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The Light only Liquid Xenon experiment : signal production, data acquisition and commissioning de St Croix, Austin 2020

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The Light only Liquid Xenon ExperimentSignal Production, Data Acquisition and CommissioningbyAustin de St CroixA THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Physics)The University of British Columbia(Vancouver)August 2020© Austin de St Croix, 2020The following individuals certify that they have read, and recommend to the Fac-ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:The Light only Liquid Xenon Experiment: Signal Production, Data Ac-quisition and Commissioningsubmitted by Austin de St Croix in partial fulfillment of the requirements for thedegree of Master of Science in Physics.Examining Committee:Dr. Fabrice Retie`re, Department Head, Science Technology (TRIUMF)Co-SupervisorDr. Reiner Kruecken, Deputy Director, Research (TRIUMF)Co-SupervisoriiAbstractThe Light only Liquid Xenon (LoLX) experiment is a small detector designed toinvestigate both scintillation and Cherenkov light emission in liquid xenon, vali-date photon transport in simulations and study Silicon Photo-Multiplier (SiPM) re-sponse. A new analytic framework for describing temporal scintillation signaturesis presented, and the relationship between xenon’s refractive index and tempera-ture is derived from literature. The energy deposition time is also calculated forrelativistic alpha and beta particles, as it pertains to future phases of LoLX whichwill aim to measure the rise time of the scintillation signal. The characterization ofthe LoLX electronics shows single photon resolution and the system linearity wasreported for prompt light pulses up to 200 photons. A framework is presented fordescribing external cross-talk (eXT), where a charge avalanche in one SiPM gener-ates photons which trigger another device. Finally preliminary data from a gaseousnitrogen cooldown of LoLX is analyzed, which shows evidence for fluorescence innitrogen and eXT, although no definitive conclusions are drawn.iiiLay SummaryNeutrinos are a basic building block of the universe. They have been measuredto be very light, although their actual mass is not known. To investigate this andother fundamental properties of neutrinos, the nEXO experiment is looking for ahypothesized type of radioactivity which is indirectly related to neutrinos. Physicsexperiments seem complex but operate in a similarly manner to humans; nEXOgains its information by light (eyesight) and electric charge (touch). nEXO usesxenon gas cooled until it is a liquid which produces UV light when it absorbs aradioactive particle. To help nEXO understand this light and how to measure it, webuilt a small experiment called Light only Liquid Xenon or LoLX. In my work Itested the electronics used to measure the light and looked at the first data to ensurethat the detector was working properly.ivPrefaceThis dissertation is composed of original, unpublished work by the author and workstemming from collaborative efforts. See signal production calculations for inde-pendent work, while the nEXO and LoLX experiments are collaborations. TheLoLX detector construction was done at McGill by Dr. Thomas McElroy. The au-thor’s role in LoLX was testing of the electronics, monte carlo testing, DAQ setup,operation and documentation of the DAQ system (with assistance from TRIUMFexperts), and run-coordination. Analysis was performed independently using theLoLX software, which was written primarily by Dr. Thomas McElroy from McGillUniversity. Electronic design and simulation of the SiPM equivalent circuit wasdone by Peter Margatek from TRIUMF. External Cross-talk simulations done byKevin Sohn at McGill University.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Neutrino Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1 Neutrinoless Double Beta Decay . . . . . . . . . . . . . . . . . . 53 The nEXO Experiment . . . . . . . . . . . . . . . . . . . . . . . . . 83.1 Liquid Xenon as detection medium . . . . . . . . . . . . . . . . . 83.2 The nEXO Detector . . . . . . . . . . . . . . . . . . . . . . . . . 93.2.1 Photon Collection and Energy Resolution . . . . . . . . . 123.2.2 Cherenkov Light and Background Discrimination . . . . . 154 Light Production in Liquid Xenon . . . . . . . . . . . . . . . . . . . 184.1 Summary of Scintillation Physics and Basis for Particle ID . . . . 18vi4.2 Temporal Structure . . . . . . . . . . . . . . . . . . . . . . . . . 204.2.1 Molecular Populations . . . . . . . . . . . . . . . . . . . 204.2.2 Excitation Channel . . . . . . . . . . . . . . . . . . . . . 214.2.3 Ionization Channel . . . . . . . . . . . . . . . . . . . . . 224.2.4 Analytical Photon Intensity . . . . . . . . . . . . . . . . 244.2.5 No escaping electrons: φ = 0 . . . . . . . . . . . . . . . 264.2.6 Monte Carlo approach . . . . . . . . . . . . . . . . . . . 264.2.7 Temporal Structure: Results . . . . . . . . . . . . . . . . 274.3 Spectral Width . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.4 Cherenkov Light . . . . . . . . . . . . . . . . . . . . . . . . . . 304.5 Optical Properties and nEXO as a lens . . . . . . . . . . . . . . . 324.6 Energy Deposition Time . . . . . . . . . . . . . . . . . . . . . . 375 Light Detection: Silicon Photomultipliers . . . . . . . . . . . . . . . 425.1 Working Principle . . . . . . . . . . . . . . . . . . . . . . . . . . 435.1.1 PN Junction . . . . . . . . . . . . . . . . . . . . . . . . . 435.1.2 Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . 435.1.3 Silicon PhotoMultiplier . . . . . . . . . . . . . . . . . . . 465.2 Sources of Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 505.3 Photon Detection Efficiency . . . . . . . . . . . . . . . . . . . . 535.4 Hamamatsu VUV4 . . . . . . . . . . . . . . . . . . . . . . . . . 566 The LoLX Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 586.1 Motivation and relation to nEXO . . . . . . . . . . . . . . . . . . 596.2 Detector Body and Cryostat . . . . . . . . . . . . . . . . . . . . . 606.3 Radioactive Sources . . . . . . . . . . . . . . . . . . . . . . . . . 626.4 Optical Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656.5 Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666.6 Linearity Correction . . . . . . . . . . . . . . . . . . . . . . . . . 726.7 Data Acquisition System . . . . . . . . . . . . . . . . . . . . . . 757 External XT Framework . . . . . . . . . . . . . . . . . . . . . . . . 808 Commissioning and First Results . . . . . . . . . . . . . . . . . . . . 84vii8.1 Electronics Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 848.2 SiPM Trigger Rates: S-Curve Analysis . . . . . . . . . . . . . . . 858.3 SPE Charge versus Voltage . . . . . . . . . . . . . . . . . . . . . 868.4 Induced Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 888.5 Large Pulses and Occupancy . . . . . . . . . . . . . . . . . . . . 908.6 External SiPM Cross-Talk . . . . . . . . . . . . . . . . . . . . . 949 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . 99Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100A Supporting Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 111A.1 Waves, Phases and Group Velocities . . . . . . . . . . . . . . . . 111A.2 External Cross-Talk: Degeneracy . . . . . . . . . . . . . . . . . . 112A.3 External Cross-Talk: Dark Noise method . . . . . . . . . . . . . . 113A.4 Analytic Dimer Populations . . . . . . . . . . . . . . . . . . . . 115viiiList of FiguresFigure 2.1 The schematic on the left gives the normal hierarchy, with thelarge gap labelled with ∆m2atm corresponding with ∆m231 and∆m2sol to ∆m212. The ‘atm’ and ‘sol’ subscripts are used be-cause each parameter is constrained by atmospheric and solarneutrinos, respectively. The colors in each bar correspond thelinear contribution of each flavour state to each mass state; ν1is primarily electron flavour. Image taken from [61] . . . . . . 5Figure 2.2 The energy of the nucleus versus number of protons. The z±3nucleons may undergo one single beta decay to reach a lowerenergy state. However the z±2 states must undergo the dou-ble beta decay to reach a favourable energy state. The upperparabola has and odd number of protons and neutrons. Imagetaken from [51]. . . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 3.1 The neutrino mass parameter space showing previous resultsfrom EXO-200 in blue and the next-generation Enriched XenonObservatory (nEXO) projected sensitivity in red. The normalhierarchy parameter space is shown on the left and the invertedparameter space on the right. . . . . . . . . . . . . . . . . . . 10Figure 3.2 A diagram of the nEXO TPC showing a double beta decay pro-ducing scintillation (red lines) and electrons as the blue dots.The electrons drift towards the anode at the top of the detector.The light detection system sits behind the field shaping rings.Image taken from [57]. . . . . . . . . . . . . . . . . . . . . . 11ixFigure 3.3 Radioactive backgrounds from a nEXO simulation. The x-axisis the reconstructed energy and the y axis the number of countsfor 10 years of data taking. The different color lines showthe contribution from the dominant isotopes contributing to thebackground. The neutrinoless double beta decay (0νββ ) pro-cess is the blue bump at 2.45 MeV. Taken from [57]. . . . . . 13Figure 3.4 Energy resolution curves for Equation 3.4. The second itemin the label is the fraction of quanta that are electrons, thus(20% elec) corresponds to a low field. The 63% sharing is theexpected sharing in nEXO operating at 400 V/cm. . . . . . . . 14Figure 3.5 The cross-sections for gamma rays in the energy regime around2MeV. Compton scattering will dominate at 2MeV over pho-toelectric effect and pair production. Data taken from NIST-XCOM database. . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 3.6 image taken from [64], showing the difference in simulatedevent topologies for a 2.5 MeVevent with electron (Left) andtwo electrons. (Right) . The average events do not show suchcontrasting topologies. The small red bar in the bottom left is10cm (scaling). . . . . . . . . . . . . . . . . . . . . . . . . . 16Figure 3.7 plot taken from [18], showing the difference in cherenkov yieldfor a 0νββ event or a gamma undergoing a photoelectric in-teraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Figure 4.1 Charge and light yields in liquid xenon. The y axis representsthe fraction of light (blue) or charge(red) collected for differentapplied fields. The yields are normalized to those at very lowfield. The strong recombination for alpha particles is evidentby the alpha yield being almost independent of applied field,while the beta and gamma (ER for electron recoil in diagram)yields change by more than 50%. Nuclear recoils (a movingxenon atom) also have a weak field dependence. [10]. . . . . . 20xFigure 4.2 To normalize the comparison of the functions for φ 6= 0 and φ = 0,the recombination fraction for φ 6= 0 is calculated for 1−φ , givingthe same asymptotic value. . . . . . . . . . . . . . . . . . . . . 25Figure 4.3 The simple Monte Carlo sampled photon intensity and the curvesplotted with equation 4.17. The agreement helps confirm the validityof equation 4.17 as the physical representation of the light production. 28Figure 4.4 An example of using the equations derived in the previous sectionto fit a 45 ns decay curve, which describes the liquid xenon lightintensity for MeV scale betas with zero applied electric field. Theφ 6= 0 equation has the more physically accurate spectrum for largertimes, due to the faster recombination. The parameters that are fixedand floating are described in the text. . . . . . . . . . . . . . . . 29Figure 4.5 Cherenkov yields calculated for 4 different energy beta particles, cut-off at 155nm. The total number of photons is given in the legend. . 32Figure 4.6 The general trend for n as a function of wavelength, calculated from[13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 4.7 Same image as Figure 4.6 but zoomed in on the liquid xenon (LXe)scintillation region. . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 4.8 The lower x axis is temperature, with the upper x axis giving the cor-responding density following Terry’s fit. The assymetric differencesbetween the different wavelengths is due to n increasing non-linearlywith photon energy (see Figure 4.6). . . . . . . . . . . . . . . . 