SiPM, including n-on-p devices.Furthermore, they provide key insight into the electric field structure within SiPMs,which can explain the limitation of existing devices and can be used to optimizethe performance of future SiPMs.159Chapter 7ConclusionsNext-generation noble liquid Xe detectors are emerging as the most promisingcandidates for neutrinoless double beta decay search due to their scalability for verylarge target masses and potential for extremely low background operations.Over the last years, the nEXO collaboration has designed a new tonne-scale(0νββ ) decay experiment conceived to push the search to the next frontier. ThenEXO detector is based on a Time Projection Chamber (TPC) filled with fivetonnes of Liquid Xenon (LXe) (5109 Kg) enriched 90% at 136Xe. A careful se-lection of the TPC material, with also the intrinsic capability to simultaneouslydetect signal and background, will be the primary strength of the nEXO detector.Its design is conservative and very few assumptions of material radio-purity weremade beyond what was already experimentally demonstrated and measured withits precursor: the EXO-200 detector. Additionally, the nEXO experiment is de-signed to provide the best possible energy resolution for a LXe TPC with a finaldesign goal of 1% energy resolution (σ/Q) for the 0νββ decay of 136Xe (Q-valueat 2458.07± 0.31 keV). In order to achieve this objective the nEXO TPC needsto read out with high efficiency both the charge clouds and the light produced bythe LXe ionization and scintillation, respectively. nEXO plans to use VUV sensi-tive Silicon Photo-Multipliers (SiPMs) as photon-sensors for the detection of the175 nm scintillation light of LXe.SiPM technology represents an unprecedented attempt to create an ideal solid-state photon detector combining the low-light detection capabilities of the previous160device generations with all the benefits of a solid-state sensor. In contrast to thewidely used Photomultiplier Tubes (PMTs), SiPMs are low-voltage powered, op-timal for operation at cryogenic temperatures, and have low radioactivity levelswith high gain stability (∼ 106) over the time in operational conditions. For thesereasons, not only the nEXO experiment, but also other large-scale low-backgroundcryogenic experiments, such as DarkSide-20k, are migrating to a SiPM-based lightdetection system. This work was focused on two aspects that are now under studyby the nEXO collaboration: (i) Analysis of the characteristics of several SiPMscandidates for nEXO; (ii) Theoretical study of Geiger properties of SiPMs. Moreprecisely, in Chapters 3 and 4 we studied two SiPMs as possible candidates lightsensors for the nEXO experiment: the Hamamatsu VUV4 MPPC and the newestgeneration of FBK devices: the FBK VUV HD 3 SiPM. For each device variousfeatures such as: dark noise, gain, correlated avalanches and direct CrossTalk weremeasured, with new dedicated setups, at 163 K and compared against the nEXOrequirements for the light detection subsystem. For the Hamamatsu VUV4 MPPCwe also measured its Photon Detection Efficiency (PDE) at 175 nm. The PDE ofthe FBK VUV HD 3 SiPM could not be finalized in this work due to an ongoingstudy of the light beam profile in one of the new commissioned setup. As summary,both devices meet the nEXO Dark and Correlated Avalanche noise requirements at163 K giving comparable performances. Additionally, the FBK VUV HD 3 device,with its triple doping technology, suppresses significantly the sensor after-pulsingprobability allowing to increase the operational over-voltage of these devices of1 V if compared with its previous generation (FBK VUV HD 1), while fulfilling thenEXO requirements. The results of the Hamamatsu VUV4 and FBK VUV HD 3characterization were then used, at the end of Chapter 4, to estimate the nEXOenergy resolution as a function of the SiPM over voltage including also the contri-bution of the charge channel. In [1] the nEXO collaboration in fact showed as thefirst generation of FBK devices (FBK VUV HD 1) satisfies the requirement on thenEXO energy resolution (1% energy resolution for the 0νββ decay of 136Xe), butin a limited over voltage range (up to 3 V of over voltage). At the end of Chap-ter 4, using a 20% baseline value for the nEXO detector light collection efficiency,we have shown that, if the PDE of the FBK VUV HD 3 will be the same of itsprevious generation, it would allow to consider this device as an excellent candi-161date for the nEXO experiment, not only because it satisfies the 1% nEXO energyresolution requirement, but because it does that up to 4 V of over voltage. Thechoice of the FBK VUV HD 3 SiPM, if compared with its previous generation,would therefore be beneficial since it would result in a higher S/N for the overalllight detection channel. The Hamamatsu VUV4 MPPC instead, due to it lower ef-ficiency, marginally satisfies the energy resolution requirement considering a 20%baseline value for the nEXO detector light collection efficiency. This suggests that,with modest improvements in its efficiency, or with an overall higher baseline valuefor the light collection efficiency in the nEXO experiment, the Hamamatsu VUV4MPPC could be considered as a possible alternative to FBK SiPMs.The last two chapters of this thesis (Chapters 5 and 6) are part of a broaderstudy that is not only limited to the nEXO experiment, but it looks forward thenext generation of noble liquid detectors. The outcome of this study will be thedevelopment of a new Back Side Illuminated SiPM light sensor to dramaticallyimprove energy and timing resolution of future noble liquid detectors, significantlyenhancing their background rejection capabilities relative to the current generationof dark matter and double beta decay experiments. More precisely, the secondpart of this thesis explored from a theoretical prospective Geiger mode propertiesof SiPMs. The first step was the derivation of the model presented in Chapter 5.In this chapter in fact we introduced a physics motivated parameterization of theavalanche triggering probability that describes the PDE of a SiPM as a functionof its reverse bias voltage, at different wavelengths. This parameterization wasbased on the fact that in p-on-n SiPMs the induced avalanches are electron-drivenin the UltraViolet (UV) range, while they become increasingly hole-driven towardsthe infrared range. In particular, the model was able to predict the SiPM PDE asa function of the reverse bias voltage and wavelength, corresponding to attenua-tion lengths in silicon between a few nanometers and several tens of micrometers,specifically accounting for the transition from electron-driven avalanches (close tothe surface), to hole-driven avalanches (deeper inside the silicon). Additionally wedemonstrated as a low and wide electric field in the junction is crucial to achievea faster saturation of the electron probability and therefore a higher ionization effi-ciency.The framework introduced in Chapter 5 was then used in Chapter 6 to explain162not only the voltage dependence of the SiPM efficiency, but also the temperaturedependence of the principal SiPM nuisance processes named: direct CrossTalk,correlated delayed avalanches and dark noise rate. In particular, in this chapterwe showed how all the nuisance processes in p-on-n SiPM are initialised by holes,probably due to the higher absorption volume of holes compared to electrons inp-on-n SiPM. Additionally, we have shown how the source of the dark noise ratein Geiger mode devices can not only be reduced to Shockley-Read-Hall thermalrecombination, but it has also a strong component of enhancement due to trap-assisted recombination.The models presented in Chapters 5 and 6 were tested to analyze the responseof two p-on-n SiPMs and they can naturally be extended to any SiPM, includingn-on-p devices. Overall the last two chapters of this work show as SiPMs are anextremely promising technology that still needs a strong research and developmentwork to improve its current weaknesses: high correlated avalanche noise and lowphoton detection efficiency for vacuum ultraviolet wavelengths. Next generationdouble beta decay and dark matter liquid based cryogenic experiments need in factunprecedented light detection efficiency and excellent background discriminationstrategies to succeed in their respective searches. 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Thesis/Dissertation
eng
Physics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Development of a single vacuum ultra-violet photon-sensing solution for nEXO
Text