36Figure 4.9 dE/dx data taken directly from NIST. At lower energies the nuclearcollisions begin to dominate for alphas, and for radiative effects be-come negligible for betas. Only data for xenon is shown. . . . . . . 38Figure 4.10 Ranges for alphas and electrons in liquid xenon and argon, calculatedusing densities given above. The betas have a much longer tracklength, with the tracks in argon being slightly longer than in xenon. 39Figure 4.11 Time for total energy deposition vs initial energy on the x axis. . . . 40xiFigure 5.1 Image showing the electric field and carrier concentrations acrossa PN junction. dP and dW mark the edges of the depletion lay-ers, while those with asterisks mark the region where holes orelectrons can still diffuse to the depletion region, giving an ef-fective depletion region. Taken from [28]. . . . . . . . . . . . 44Figure 5.2 (Left) A PN junction with a small reverse bias, showing thephoton absorption creating 1 electron-hole pair. (Right) A PNjunction operating as an avalanche photo-diode (APD) in thelinear region. The lower diagram shows the IV curve for ajunction, with the kink at large negative voltage showing thebreakdown voltage where a small increase in voltage producesa large change in current. Images taken from [1]. . . . . . . . 45Figure 5.3 The equivalent circuit in SPICE for one firing single-photonavalanche photodiode (SPAD) outlined in the red box. A 200pspulse is produced inV3 to close the switch simulating the avalanchein the PN junction. Cd and Rd emulate the diode’s capacitanceand internal resistance, and V2 is the overvoltage. C4,Rq1 andC3 representing the parasitic capacitance due to the other mi-crocells and silicon substrate respectively [23]. Equivalentlythe quenching resistor Rq has a parasitic capacitance Cq. Theoutput load is R5. Circuit simulation and analysis in SPICE byPeter Margetak. . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 5.4 Voltage and current pulses from SPICE simulation of SiPMequivalent circuit. Blue is voltage on SPAD, red the outputvoltage, green the parasitic voltage. See text for detailed de-scription. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 5.5 Close up image of two SiPM pixels with a different pitch. Thequencing resistor is the rectangle wrapping around each pixel.Left image has 25µm pitch (SPAD spacing), while right has50µm pitch. Image taken from [11] . . . . . . . . . . . . . . 49xiiFigure 5.6 (clockwise from top left) A ‘standard’ single photo electron(SPE) pulse, a two photo-electron (PE) pulse (likely delayedcross-talk (XT)), delayed correlated avalanche, delayed corre-lated avalanche suffering from XT on the second pulse. Pulsesfrom a VUV4 device cooled to -40C at roughly 4V overvolt-age, measured using preliminary LoLX amplifiers with a highergain than the final electronics. . . . . . . . . . . . . . . . . . 49Figure 5.7 Histogram of pulse charges showing the one and two PE dis-tributions. The shoulder on the right of each distribution is at-tributed to afterpulsing creating slightly larger charges. Pulsesfrom a VUV4 device at ∼4V overvoltage, cooled to -40C, mea-sured using preliminary LoLX amplifiers. . . . . . . . . . . . 50Figure 5.8 The dark noise rate normalized by SiPM surface area for aVUV4, measured at TRIUMF for various temperatures andovervoltages. The gaseou nitrogen (GN2) data taken in LoLXis in the temperature range from 193K to 163K. Plot from [27] 51Figure 5.9 The total number of correlated avalanches for the VUV4 SiPMsand for two Fondazione Bruno Kessler (FBK) devices at ∼170K,taken from [36]. At 4V the effect is ∼20% meaning if a 100PEsignal is measured, 80 photons were absorbed by the device. . 52Figure 5.10 The 2d histogram of charge and time between pulses for anFBK ‘low field E’ device, which shows distinctly the differentnoise populations. The purple dotted line is an artifact fromthe analysis. Taken from [36] . . . . . . . . . . . . . . . . . . 53Figure 5.11 Reflectivity measurements of 1.5µmSiO2 on bulk silicon. Thisis for an incidence angle of 45 degrees. The oscillation due tothe thin-film interference is evident. The red line is an averageof the data. This is preliminary data taken with the VERAsetup at TRIUMF by Mark Ward. . . . . . . . . . . . . . . . 55Figure 5.12 The attenuation length of magnesium fluoride and calcium flu-oride. Data taken from [58] . . . . . . . . . . . . . . . . . . . 56xiiiFigure 5.13 PDE values measured for the Hamamatsu VUV4 devices andsome devices from FBK, as reported in [27]. Measued for∼180nm light. Orange and yellow data points taken from ref-erence [7] in [27]. . . . . . . . . . . . . . . . . . . . . . . . . 57Figure 5.14 An image of two of the VUV4 devices used in LoLX. . . . . . 57Figure 6.1 Illustration of the LoLX detector, showing a beta decay fromneedle producing the scintillation and cherenkov light. Thiscross-section is down the middle, so the left and ride side aretwo side of the octagonal barrel. . . . . . . . . . . . . . . . . 59Figure 6.2 The 3D printed detector body without the top cap and the farSiPM installed. Resting on the bottom plate and springs whichseparate the detector from the cooling chuck. The four supportrods are wrapped in kapton tape. . . . . . . . . . . . . . . . . 61Figure 6.3 The fully assembled detector with and without SiPM wiring.The small gold nipples pointing out from the bottom are theneedle holders, and the hexagonal aluminum plates are for ca-ble routing. The white backsides of the SiPM packages canbe seen with their inputs being the small gold needles stick-ing out. The rod exiting from the top of the photo holds thedetector in the main vacuum vessel. . . . . . . . . . . . . . . 62Figure 6.4 (Left) The wired detector held in the six way vacuum T. Thewires are fed into the custom made feedthrough, which is shownclose-up on the right. . . . . . . . . . . . . . . . . . . . . . . 63Figure 6.5 (Left) The lower plate of the copper cooling chuck, showingthe path the liquid nitrogen (LN2) is pumped through. (Right)The lower portion of the vacuum chamber, where the detectorrests upon the assembled cooling chuck. . . . . . . . . . . . . 63xivFigure 6.6 (Left) The decay chain of strontium 90, including the secondmost intense transition of yttrium 90 (90Y) labelled E0. Athird even less intense transition is not shown. (Right) Theenergy spectrum of the strontium 90 (90Sr) and 90Y decays,overlapped. EC is the experimental cutoff energy, with E02 andE02 giving the 90Sr and 90Y endpoints, respectively. Both fig-ures taken from [32]. . . . . . . . . . . . . . . . . . . . . . . 64Figure 6.7 Preliminary optical data for the longpass filters, taken with theVERA setup at TRIUMF by Shirin Edalatfar. Data taken at 0◦incidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 6.8 Scaled scintillation and Cherenkov spectra overlayed with fil-ter data taken at normal incidence. VUV filter data taken frommanufacturer, longpass filter same data as Figure 6.7. Cherenkovspectra should be taken as approximate, and scintillation spec-trum taken from [26]. . . . . . . . . . . . . . . . . . . . . . . 67Figure 6.9 The second stage of the amplifer. The RF amplifier input comesfrom ‘AmpOut’. By changing the ratio of R4 and R15 the gaincan be tuned. . . . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 6.10 Example pulses taken from the installed LoLX detector at around10◦C. Channel 2 and 3 are unsummed while channel 4 has thecontributions from an entire package (4 SiPMs). . . . . . . . . 68Figure 6.11 Histogram of the baseline subtracted peak height for an over-voltage slightly higher than 4V. At 4V overvoltage the peakheight is 40ADC units. The noise peak at ∼10 ADC is dueto induced noise from the digitizer power crate. Data takenamplifier with gain factor of 2 too high. . . . . . . . . . . . . 69Figure 6.12 Example pulse taken on the oscilloscope with 1GHz band-width, showing the distorted pulse shape. Taken for a VUV4device at 4 V overvoltage, large pulse generated with a 444 nmpulse laser. The peak height shown here is ∼1.72 V. . . . . . . 70xvFigure 6.13 IV curves taken for the LoLX detector installed at McGill.Taken at room temperature in december 2019 with the systemunder vacuum. Three of the dead channels are due to a wiringissue in the detector and a fourth due to a blown amplifier. . . 71Figure 6.14 The charge distributions for four largest attenuations. The left-most peak from 0 to 1000 ADC x ns is the zero count pop-ulation, which has various charges due to baseline noise. Asexpected the zero count population decreases with the opticalattenuation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Figure 6.15 An example large pulse showing the different integral win-dows. The horizontal red line represents the baseline, the dot-ted black line the beginning of the integration window and alsothe peak height. The green line is the variable window size,the dark blue the fixed 500 ns window and the pink the largewindow. The small purple line represent the magnitude of thepulse overshoot. . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 6.16 The x-axis gives the expected PE while the y-axis the measuredPE. The first 3 data points used to fit Equation 6.1 used the 500ns integration window. The blue dots shows the error inducedby overshoot for a large integration window. The green andblack data points show a better estimate for the non-linear re-sponse of the electronics for large pulses. . . . . . . . . . . . 74Figure 6.17 The variable window length charge histograms in pink and red,scaled by 22.98± 0.017 mV/(ADC x ns) to match the baselinesubtracted peak height distributions. The rightmost pulses ex-ceed the dynamic range of the digitizer resulting in the popu-lated bin and shape mismatch. . . . . . . . . . . . . . . . . . 76Figure 6.18 The overshoot (measured in ADC units) on the x-axis and themeasured charge on the y axis. The second less intense linearpopulation is likely an artifact of the analysis, as the overshootvalue is found by taking the maximum value of the waveformwithout performing any averaging of nearby bins. . . . . . . . 77xviFigure 6.19 A image of the outputs from the cryostat to the six amplifierboards on the rack. This rack also holds the amplifier board’spower source (top), V1740 in a power crate and LoLX-DAQcomputer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 6.20 Diagram of the major components of the data acquisition sys-tem (DAQ) system, with all the connections relevant to oneSiPM given in the bottom right corner. The number of wiresor channels is given above each line. . . . . . . . . . . . . . . 79Figure 7.1 The total, random and eXT dark noise (DN) rates for two SiPMsat either 4V or 7V overvoltage. Random coincidences are com-puted using a 16ns time window. A colder detector improvesthe signal to noise ratio. . . . . . . . . . . . . . . . . . . . . 81Figure 7.2 The expected ratio between signal NX and random coincidencefluctuations√NR, assuming the Pi, j is Pi, j = 10−5. The linedrawn is for 4V overvoltage and a temperature of -110C. . . . 82Figure 7.3 The LoLX detector unfolded, with dotted lines showing onlythe geometric orientation between 1 layer with a 45 degree in-cidence angle (giving a degeneracy of 8 for 45◦ incidenceson one layer). The notation on the right describes the anglebetween SiPM surfacenormal vectors and the degeneracy inbold, with the + sign indicating moving one layer up the barrelslightly decreasing the angle between SiPM normal vectors.The squares are the SiPM packages, with the pink and graybeing the bandpass and bare SiPMs respectively. . . . . . . . 83Figure 8.1 An example S-curve fit, showing several different fits; f2 is anerror function shifted and scaled, f3 is Equation 8.1 withoutC and finally f4 is the complete Equation 8.1. The fit for f4is much better than the others given by it’s low chi2 value,indicating the model is accurate. . . . . . . . . . . . . . . . . 86xviiFigure 8.2 Charge histograms and their gaussian fits in red, for three volt-ages. The signal is from all 4 SiPMs on the channel. Thecharge on the x-axis is the charge returned from the pulse fit-ting algorithm. The charges from these histograms are used inFigure 8.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . 87Figure 8.3 The data from Figure 8.2 fit with a line. The y error bars are thefull width half maximum (FWHM) of the charge distributionsOther channels had a similar good linearity between the threedata points. . . . . . . . . . . . . . . . . . . . . . . . . . . . 88Figure 8.4 The distribution of voltages for each SiPM, transformed totemperature. SiPMs locations in the detector are given in thelegend. The absolute scale much colder than the coldest ther-mocouple but the gradient from top to bottom agrees qualita-tively with the thermocouple gradient. . . . . . . . . . . . . . 89Figure 8.5 The 2d distribution of pulse width (in ADC samples of 16nseach) on the y-axis and raw charge on the x-axis. The differentPE populations are visible as the yellow populations centeredaround the y-value of 10. The small width events also have alow charge, further indication that they are not SiPM pulses. . 90Figure 8.6 The distribution of the ratio of peak height divided by fit charge,both before and after the three cuts listed. . . . . . . . . . . . 91Figure 8.7 Number of PE per channel versus channel ID, for the threegroup coincidence data. This shows the light is seen isotropi-cally throughout the detector. The populated zero NPE bin isnot understood as the 0.5 PE cut should prevent this. The VUVfiltered channels are ch 0 to 4 and the bare SiPM channels 26-29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92xviiiFigure 8.8 The total PE detector per event on the y-axis, and the numberof channels with pulse larger than 0.5 SPE on the x-axis. Datais from the 2 group coincident trigger data. The x axis projec-tion is shown above (Nhit spectrum) and the y axis projectionto the right (NPE spectrum). The spectrum for the 3 group co-incident is similar but with less of a knee in the PE spectrum,and less Nhit = 3 events. . . . . . . . . . . . . . . . . . . . . 93Figure 8.9 The time to next pulse spectrum for the Nhit = 2 populationof the low threshold 2 group coincidence data. The fit is forthe two term exponential function with parameters [1] and [2]being the slow and fast time constants. . . . . . . . . . . . . . 95Figure 8.10 The simulation of isotropic eXT overlayed with the data forchannel 24. The normalization for the raw data skips channel24 as it has a very high count due to bias from the analysis;every event includes channe 24. The raw data still enforcestime between pulses to be less than 8ns. . . . . . . . . . . . . 96Figure 8.11 The simulation of isotropic eXT overlayed with the data forchannel 4. The normalization skips channel 4 for the reasonmentioned previously. The low count rate in channels 5, 6 and7 is due to trigger bias; channel 4, 5, 6 and 7 are on the sametrigger group. The raw data still enforces time between pulsesto be less than 8ns. . . . . . . . . . . . . . . . . . . . . . . . 97Figure 8.12 The same data for Nhit = 2 and including channel 25, nowwith distributions for multiple time between pulses. The dis-tributions are again normalized within channels 4 and 23. . . 98Figure A.1 Equation A.18 with the correct constant C plotted for a 1MeV elec-tron with given parameters. . . . . . . . . . . . . . . . . . . . . 116xixGlossaryA list of terms or names like SPE used frequently throughout this report.MIDAS Maximally Integrated Data Acquisition System . . . . . . . . . . 75System designed primarily at TRIUMF and PSIDAQ data acquisition system . . . . . . . . . . . . . . . . . . . . . . . 59ADC analog to digital converter . . . . . . . . . . . . . . . . . . . . . . 71DAC digital to analog converter . . . . . . . . . . . . . . . . . . . . . . 71SPI Serial Peripheral Interface . . . . . . . . . . . . . . . . . . . . . . 71PSI Paul Scherrer Institut . . . . . . . . . . . . . . . . . . . . . . . . 75TRIUMF Tri-University Meson FacilityFE front-end . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75LSB least significant bit . . . . . . . . . . . . . . . . . . . . . . . . . 76PMT Photo-Multiplier Tube . . . . . . . . . . . . . . . . . . . . . . . . 42APD avalanche photo-diode . . . . . . . . . . . . . . . . . . . . . . . 42GAPD Geiger avalanche photo-diode . . . . . . . . . . . . . . . . . . . 45MCX micro coaxial connector . . . . . . . . . . . . . . . . . . . . . . . 61HV high voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42SM standard model . . . . . . . . . . . . . . . . . . . . . . . . . . . 3LXe liquid xenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1GN2 gaseou nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . 51xxLN2 liquid nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60LoLX Light only Liquid Xenon . . . . . . . . . . . . . . . . . . . . . . 1nEXO next-generation Enriched Xenon Observatory . . . . . . . . . . . 1TPC time projection chamber . . . . . . . . . . . . . . . . . . . . . . 8ROI Region of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . 9SS single-site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15MS multi-site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162νββ two neutrino double beta decay . . . . . . . . . . . . . . . . . . . 50νββ neutrinoless double beta decay . . . . . . . . . . . . . . . . . . . 1IH inverted hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . 4NH normal hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . 4210Po polonium 210 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6290Sr strontium 90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6290Y yttrium 90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6290Zr zirconium 90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64SiPM Silicon Photo-Multiplier . . . . . . . . . . . . . . . . . . . . . . 1MPPC multi-pixel photon counter . . . . . . . . . . . . . . . . . . . . . 46Vbr breakdown voltage . . . . . . . . . . . . . . . . . . . . . . . . . 44DN dark noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50XT cross-talk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49eXT external cross-talk . . . . . . . . . . . . . . . . . . . . . . . . . . 2CA correlated avalanche . . . . . . . . . . . . . . . . . . . . . . . . . 51AP after-pulsing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51FBK Fondazione Bruno Kessler . . . . . . . . . . . . . . . . . . . . . 52PE photo-electron . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49SPE single photo electron . . . . . . . . . . . . . . . . . . . . . . . . 49xxiSPAD single-photon avalanche photodiode . . . . . . . . . . . . . . . . 46PDE photon detection efficiency . . . . . . . . . . . . . . . . . . . . . 53FWHM full width half maximum . . . . . . . . . . . . . . . . . . . . . . 29SNR signal to noise ratio . . . . . . . . . . . . . . . . . . . . . . . . . 67TOF Time of flight . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59PET Positron Emission Tomography . . . . . . . . . . . . . . . . . . . 2MEGII Mu to E Gamma 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 42xxiiAcknowledgmentsFirst off I would like to thank my parents Andy and Teddie for trusting me tomake decisions and instilling in me a sense of wonder of the world, from stars totrees. I thank my undergraduate supervisor Razvan for showing me professionalexcitement for science and taking me under his wing. I thank Pietro for all of hishelp and advice both academically and personally. I thank Fabrice for teaching meto remember what is relevant in a given experiment, and the importance of beingconcise. I thank Giacomo and everyone else at TRIUMF who helped me withvarious things. I want to thank my sister Moira for keeping me grounded. I wouldnot have finished this work, nor mentally made it through my broken collarboneand quarantine without the support of my girlfriend Elyn. I want to thank all myfriends in Ottawa for helping me enjoy non-physics moments in undergrad, and allmy old and new friends in Vancouver for doing the same. Finally I want to thankskiing and biking for providing the ultimate escape and hip-hop for showing methat science can be cool.xxiiiChapter 1IntroductionNeutrinos are currently an active area in particle physics research, with problemssuch as the ordering of the mass states (hierarchy problem) and absolute neutrinomass remaining unsolved. It is also unknown if neutrinos are Majorana fermions,meaning they are their own antiparticle. The hypothesized nuclear process ofneutrinoless double beta decay (0νββ ) decay requires neutrinos to have Majo-rana nature and can probe these neutrino mass parameters, as the decay rate isdirectly related to the neutrino masses. The next-generation Enriched Xenon Ob-servatory (nEXO) experiment is a proposed detector with a projected sensitivitythat will improve upon current limits by roughly two orders of magnitude, prob-ing properties of neutrinos well beyond what has been previously measured. ThenEXO detector is a large cylindrical time projection chamber holding five tonnesof liquid xenon (LXe) which acts as both the detection medium and source as theisotope xenon 136 is a candidate for neutrinoless double beta decay.The success of the nEXO detector depends critically upon having an energyresolution of 1% or better at the 0νββ decay energy of xenon 136 [57]. Achievingthis resolution is dependent upon the detector light collection efficiency, which inturn depends on the photon propagation to the light sensors and the sensor’s effi-ciency. In order to independently investigate these processes the Light only Liq-uid Xenon (LoLX) detector was constructed. The detector is an octagonal prismroughly three centimetres in height and width. It uses Silicon Photo-Multipliers(SiPMs) for light detector, the same technology planned for use in nEXO. As it1pertains to the success of nEXO LoLX aims to validate photon transport simula-tions and better understand SiPM operation in liquid xenon. In addition LoLX aimsto further investigate the properties of scintillation light production and measure theCherenkov yield in LXe. This measurement would have applications in PositronEmission Tomography (PET) imaging, with possible applications to 0νββ exper-iments. LoLX also aims to investigate external cross-talk (eXT) between SiPMs,where one device triggers another device.This thesis first outlines some neutrino physics and how neutrinos are con-nected to the 0νββ process. The nEXO detector is summarized with emphasis onthe light collection efficiency and possible application of Cherenkov light in LXe0νββ experiments. This is followed by detailed calculation with respect to signalproduction in liquid xenon; a new analytic framework for temporal signal of scin-tillation light is derived and Cherenkov spectra are calculated. The relationshipbetween refractive index and temperature of LXe is derived from previous mea-surements and finally the energy deposition time for charge relativistic particles iscalculated.The physics of Silicon Photo-Multipliers described in detail, summarizing theworking principle, sources of noise and photon detection efficiency. This is fol-lowed by the discussion on LoLX detector, highlighting information about the de-tector body, cryosystem and optical filters. The characterization of the electronicsare described including a linearity correction, and finally the data acquisition sys-tem system is briefly discussed. Next a framework is presented for describingexternal cross-talk in SiPMs as LoLX hopes to be sensitive to this process. Lastlythe detector commissioning is discussed, showing preliminary data from gaseousnitrogen data.2Chapter 2Neutrino PhysicsNeutrinos are weakly interacting fundamental particles and are the lightest of thefermions in the standard model (SM). The neutrino is a neutral lepton and comein three flavours corresponding to the charged leptons flavours; electron, muonand tau. The existence of the neutrino was initially posited in 1930 by WolfgangPauli to explain the otherwise missing spin and momentum observed in beta de-cays and was first detected by Clyde Cowan and Frederick Reines in 1956 byobserving inverse beta decay in scintillators near a nuclear reactor [29]. Sincethen much progress has been made in neutrino physics although some fundamen-tal questions remain unsolved. These questions include understanding the abso-lute neutrino mass scale, the mass hierarchy and if the neutrino is a Majorana orDirac fermion. The observation of the nuclear process neutrinoless double beta de-cay (0νββ ) would prove Majorana particles exist, show violation of lepton numberand may constrain the absolute mass of neutrinos. The physics of these problemsand relation to 0νββ is outlined below.The discovery of neutrino oscillations, where one flavour state changes to an-other when propagating through space, requires that atleast two neutrinos havemass [29]. This is in disagreement with the SM which predicts massless neutrinos[29].The three mass eigenstates are given by ν1,ν2,ν3 and do not each correspond toone of the flavour eigenstates νe,νµ ,ντ . Instead each flavour state is a linear com-bination of the three mass eigenstates, with the mixing between the flavour states3and mass states given by the so called PMNS matrix1[61]. By measuring neutrinooscillations some of the parameters in PMNS mixing matrix can be extracted, in-cluding the mass difference squared ∆m221 =m22−m21 where mi is the mass of stateνi. However current experiments cannot distinguish if the second mass splittingterm ∆m231 is positive or negative. This leads to the problem of the mass hierarchy;its unknown if the mass of state ν3 is heavier or lighter than the two states ν1 and ν2.The squared difference between m1 and m2 is about 30 times smaller than the abso-lute squared difference between state ν3 and either ν1 or ν2. The mass ordering isrepresented schematically in Figure 2.1, which also shows the flavour compositionof each mass state. The case for ∆m231 > 0 is labelled the normal hierarchy (NH)because the lightest state is ν1, which is composed primarily of electron flavour,so the neutrino hierarchy would match that of the charged leptons. The invertedhierarchy (IH) is the opposite case. In addition to the mass hierarchy, the absolutemass scale of the neutrinos is not known, meaning the mass of the lightest neutrinois unknown. The upper limit for the sum of the three masses from cosmology is0.23 eV [3].The SM can be extended to accommodate neutrino masses in the simplest man-ner by adding one of two terms to the SM lagrangian. Introducing a Dirac massterm leads to neutrino masses many orders of magnitude larger than current exper-imental constraints, and requires smaller coupling to the Higgs field than expected[57]. Both of these elements make adding the Dirac term for the neutrino massescumbersome, as further mechanisms are required to agree with experimental data.This would give neutrinos the familiar properties of other Dirac particles where theparticle and its antiparticle are distinct from one another. A different mass termcan be added to the SM, the Majorana mass term, which avoids the issues createdby adding the Dirac term [57]. This would imply that majorana fermions exist,a type of particle that is also its antiparticle. This concept was first hypothesizedin 1937 by Ettore Majorana but has yet to be experimentally observed [51]. IfMajorana fermions exist then two fermions can annihilate one another, violatinglepton number conservation. This may also play a role in big bang cosmology,which requires a violation of charge-parity (CP) symmetry to produce the universe1Named for the physicists Pontecorvo, Maki, Nakagawa and Sakata4Figure 2.1: The schematic on the left gives the normal hierarchy, with thelarge gap labelled with ∆m2atm corresponding with ∆m231 and ∆m2sol to ∆m212.The ‘atm’ and ‘sol’ subscripts are used because each parameter is constrainedby atmospheric and solar neutrinos, respectively. The colors in each bar cor-respond the linear contribution of each flavour state to each mass state; ν1 isprimarily electron flavour. Image taken from [61]we observe today. Current measurements of CP violation in the quark sector arenot sufficient to provide the matter dominated universe observed, however leptonnumber violation in the neutrino sector may imply a CP violating phase sufficientto explain cosmological data [57].2.1 Neutrinoless Double Beta DecayIn a two neutrino double beta decay (2νββ ), a nucleus with an even number ofprotons and neutrons has a rest mass above it’s most stable point for its total numberof nucleons. However a single beta decay is energetically forbidden or at leaststrongly suppressed. By the uncertainty principle conservation of energy may betemporarily violated and the system will undergo a virtual decay to the higherenergy state, then undergo a second decay to the final more energetically favouredfinal state (see Figure 2.2). In this process two electrons and two antineutrinos areemitted sharing a total energy Q which is the difference in rest mass between theinitial and final states of the nucleus. The lifetimes of isotopes that undergo thisdecay are very long, on the order of 1018− 1021 years due to the suppressed or5forbidden first decay.Figure 2.2: The energy of the nucleus versus number of protons. The z±3 nu-cleons may undergo one single beta decay to reach a lower energy state. How-ever the z±2 states must undergo the double beta decay to reach a favourableenergy state. The upper parabola has and odd number of protons and neutrons.Image taken from [51].In the 0νββ process a light Majorana neutrino can be exchanged between nu-clei [29] and two electrons are emitted with no neutrinos. In this process, theneutrinos annihilate one another, and the process requires the neutrino to be a Ma-jorana particle. For 0νββ both electrons share the total energy Q of the decay asthere are no neutrinos to carry away any energy. Thus in the 2νββ energy spectrumthe 0νββ events will be present as a very small bump at the endpoint energy. Theneutrino effective Majorana mass 〈mββ 〉 is important to 0νββ decay and is definedas the sum of mass eigenstates over the PMNS matrix, with the matrix denoted asU :mββ =∣∣∣∣∑iU2i mi∣∣∣∣= ∣∣∣∣m1cos2 θ12 cos2 θ13+m2 sin2 θ12 cos2 θ13eiα+m3 sin2 θ13eiβ ′∣∣∣∣(2.1)The θi j represents the mixing angles between states i and j, and are constrained byoscillation measurements. β ′ is defined as β ′ = β +δCP, with the phases α and β6representing the Majorana nature of the neutrinos. For Dirac neutrinos α = β =0. Lastly δCP is the charge-parity violating phase. Assuming that light neutrinoexchange drives the decay process2, the 0νββ halflife T1/2 is proportional to theeffective neutrino mass squared:1T= G0ν · ∣∣g2A(M0νGT +M0νT )−g2VM0νF ∣∣2 · 〈mββ 〉2m2e (2.2)The G0ν is a phase space factor which is related to how the coulombic forcefrom the daughter nucleus affects the emitted electrons. The gA and gV terms areweak force coupling constants and the different M0ν values are for matrix elementswhich describe the overlap between the initial and final states of the nuclei. me isthe electron mass. The vector coupling constant gV = 1 adds little uncertainty to therelation between decay rate and 〈mββ 〉 [57]. It was previously understood that theaxial coupling constant gA is ‘quenched’ within nucleons due to the inner structureof hadrons [57]. Experiments show that in a nucleus undergoing beta decay thequenched coupling value is gA ≈ 1.27 while for a free neutron it is ∼1.3 timeshigher [31]. A recent theoretical study derive this behaviour from first principles,greatly reducing the uncertainty on the calculation of the matrix elements [31].This work along with recent calculations of matrix elements for 0νββ decay inxenon [62] help greatly reduce the uncertainty in the relationship between decayrate and the effective Majorana mass.Because the 0νββ decay rate is directly related to the effective Majorana mass,constraining the lifetime for a given 0νββ process also constrains the value uppervalue for mββ . If this value is constrained, using the mixing data from oscillationexperiments the lightest neutrino mass can be extracted. The observation of 0νββwould imply that Majorana fermions exist, meaning lepton number is violated.The relationships between the 0νββ decay rate and neutrino properties, combinedwith the fact that decay energies on the MeV scale are detectable, makes the 0νββprocess a compelling probe for new neutrino physics.2Other models exist which give different relationships between the lifetime and effective neutrinomass other than that in Equation 2.27Chapter 3The nEXO ExperimentNeutrinoless double beta decay provides an accessible and effective method tomeasure properties of neutrinos and probe for Majorana fermions. The next-generationEnriched Xenon Observatory (nEXO) is an 0νββ experiment with plans to be builtat SNOLAB, pending funding and approval. The nEXO detector is a time projec-tion chamber (TPC) with 5 tonnes of LXe enriched in the isotope 136Xe whichundergoes 2νββ decay. The projected sensitivity of nEXO to 0νββ decay will beon the order of 1028 years, two orders of magnitude better than the current limit[57]. This sensitivity will constrain the lightest neutrino mass and probe the phasespace covered by the IH. This section will outline the motivation for using LXeand the basics of the nEXO detector, with emphasis on the light collection systemas it pertains to the work of this thesis.3.1 Liquid Xenon as detection mediumThe isotope 136Xe undergoes double beta decay with a lifetime of 2.1×1021 years,as measured by the EXO-200 detector [5], the predecessor experiment to nEXO.This makes the isotope a candidate for undergoing 0νββ , which would have en-ergy of Q0νββ = 2.456 MeV. The natural abundance of 136Xe is roughly 9% so toincrease the detector signal strength nEXO will use xenon enriched to ∼90% xenon136. Xenon is fairly radioactively pure, with the only relevant isotope contributingto the backgrounds in nEXO being 137Xe which is produced by cosmic rays. 137Xe8beta decays with an endpoint energy of 4.16 MeV and has no sharp features con-tribution in the Region of Interest (ROI) located at Q0νββ , see the broad gray linein Figure 3.3 for the simulated 137Xe signal in LXe.Liquid xenon is also an excellent detection medium due to its high proton num-ber and large signal yields. Most charge readout devices or scintillators with similarefficiencies have a much lower proton number. The LXe density of ∼3 g/cm3 andhigh proton number of 54 leads to a high stopping power. This shields the internalvolume of LXe from gamma rays originating from the detector walls; gammas withan energy of 2.4 MeV (close to the ROI) have an attenuation length of roughly 8.7cm. Therefore for a large volume of LXe the center of the volume will be shieldedfrom radiation from the outer environment, this is referred to as ‘self-shielding’.Gamma rays undergo either Compton or photoelectric interaction producing rela-tivistic electrons, therefore mimicking an 0νββ signal. For this reason shieldingfrom gamma rays is favourable.Finally xenon has high scintillation and charge yields, energy deposited asatomic ionization and excitations produces light in the VUV region and the elec-trons can be collected via an applied electric field. See Chapter 4. At a field strengthof 500 V/cm, a 2.5 MeV beta will produce approximately 125 000 electrons and62 500 scintillation photons [67]. The variable W is defined as the average energyto produce a quantum of either charge or light. The numerical value of W is dif-ferent for various energies and types of ionizing particles but has been measuredand reported on extensively in the literature, with W =13.7 eV being reported byEXO-200 for the ROI in nEXO [9]. Using a known W value, or equivalently thenumber of quanta produced per deposited energy, the energy deposited in the detec-tor E can be reconstructed by multiplying the number of each quanta I (ionization)and P (photons) by W , simply written as E =W (I+P). Relating this equation todetector observables is detailed further in Section The nEXO DetectorThe baseline goal of nEXO is to measure the 0νββ lifetime with a sensitivity of9× 1027 years [57]. The current limit for mββ is around 0.5 eV, with the targetednEXO result constraining this to 15 meV if a null result is measured. This would9probe a portion of the normal hierarchy (NH) paramter space and the entire in-verted hierarchy (IH), as the IH results in a larger value for mββ than the NH.Figure 3.1 shows the previous limit for mββ set by EXO-200, plotted on the mββand neutrino minimum mass mmin parameter space. The bands for the NH and IHare also shown, with the projected nEXO result in red. The width of the nEXO andEXO-200 results are due to uncertainties in the nuclear matrix elements discussedin Section 2.1 [57].Figure 3.1: The neutrino mass parameter space showing previous results fromEXO-200 in blue and the nEXO projected sensitivity in red. The normal hier-archy parameter space is shown on the left and the inverted parameter spaceon the right.The inner detector of nEXO, which contains the liquid xenon, is a cylinderroughly 1.2 m in height and diameter oriented vertically. This chamber is housedin a large outer detector which is filled with water to detect and tag cosmic muons.A schematic of the inner detector is shown in Figure 3.2. To attain the desired sen-sitivity nEXO requires minimal radioactive backgrounds, as decay processes fromother isotopes may mimic the 0νββ signal (see Figure 3.3). Therefore extremecare is taken in selecting the materials and components of which nEXO is built.The xenon acts as both the 0νββ source and as the detection medium, with nEXO10measuring the charge and light produced in the xenon. The detector collects theelectrons via an applied electric field of around 400 V/cm oriented along the ver-tical axis, with field shaping rings along the barrel to ensure the electric field is asvertical and uniform as possible. The charge readout occurs at the top of the detec-tor using segmented readout tiles located in front of the anode. Each tile consistsof orthogonal metal strips, with current designs giving the strips a center to centerdistance of 3 mm and each pad being 10x10 cm in surface area.Figure 3.2: A diagram of the nEXO TPC showing a double beta decay pro-ducing scintillation (red lines) and electrons as the blue dots. The electronsdrift towards the anode at the top of the detector. The light detection systemsits behind the field shaping rings. Image taken from [57].The charge readout signal allows position reconstruction to the mm scale [48].Because the charge drift times are on the ms timescale and the scintillation lightthe ns scale, the time delay between the initial flash of light and detected charge isproportional to the depth along the vertical z-axis where the interaction occurred.The position of the charge collection on the readout tiles gives the event position inthe x and y axis. This position reconstruction is a key feature of a TPC and allowsevents occurring close to the detector walls to be rejected as they may be due to11radioactivity from the detector. The internal volume of LXe within which eventsare accepted is known as the fiducial volume; maximizing the fiducial volume isthe main motivation for nEXO having a height roughly equal to its diameter.For the detection of the scintillation light the detector will use roughly 4.5 m2of Silicon Photo-Multipliers (SiPMs) placed behind the field shaping rings. For afull description of SiPMs see Chapter 5. The devices will be mounted on 24 stavesforming a polygon around the field shaping rings, with a large number of SiPMsgrouped into a single ‘tile’ with the signals summed in the LXe using an ASICchip. The light detection efficiency of nEXO is of crucial important to the successof the detector and is outlined below.3.2.1 Photon Collection and Energy ResolutionIn nEXO the energy reconstruction process is one of the main methods used toreject background events which occur within the fiducial volume. The better theenergy resolution the more backgrounds and events at the tail of the 2νββ spec-trum can be separated from the 0νββ events. See Figure 3.3 for an overlay ofspectra from various backgrounds. The better the energy resolution, the narrowerthe 0νββ signal apprears (shown as light blue in the figure).Due to the fact that the SiPMs do not cover the entire detector surface areaand are behind the field shaping rings the efficiency of photons to be transported tothe SiPM surface area is less than 15%. Placing eflective materials on the cathodeand field shaping rings can improve this transport efficiency. Additionally currentSiPMs technologies have low efficiency for detecting VUV photons, saturating atunder 30%. This results in a detector photon detection efficiency of only ∼5% orless. The energy reconstruction process depends on the number of total photonsand electrons, each which must be estimated by dividing the measured numberby the detector collection efficiency. In pure liquid xenon the charge collectionefficiency εi is almost 100% efficient at non-zero electric fields, while as explainedabove the efficiency for light detection εp is small. Ignoring fluctuations in therecombination process the estimated reconstructed energy resolution σ〈E〉〈E〉 is givenbelow for i detected electrons and p detected photons, where εpP= p:12Figure 3.3: Radioactive backgrounds from a nEXO simulation. The x-axis isthe reconstructed energy and the y axis the number of counts for 10 years ofdata taking. The different color lines show the contribution from the dominantisotopes contributing to the background. The 0νββ process is the blue bumpat 2.45 MeV. Taken from [57].σ〈E〉〈E〉 =√σ2I +σ2Piεi +pεp(3.1)In this approximation the only fluctuations come from the measurement statistics.The variation σI is given by the electronic noise on each charge readout channeladded that detects charge. Thus σI is constant for fixed channel occupancy and isroughly only 600 electrons, which is roughly a 0.3% variation of the total numberdetected. The low light occupancy and detection efficiency gives σp a binomialvariance in addition to the poisson variance of p. Using σp = σPεp:σP =σpεp=√pεp=√P(1− εp)εpεp(3.2)In addition a noise factor η is added, which is required to account for the correlatednoise that occurs in SiPMs. It contributes linearly with the number of detectedphotons p so the added term is pη = Pεpη , thus the variation for light signal isgiven as below:σ2P =Pε(1− εp+η) (3.3)13The energy resolution then becomes:σ2〈E〉〈E〉2 =σ2I +Pεp (1− εp+η)(I+P)2(3.4)The results of this equation are shown in Figure 3.4. Although this is a simplifiedtreatment of the physics involved, qualitatively the expression shows the expectedbehaviour. The energy resolution improves for better light collection efficiency.It also shows a higher fraction of light collected worsens the resolution, this oc-curs because εi > εp. In addition it can be seen that the correlated noise factorη also worsens the energy resolution. A complete physics simulation that incor-porates fluctuation in the signal production and detector effects shows a strongerdependence on light collection efficiency, with the energy resolution rising sharplyabove 0.8% at 4% photo detection efficiency [57].Figure 3.4: Energy resolution curves for Equation 3.4. The second item in thelabel is the fraction of quanta that are electrons, thus (20% elec) correspondsto a low field. The 63% sharing is the expected sharing in nEXO operating at400 V/cm.The importance of the light collection efficiency for the energy resolution makesthe light detection system crucial to the success of the nEXO experiment. As thelight collection efficiency depends on the SiPM response and light propagation in14LXe this provides motivating for the independent study of these effects to ensureaccuracy in nEXO.3.2.2 Cherenkov Light and Background DiscriminationA dominant background in nEXO’s ROI is gammas with energy close to Q0νββ(2.456MeV) which can interact in xenon via Compton scatter and photoelectricabsorption. When a gamma ray Compton scatters its energy will be deposited atvarious sites. A gamma ray around 2MeV is most likely to Compton scatter at leastonce before depositing its final energy via photoelectric interaction, because theCompton cross section dominates at 2MeV while the photoelectric cross sectionbecomes dominant at lower energies (see Figure 3.5). The spatial location of theinteraction sites are reconstructed using the ionization signal collected at the anodeof the TPC.Figure 3.5: The cross-sections for gamma rays in the energy regime around2MeV. Compton scattering will dominate at 2MeV over photoelectric effectand pair production. Data taken from NIST-XCOM database.In nEXO the spatial resolution for a single interaction site is less than the pitchwidth of the charge readout tiles [49] [50]. To resolve between two sites a sepa-ration of at least twice the pitch width is needed, although machine learning andin depth analysis can help to improve this resolution [48]. Due to electron’s shortpath length of a few mm in LXe the majority of 0νββ events are single-site (SS),15Figure 3.6: image taken from [64], showing the difference in simulated eventtopologies for a 2.5 MeVevent with electron (Left) and two electrons. (Right). The average events do not show such contrasting topologies. The small redbar in the bottom left is 10cm (scaling).except for a small population where bremsstrahlung gammas are produced andcarry some of the event energy away from the original site. If the interaction sitesfor gamma backgrounds are spatially resolvable the event is labelled as a multi-site (MS) scatter and can be rejected. If the gamma ray deposits an energy closeto Q0νββ within a small enough volume (radius of a few mm) via photoelectric ab-sorption, compton scatter or combination thereof, the event is a SS interaction andcannot be rejected based on SS/MS studies alone. In summary a site multiplicitycut fails to discriminate between the background SS gammas and the majority of0νββ events.However, the Cherenkov light produced by relativistic electrons can be usedto differentiate between the photoelectric gammas and 0νββ signals. BecauseCherenkov emission is a threshold process, one electron will produce more Cherenkovphotons than two electrons sharing the same total kinetic energy, demonstrated inFigure 3.7. Moreover, the mean of the 0νββ decay emits both electrons back toback giving two cherenkov signal pointing in opposite directions. However onlyminimal directionality is preserved due to hard scatters; simulations show still ananisotropic light emission in a given direction but there is no distinct Cherenkovcone [18].Two research groups have simulated how the Cherenkov signal can be utilizedto improve the half-life sensitivity of a LXe 0νββ detector; both papers workunder different ideal assumptions but do show a modest improvement in detector16Figure 3.7: plot taken from [18], showing the difference in cherenkov yieldfor a 0νββ event or a gamma undergoing a photoelectric interaction.performance. The brief study performed by Signorelli and Dussoni ([64]) simu-lated the 0νββ decay and single electron events with energy Q0νββ . They showedthat for a completely ideal detector one can use the Cherenkov signal to cut 90% ofthe single electron events while retaining 75% of the 0νββ events. Brodsky et al.([18]) performed a more in depth analysis which shows a sensitivity improvementof 43% for their baseline scenario 1, with a cut that retains 61% of the signal eventsand removes 85% of the backgrounds. Although these simulations are assumingexcellent photon collection efficiency the results are promising and the productionof Cherenkov light warrants investigation.1a spherical detector with radius of 60cm, 100% photocoverage and 30% light collection effi-ciency across all wavelengths17Chapter 4Light Production in LiquidXenonThis chapter investigates some properties of light production in liquid xenon. Thebasic mechanism of signal production and particle identification is given followedby a detailed analytic description of scintillation time signatures, with the mathe-matical framework being applicable to other liquid nobles of interest. The scintil-lation spectrum is discussed. Next the production of Cherenkov light is outlined,and the relationship between liquid xenon (LXe) refractive index and temperaturederived. The final section calculates the energy deposition time, defined as the timerequired for an ionizing particle to deposit its energy in liquid xenon.4.1 Summary of Scintillation Physics and Basis forParticle IDAs a high energy particle enters the detection medium, it slown down by depositingit’s energy via atomic excitation, ionization and nuclear recoils [7]. Excited atomsalmost immediately (within picoseconds, [53]) combine with a nearby ground stateatom to form an excited dimer Xe∗2. The two bonding electrons can have theirspin aligned (triplet state) or anti-aligned (singlet state). These dimers decay andproduce scintillation light in the VUV region, peaked around 175 nm. Xenon is avery efficient scintillator producing on the order of 50 000 photons for a 1 MeV18alpha particle1. Liquid xenon is transparent to its own scintillation light due tothe average interatomic spacing of ∼ 4 A˚ being sufficiently larger than the excitedxenon dimer’s bond length[56]. The singlet and triplet dimers decay with differenttime constants; for xenon both are fast with the singlet lifetime ∼2 ns and the triplet∼25 ns [40].The longer lived triplet is caused by the transition to ground state being for-bidden due the spin difference ∆S = 1 [39]. The transition from the triplet stateoccurs due to spin-orbit coupling which mixes in singlet state [39]. This spin-orbitcoupling is stronger for larger atoms explaining why xenon has the shortest tripletlifetime of all noble liquids2.An ionized atom forms the charged dimer Xe+2 with neighbouring xenon atompicoseconds after ionization, similar to the dimer formation step for excitations[53]. The electrons from ionized atoms thermalize and diffuse through the xenonwhile being attracted to positively charged dimers in the center of the primaryparticle’s track [59] [69]. Some electrons will recombine with charged dimers,forming the neutral singlet or triplet dimer, then relax releasing scintillation lightby the same mechanism as the excitation channel.In the absence of an applied field some electrons escape recombination due todiffusion, on the order of 10-20% [25]. An electric field can be applied to collect afraction of the ionization electrons. A higher electric field reduces recombinationresulting in less scintillation light and more charge collected [46]. The fraction ofescaping electrons is much higher for betas than alphas due to the beta’s sparsertrack core, arising from the beta’s lower stopping power (see Section 4.6 for moreon stopping power). For alpha particles only a small fraction of charge can becollected even under high electric fields of kV/cm, which can be seen in Figure 4.1taken from [10]. When a neutron scatters off a xenon atom, the recoiling xenonatom is referred to as a nuclear recoil which have similar behaviour to alphas; anapplied field produces very little change in the detected light to charge ratio. Indetectors that collect charge via an applied electric field, the ratio of charge versuslight is often used for particle identification, allowing the separation of betas andgammas from alpha events and nuclear recoils.1see W values described in Chapter 4 of [21] for more information2Hundreds of ns for krypton, µs for argon and seconds for liquid helium [39] [30]19Figure 4.1: Charge and light yields in liquid xenon. The y axis representsthe fraction of light (blue) or charge(red) collected for different applied fields.The yields are normalized to those at very low field. The strong recombinationfor alpha particles is evident by the alpha yield being almost independent ofapplied field, while the beta and gamma (ER for electron recoil in diagram)yields change by more than 50%. Nuclear recoils (a moving xenon atom) alsohave a weak field dependence. [10].4.2 Temporal StructureTo properly describe the scintillation light signal, first the various states populatedby the incident particle must be defined. Their expected scintillation intensity isdescribed using an analytic model and toy Monte Carlo.4.2.1 Molecular PopulationsThe total number of atoms ionized or excited by the incident particle is J.J = Ji+ Jex = N+M Ji ≡ N Jex ≡M (4.1)20For notation simplicity the ionization population is labelled N and excitations M.The fraction of excitation to ionization ratio will be labelled as η :η ≡= MN(4.2)The total number of states excited or ionized states can be written as:N = Ji =J1+ηM = Jex =ηJ1+η(4.3)For a complete description the singlet and triplets produced via the excitation andionization channels are described separately. This requires defining the singlet andtriple ratios for the N and M populations: ρi ≡ NsNt and ρex ≡MsMt, with the subscriptss and t representing the singlet or triplet state dimer. This gives 4 populations forthe different ionization/excitation and singlet/triplet combinations:Ns =Nρi(1+ρi)=Jρi(1+ρi)(1+η)Nt =N(1+ρi)=J(1+ρi)(1+η)Ms =Mρex(1+ρex)=Jρexη(1+ρex)(1+η)Mt =N(1+ρex)=Jη(1+ρex)(1+η)4.2.2 Excitation ChannelThe excited states enter their decay mode effectively instantaneously, as relaxationto Xe∗2 takes picoseconds [53]. Thus this relaxation time is negligible and the xenondimers are treated as created instantly at time t = 0. The excitation populations aregiven by the exponential decay:Mt(t) =Mte−t/τt Ms(t) =Mse−t/τs (4.4)For the excitation channel, the rate of dimer decays gives the measured photonsignal. The photon intensity IM(t) is the derivative IM(t) = −dMdt , which is given21below.M(t) =Ms(t)+Mt(t) =Mse−t/τs +Mte−tτt (4.5)IM(t) =−dMdt =Msτse−t/τs +Mtτte−t/τt (4.6)4.2.3 Ionization ChannelThe ionization channel’s time signature is more complex than that for excitation,especially for events such as betas where the time for electron-ion recombination ison the order of tens of ns and therefore is not negligible[40]3. In the section belowthe recombination dynamics are incorporated with the population decay.Recombination TimePreviously, Kubota et al. [40] derived an analytical form for the recombination timeusing an ODE dependent on the average charge density of the track. Representingthe charge densities with n+ and n−, and ignoring diffusion effects, the rate ofrecombination starts with N electrons and eventually produces D dimers:dn−dt=−αn+(t)n−(t) (4.7)With α being a recombination constant, having dimensionality of inverse chargedensity and time. This differential equation gives faster recombination for highercharge densities. The charge densities can be related by n−(0) = (1−φ)no with φrepresenting the fraction of electrons which escape the positive charge of the trackcore, and no = n+(t = 0) being the initial density of holes created. This is used todefine the recombination time τR = (αno)−1, characteristic for a given ionizationtrack density. The boundary conditions are (1−φ)N(t = 0) = D(t→ ∞).3In argon the recombination time is faster by roughly a factor of 10. Although the track coreis longitudinally denser in xenon, three other effects result in recombination proceeding slower inxenon than argon; electrons have a longer thermalization length due to a smaller momentum transferfor elastic scattering, coulombic screening from nearby charges is stronger in xenon, and the phasespace for the chemical recombination is smaller22No escaping electrons: φ = 0It is first assumed that no electrons escape recombination. This is approximatelyaccurate for higher density tracks caused by alpha particles, where recombinationoccurs faster and less electrons escape recombination [46] [69]. With φ = 0 thenn+(t) = n−(t):dn−dt=−αn2−(t) →dn−n2−=−αdt∫ t=t ′t=0dn−n2−=−1n−(t)− −1n−(0)=−αtn−(t) =n−(0)1+n0αt=no1+ t/τr(4.8)With the rise time defined as τr ≡ 1noα . The number of dimers D formed will begiven by the integral over volumeD(t) =∫no(1− 11+ t/τr )dV ≈ N(1−11+ t/τr)where the approximation is made that integrating over volume bring the chargedensity no to the total number of ionizations N.D(t)φ=0 = N(1− 11+ t/τr ) (4.9)Electrons: φ 6= 0For low ionization density events caused by betas, with zero applied field, the totalnumber of photons measured is lower than the total quanta (charge and photons)measured with an applied field [25]. This indicates that at zero field some electronsescape recombination, attributed to diffusion [25]. From literature the magnitudeof the effect is atleast 10% for electrons at an energy at the 100 keV - 1 MeV scale,with [25] reporting φ ≈ 0.30. For φ 6= 0 the hole and electrons densities n+ andn− are no longer equal, instead n−(t) = n+(t)−φno assuming the escape electrons23leave promptly4. The differential equation and solution is below (see appendix forsolution steps):dn−dt=−αn−[n−+φno] (4.10)αdt =dn−−n2−−φnon−(4.11)n−(t) =φno(1−φ)eφ t/τr − (1−φ) (4.12)Again with τr ≡ 1noα . As done for φ 6= 0 the density to volume approximationN ∝ no is used. The boundary condition n−(0) = (1− φ)no means D(t → ∞) =N(1−φ) and the solution becomes:D(t)φ 6=0 = N(1−φ)(1− φeφ t/τr − (1−φ))(4.13)R(t)φ 6=0 = N(1−φ)[ φ 2eφ t/τr(eφ t/τr − (1−φ))2](4.14)This results in faster recombination than for φ = 0 as shown in Figure 4.2. It isencouraging to note that taking the limit φ → ∞ and applying l’hopital’s rule toequation 4.13 produces equation Analytical Photon IntensityThe recombination rates calculated previously are used to solve the ODE for thecomplete system. For the ionization signal, taking the derivative of the dimerpopulation does not give the experimentally measured rate of photon production.This is because a simultaneous dimer decay and electron-ion recombination givesdN/dt = 0 while two photons are produced. For a calculation of the dimer popula-tions with respect to time see Section A.4. The exponential decay can be combinedwith recombination equations 4.9 and 4.13 to calculate the photon intensity dP/dtfor a dimer decay lifetime τ . The result can be adapted to the two singlet and tripletpopulations Ns and Nt , by adding the two term exponential intensity IM(t) for the4This approximating is inaccurate if the escaped electrons do not leave the electron cloud im-mediately. This could occur if the recombination in the center of the cloud occurs first, with theelectrons further from the center (the escape electrons) still play a role in the initial recombination24Figure 4.2: To normalize the comparison of the functions for φ 6= 0 and φ = 0, therecombination fraction for φ 6= 0 is calculated for 1−φ , giving the same asymptoticvalue.Ms and Mt populations the complete scintillation signal described.At time t ′ the number of photons being produced will be given by the integralof the rate of dimer formation RN(t)dt between time 0 to t ′, weighted by the de-cay intensity Iexp(t ′− t) = (e−(t ′−t)/τ)/τ since the time of production at t. Thisis a ‘exponential-intensity weighted average’ of the dimers created. To simplifynotation λ ≡ 1/τ will be used. This gives the photon intensity dP/dt from therecombination rate R(t) producing dimers with lifetime τ as below.dPdt(t ′) =∫ t ′0Iexp(t ′− t)R(t)dt (4.15)The treatment above is the convolution of two real-valued functions. This assumesthe dimer state produced (singlet or triplet) is independent of the recombinationprocess, although the ratios ρi,ρex may be functions of the primary particle’s stop-ping power. The equation is solved analytically for φ = 0 and numerically forφ 6= 0, with the analytic derivation shown below Section No escaping electrons: φ = 0This configuration can be solved by integrating by parts5, with dv = RN(t) in∫udv= uv− ∫ vdu. Equation 4.9 is substituted in for R(t):dPφ=0dt(t ′) =−Nλ ( 11+ t ′/τr− e−λ t ′)−Nλ 2∫ t ′0e−λ (t ′−t)1+ t/τrdt (4.16)The remaining integral can be solved by substitution and then re-writing the sin-gle integral as two integrals going to infinite, to give the form of the exponentialintegral.∫ t ′0e−λ (t ′−t)1+ t/τrdt =λτre−λ (t′+τr)∫ t ′0eλ (t+τr)λ (t+ τr)dt x=−λ (t+ τr) → dx/dt =−λ=τre−λ (t′+τr)∫ −λ (t ′+τr)−λτre−xxdx=τre−λ (t′+τr)(∫ ∞−λτre−xxdx−∫ ∞−λ (t ′+τr)e−xxdx)=τre−λ (t′+τr)(Ei(λ (t ′+ τr))−Ei(λτr))Subbing back into the original equation gives the photon intensity for a single life-time.dPφ=0dt(t ′) =−Nτ[ 11+ t ′/τr− et ′/τ − τrτe−(t′+τr)/τ(Ei( t′+τrτ )−Ei( τrτ ))](4.17)The total photon intensity from the ionization channel will have two differentterms, each given by Equation 4.17. The two contributions are for each popula-tion Ns and Nt with their corresponding singlet and triplet lifetimes.4.2.6 Monte Carlo approachA monte carlo approach provides a method to validate the analytical solution. Thetotal population functions, once normalized, serve as the CDF versus time. The5note that v 6=D(t) because the indefinite integral is taken, so the expanded form of equation 4.15becomes dPdt = Iexp(t′− t)[D(t ′)−D(∞)]−λ ∫ Iexp(t ′− t)[D(t ′)−D(∞)]dt. The negative sign staysin front of the second term because u ∝ eλ t . A negative comes from D(t ′)−D(∞) making the entiresecond term positive.26exponentially decaying populations can be easily inverted to give a sample-abledistribution:Pi(t) = 1− e−t/τi → t =−τi ln(1−P) (4.18)The recombination functions are inverted below to give the recombination timet as functions of probability P. Equation 4.9 is written as P0(t), the fraction ofrecombined electrons at some time t for φ = 0.P0(t) = 1− 11−t/τr → t =( 11−P0 −1)τr (4.19)And Equation 4.13 gives Pφ (t), the fraction of recombined electrons after time tfor φ 6= 0:Pφ (t) =(1− φeφ t/τr − (1−φ))→ t = τrφln(1+φP1−P)(4.20)To simulate the times of photon production the excitation populations sample onlyEquation 4.18 while the ionization populations sample Equation 4.19 or Equa-tion 4.20 followed by the exponential equation summing the times together.4.2.7 Temporal Structure: ResultsThe agreement between the simulations and analytic functions is shown in Fig-ure 4.3. The total number of events J = 72.4×103 is given by the energy 1 MeVdivided by theW value, which is the minimum energy to create a scintillation pho-ton as reported in [21]. The other parameters used in the plot, listed in the bluecome from a variety of sources and are simply used to show the functions. Nopaper has reported all of these parameters together, and degeneracy between themmakes using values from different papers inaccurate. For example a larger excita-tion to ionization ratio may look similar to less excitation with a higher singlet totriplet ratio, or the recombination time may emulate a longer triplet life time if thetwo effects are combined together.27Figure 4.3: The simple Monte Carlo sampled photon intensity and the curves plot-ted with equation 4.17. The agreement helps confirm the validity of equation 4.17 asthe physical representation of the light production.One application of this framework is to show how the recombination timesmears the timing distribution to look like one single exponential. Hitachi et al.reported that for a 1 MeV beta in LXe at zero applied field, the scintillation sig-nal is described by a single 45 ns time constant (many other values summarized in[55]). The parameters of the functions described above are fixed with data fromKubota et al. used to fix ρe, τs, τt , η and φ = 0.36 taken from [25]. Next the func-tions plotted above are used fit to a single 45 ns exponential, allowing τr and ρi tofloat.The fit was only perfomed on the region from 30 to 150 ns to be consistentwith the fit region of the paper measuring 45 ns [70]. The fit in Figure 4.4 showsthat at longer time the equation for φ 6= 0 is more accurate, and this fit returns τr =24.7±0.17ns and ρi= 0.183±0.001. Although the result is extremely preliminary,and better data sets and fit methods can be used, the application of this frameworkmay help to resolve uncertainty in some LXe parameters in the future.28Figure 4.4: An example of using the equations derived in the previous section to fita 45 ns decay curve, which describes the liquid xenon light intensity for MeV scalebetas with zero applied electric field. The φ 6= 0 equation has the more physicallyaccurate spectrum for larger times, due to the faster recombination. The parametersthat are fixed and floating are described in the text.4.3 Spectral WidthThe scintillation light emitted from liquid xenon has a broad spectrum, with mea-surements reporting a mean from 175-178 nm with a full width half maximum(FWHM) between 10 and 14 nm [37] [26] [14]. There is disagreement in the liter-ature, however the measurements were performed at slightly different temperatureswith different ionizing particles used to produce the radiation. Jortner et al. mea-sured the spectrum to be centered at 177.8 nm with a FWHM of 14.25 nm, usingan alpha source at a temperature of 160 K. Basov et al. measured the spectrum tobe centered at 176.7 nm with a width less than 10 nm6, at a temperature of 165K using 300-900 keV electrons. A more modern measurement was performed byFujii et al. who reported two data sets with values of 174.77 (175.08) nm with awidth of 10.10 (10.04) nm at a temp of 168 (169)K. Fujii et al. used 1.17 and 1.3MeV gammas from a cobalt 60 source. The spectrum measured by [26] is plotted6The reported spectra looks hand-drawn, the FWHM was estimated by inspection29in Figure 6.8 in Section 6.4.The difference may be due to particle type, possibly temperature, or a system-atic error in any of the apparatus. There is a correlation between exciting particlestopping power and the spectral mean; the alpha measurements give the longestwavelength and have the highest stopping power. The ionization track for the 300-900 keV electrons be similar to that for the ∼1 MeV gammas, with those mea-surements reporting similar values for the spectrum’s center. The deviation of ∼3nm between measurements is important for the accurate simulation of large exper-iments. In the following section, Figure 4.7 shows the relationship between n andwavelength. A difference of 3 nm corresponds to a difference in n of approximately0.03 (see Figure 4.7). As the refractive index changes quickly in this region, theaverage of these spectrum over n may result in an even larger difference biassingsimulations detectors.4.4 Cherenkov LightCherenkov light is produced when a charged particle is travelling faster than thephase velocity of light in a medium. Precisely, light is emitted at wavelength λwhen the particle’s velocity in the medium is larger than c/n(λ ) [35]7; β > 1/n(λ )where β ≡ v/c and c is the speed of light in vacuum. In this scenario the chargedparticle is travelling faster than the medium can respond to the photons emittedby the particle. Thus the wavelets produced by the moving particle interfere toproduce cone of light, emitted around the ionizing particle with a characteristicangle θC. This angle is defined by the particle velocity with respect to particlevelocity β and refractive index of the medium n for the far-field observer, with thecone being projected out at θC from the axis of the particle’s path.cosθC =1βn(4.21)For a particle near the velocity threshold to produce Cherenkov light, the denom-inator in Equation 4.21 will approach 1 giving a very large Cherenkov cone (al-though very little light will be produced). A more energetic particle with β ap-7Here the approximation is used that n(λ )≈√ε(λ )30proaching unity will produce a more focused light cone, with the most narrow lightcone possible at cosθC = 1/n when β ≈ 1. The Cherenkov yield is given in termsof the produced photon energy E per distance travelled x and frequency of light ω[35]:d2Edxdω=q24piµ(ω)ω(1− 1β 2n2(ω))(4.22)This equation can be transformed to the number of photons N produced per wave-length λ by using the two relations E = Nhc/λ , ω = 2pic/λ and some calculus8.The permeability is approximated as the vacuum permeability µ(ω)≈ µ0 which isvalid for a non-magnetic medium such as LXe [35].d2Ndxdλ=2piαλ 2(1β 2−1)(4.23)α is the fine structure constant. This functional form shows the λ−2 dependencewhich accounts for the higher photon yield at shorter wavelengths, responsiblefor the characteristic blue glow often associated with Cherenkov light producedin water. Liquid xenon refractive index data taken from Laporte and Steinberger([42]) was used in conjunction with range data from the NIST-estar database [16] tocalculate the Cherenkov spectra for various electron energies, shown in Figure 4.5.The spectra does continues to shorter wavelengths below 155 nm (8 eV), but above8 eV the attenuation coefficient in LXe becomes non-zero [42]. The integral overthe path length dx was performed for each λ that satisfied β > 1/n(λ ). The pathlength and particle velocity versus distance while the electron satisfied β > 1/n(λ )was calculated using the NIST range data, using a similar technique to that outlinedin Section 4.6.8The change of variable is as follows: dEdω =∂E∂N∂N∂λ∂λ∂ω =− ∂N∂λ hλ2pi31Figure 4.5: Cherenkov yields calculated for 4 different energy beta particles, cutoffat 155nm. The total number of photons is given in the legend.The change in spectral shape for higher energy events is due to the increase of nin liquid xenon at shorter wavelengths. Because the threshold for light productionis a function of wavelength, high n corresponds to small λ and requires a largervelocity to be above threshold. Lower energy betas only spend a small fractionof their time above threshold for small λ while high energy betas will be abovethreshold for longer wavelength λ for a longer fraction of their path. The non-linearity in total photon yields with energy, previously discussed in Section 3.2.2,is evident here as the yield for the 2 MeV beta is more than twice the yield of the 1MeV beta.4.5 Optical Properties and nEXO as a lensThis section outlines optical properties of liquid xenon, focusing on the relationshipbetween refractive index, temperature and liquid density. The refractive index isdependent upon the liquid density, which is a function of temperature. Therefore atemperature gradient will produce a refractive index gradient, which belongs to abranch of optics known as gradient-index optics. Depending upon the temperaturegradient in nEXO this may result in the detector behaving as a liquid xenon lens.32Claussius-Mosotti RelationThe refractive index of a material is related to the relative permittivity and perme-ability, n =√εrµr ≈ √εr, as µr ≈ 1 at optical wavelengths. The approximationn2 = εr additionally takes εr as real, meaning there is minimal light attenuation inthe medium (κ , the imaginary part of εr is small). This approximation should holdfor liquid xenon’s 178nm (7eV) scintillation light, to which LXe is transparent.The first photoabsorption peak in LXe is centered at 8.4eV, so for photon energiescloser to this absorption peak k becomes non-negligible and the approximationn2 = εr will no longer hold [13].εr−1εr+2=n2−1n2+2=Nα3εo(4.24)α is the molecular polarizability and N the number density of the medium. Equa-tion 4.24 is known as the Claussius-Mossoti relation, also known as the Lorentz-Lorenz equation. It relates the molecular polarizability to its relative permeativity,giving a relation between the material’s microscopic and macroscopic quantities9.This relation is derived under a classical approximation that the electric field fromthe radiation is constant throughout the entire molecule [35]. This equation is lessaccurate for deap UV photons above ∼8 eV, which also have a non-zero κ and soalready invalidate the first approximation n2 = εr.Equation 4.24 is linear in N, giving it a linear dependence on density for lowpressure gases when N ∝ ρ . In deriving this relation, the dependence on N entersvia the local polarization ~P which scales with number density and average molec-ular dipole moment, ~P = N 〈~pmol〉. For some liquids a higher density will change~pmol due to induced dipoles, and a non-linear dependence between ~P and densitycan occur10. Thus for dense media α = α(ω,T,ρ) whereas in gases α = α(ω),with ω the photons angular frequency. To treat this expected behaviour a virialexpansion can be performed to write the RHS of equation (4.24) as a polynomialin powers of density (the variable FLL is introduced).FLL =n2−1n2+2= [A+Bρm+Cρ2m+ ...]ρm (4.25)9In CGS units εr→ ε , α → α4piεo and the RHS of Equation 4.24 becomes 4pi3 Nα10The equation ~P= N 〈~pmol〉 becomes ~P= N 〈~pmol(N)〉33Where A,B,C... are functions of frequency and temperature. The first term rep-resents the single electron polarizability identical to gases, and mth order termsrepresent the n-body interaction contributing to the increased polarizability of themedium. For the scintillation light, which is about 1.4 eV below the first photoab-sorption line, FLL can be reduced to the first term and the temperature dependencecan be dropped, giving a simple linear dependence on density [13]. For photonsabove ∼7.5 eV in energy, this linear approximation does not hold. Therefore thefollowing relation can be used to solve for n:FLL ≈ A(ω)ρm → n2−1n2+2≈ A(ω)ρm (4.26)Xenon Density vs. TemperatureA virial parametrization of LXe’s molar volume was done by Terry et al. whichgives a roughly linear dependence on temperature11.Vm =Vr+A(T −Tr)+B(T −Tr)2+ ...+E(T −Tr)5 (4.27)The data is described with a 5 term polynomial, with Vm the molar volume, T thetemperature, Tr a reference temperature and A,B, ...E the coefficients. For nEXOthe molar density is approximately 0.022 mol/cm3 which translates to 2.96 g/cm3.Refractive Index vs Density and TemperatureThe simplified Claussius-Mosotti virial expansion, Equation 4.26, can be com-bined with equation 4.27 to calculate the dependence of n on temperature andwavelengths, for wavelengths close to or longer than 178nm. The coefficient ofthe expansion A(λ ) was parametrized by Baldini et al. using existing data.11Parameters are Vr = 44.312 cm3/mol, Tr = 161.38 K, A = 0.0937, B = 3.25 ×10−4, C =5.39×10−6, D = -2.97×10−8 with proper units to give Vm in cm3/mol34Figure 4.6: The general trend for n as a function of wavelength, calculated from[13].Figure 4.7: Same image as Figure 4.6 but zoomed in on the LXe scintillation region.35Figure 4.8: The lower x axis is temperature, with the upper x axis giving the cor-responding density following Terry’s fit. The assymetric differences between thedifferent wavelengths is due to n increasing non-linearly with photon energy (seeFigure 4.6).During the 2019 collaboration meeting it was remarked that“... we are buildinga big lens”. The temperature gradient across nEXO can result in a density gradientfrom the top to bottom of the detector, which in turn affects the refractive index viathe relationships outlined previously. The pressure gradient has a negligible effecton the density gradient. The effect of density gradient on n is outlined below, whichturns out to be quite small.Firstly, it must be verified that the extra pressure from the upper liquid on thelower volume does not change the density significantly. The pressure from theupper LXe on the bottom layer is calculated using nEXO geometries from thepreCDR (h is height):∆P= ghρ =125 cm×3 g/cm3×10 cm2kgm2g×9.81 m/s2×10−5 bar/Pa= 0.35 barChecking in the NIST database for xenon, the dependence of density on pressure36in this regime is negligible and the density is unchanged, so the pressure gradientcan be ignored.The temperature difference ∆T from top to bottom in the LXe vesel is estimatedas 1K, consistent with a previous thermal simulation which reports ∆T ≈ ∼0.7K[60]. Using the relationship between n and T , plotted in Figure 4.8, will give adifference of ∆n ≈ 0.02 across the detector. The uncertainty in literature for n inliquid xenon is close to this value [13], and the effect is fairly negligible. If theheat load in nEXO becomes higher this gradient may increase, in turn making thisn gradient more extreme and worth a more accurate study. Note that this onlystudied the effect along the vertical axis of the detector. The radial effect may bemore relevant, especially close to the barrel walls.4.6 Energy Deposition TimeDetectors with fast timing resolution may be able to measure the scintillation risetime in xenon. This rise time is expected to be dominated by the atomic physicsof the excimer relaxation and ion recombination. The lower bound will be set bythe energy deposition time; how quickly the primary ionizing particle deposits it’senergy in the medium. In the following the energy deposition time is extractedfrom the easily available data (from NIST) of Range vs Energy.The stopping power of a particle, how quickly it looses energy in a givenmedium, is described with dE/dx, the infinitesimal energy loss dE due to travers-ing a distance dx. As the particle enters the medium it begins slowing down viaelectronic interactions with the surrounding atoms. Betas loose their energy toatomic electrons, while heavier particles also loose a small fraction of energy tonuclear recoils and heat. Compared to a beta, the higher charge of an alpha al-lows for a stronger electro magnetic interaction with the atomic electrons whilethe mass allows for more efficient momentum transfer to nuclei. For this reasonthe stopping power for an alpha particle is orders of magnitudes higher than a beta(see Figure 4.9). These curves can be integrated over a length to get the range of aparticle for a given energy. These values are reported in units of g/cm2 such thatdividing by density gives the range in cm, making calculations relevant to gaseousdetectors with varying pressure straightforward. The calculation is extended to ar-37Figure 4.9: dE/dx data taken directly from NIST. At lower energies the nuclearcollisions begin to dominate for alphas, and for radiative effects become negligiblefor betas. Only data for xenon is shown.gon for its application in many detectors [21]. The densities used for liquid xenonand argon are:ρXe = 2.97 g/cm3 ρAr = 1.41 g/cm3Where the xenon density has been scaled by 1.011 to account for the increaseddensity due to xenon 136 enrichment in nEXO12. The range data from NIST13,scaled by the medium’s density are plotted in Figure 4.10. A 1 MeV beta has atrack length of approximately 3 mm while the alpha is closer to 10 um.By inverting the curves in Figure 4.10, one can attain the kinetic energy Kas a function of distance, K(r). For a given range r, this will give the particle’sinitial energy. A primary particle with energy Ko and range ro can be thought of12This is for 90% enrichment, although the effect is negligible13CSDA (Constant Slowing Down Approximation) range data used, which neglects energy fluc-tuations. Range(E) =∫ −( dEdx )−1dE38Figure 4.10: Ranges for alphas and electrons in liquid xenon and argon, calculatedusing densities given above. The betas have a much longer track length, with thetracks in argon being slightly longer than in ‘starting’ at K(ro) = Ko on the inverted plot. Moving towards the origin r < rothe particle will have K(r)< Ko. The relation K(r) gives the energy of the particlealong it’s track; at some position r < ro the particle will have energy K(r) with theorigin representing the end of the track. Using the relativistic velocity relation onecan convert K to a particle velocity giving v(r). In the equations below c is thespeed of light in vacuum, γ the Lorentz factor and mo the rest mass of the particle.v= c√1− 1γ2 γ = 1+Kmoc2→ v(K) = c√1− (1+ Kmoc2 )−2 (4.28)The next step is to relate v(r) to a total time for complete energy deposition. Thiscan be done using v= dxdtt(E) =∫ t(E=0)t(E=E0dt =∫ dtdxdx=∫ r(E)r=0dxv(x)(4.29)The upper limit of the integral introduces the energy dependence to t(E). Per-39forming this transformation and integration numerically yields the time for energydeposition of a particle with given initial energy E. The results are plotted belowwith some values stated for energies and particles of interest.Figure 4.11: Time for total energy deposition vs initial energy on the x axis.It should be noted that for betas (alphas) this integral is only computed to alower energy of 1 keV (10 keV) due to incomplete range data. This means theenergy deposition will be slightly longer than computed, as an additional 1keV(10keV) is deposited for electrons (alphas). Because the dE/dx is large at low ve-locities this additional energy of 1 or 10 keV should have a very small contributionto the rise time, and this leftover energy will result in the order of 100 to 1000events generated in the liquid argon or xenon.These calculation show that a beta at the ytterbium 90 (daughter of strontium90) end point energy of 2.28MeV gives an energy deposition time of 21.5ps in liq-uid xenon and in liquid argon. The alphas are an order of magnitude faster;the deposition time for the 5.4MeV alpha from polonium 210 is 5.0ps in xenonand 6.2ps in argon. Both of these times are extremely fast in comparison to singlet40lifetimes (order nanosecond). For experiments with nanosecond timing resolutionthis deposition time can be treated as instantaneous, however if ∼10ps timing res-olution is achieved these deposition times may play a roll in scintillation rise timecharacterization, and they set part of the time window over which Cherenkov lightwill be distributed.41Chapter 5Light Detection: SiliconPhotomultipliersSilicon Photo-Multipliers (SiPMs) are semiconductor devices which are quicklygaining popularity in the particle astrophysics community, replacing Photo-MultiplierTubes (PMTs) for many light detection applications due their favourable properties.Compared to the nearly 100 year old technology of PMTs, SiPMs do not requirea high voltage (HV) source. This can greatly simplify the design of cryo-systemswhere HV feedthroughs can increase system complexity and/or cost. Unlike PMTs,SiPMs do not have an electron drifting a macroscopic distance to the cathode soare very robust to operation in magnetic fields, and have been measured to be un-affected by operation in electric fields up to 30kV/cm [66]. They are also lessfragile than PMTs, are more durable to cryogenic shock and typically have betterradioactive purity than PMTs [15]. Compared to avalanche photo-diodes (APDs),SiPMs are much less sensitive to gain fluctuations caused by temperature fluctu-ations [21]. Importantly SiPMs offer excellent photon counting resolution due totheir low noise and minimal gain fluctuations, as APDs suffer from a higher noisefactor especially at larger applied voltages [21].Due to their numerous benefits nEXO and LoLX are using SiPMs for their lightdetection system. The section will outline the basic working principle of SiPMs,forms of noise and photon detection efficiency. The devices used in LoLX arethe Hamamatsu VUV4 Mu to E Gamma 2 (MEGII) model. They are mentioned42throughout this section with technical details reported in Section 5.4. A frameworkfor modelling external crosstalk between SiPMs is introduced in Chapter 7.5.1 Working PrincipleThis section is broken into three parts; the first describes the fundamental elementof an SiPM, the PN junction. The second section describes how a PN junctioncan be used for photon detection in a simpler application, namely the photodiodeand avalanche photodiode. Building upon the previous explanations, the completeSiPM is described in the third section.5.1.1 PN JunctionThe basic element of a SiPM is a silicon PN junction; the silicon on the P side isdoped with elements from group III and N side is doped with group V elements.This results in the P (N) side having holes (electrons) as mobile charge carriers.Applying a voltage across this junction yields the behaviour desired for photondetection.The physics of interest occurs inside the PN junction. The high concentrationof holes in the P side will diffuse towards the N-side and combine with the elec-trons, equivalently the electrons diffuse towards the N region. As the mobile posi-tive charge have left the P side the atoms in the lattice become negatively charged(and vice versa in N). This creates an electric field which pulls the mobile chargesback towards the N-doped region counteracting the diffusive force. These forcesreach equilibrium resulting in a depletion or space charge region where there is ahigh electric field, with very few mobile charge carriers due to the recombination.Figure 5.1 shows the electric field and the charge carrier concentration around thedepletion region. With zero applied bias the size of this depletion region is on theorder of micrometers, and the built-in difference in electric potential between eitherside is commonly around ∼0.6-1V in silicon depending on the doping profile.5.1.2 PhotodiodesFor photon detection a PN junction is operated in reverse bias, with the negativebias connected to the P side and positive bias on the N side. This increases the elec-43Figure 5.1: Image showing the electric field and carrier concentrations acrossa PN junction. dP and dW mark the edges of the depletion layers, while thosewith asterisks mark the region where holes or electrons can still diffuse to thedepletion region, giving an effective depletion region. Taken from [28].tric field strength across the junction. A photon enters the medium and is absorbedinside the depletion region via the photoelectric effect producing an electron-holepair, with the electron and hole moving to their respective electrodes. Typically thisphoton must travel at least a couple µm through bulk silicon to reach the deple-tion region [21]. At low applied voltage this produces a current proportional to thenumber of photons absorbed; there is no multiplication occurring and is thereforeonly useful for intense photon fluxes or with very sensitive current readout elec-tronics. By increasing the reverse bias voltage the electric field grows giving thedrifted electrons more energy. As these electrons and holes drift they are constantlyslowing via collisions with atoms in the lattice producing phonons. When their ki-netic energy increases above the silicon bandgap the drifting electron or hole willproduce secondary electron hole pairs via impact ionization [11]. This multipli-cation process increases the signal strength. Increasing the voltage produces evenmore extreme multiplication until a certain voltage, known as the breakdown volt-age (Vbr), where large amounts of current flows easily across the junction. This44breakdown process is referred to as a charge avalanche. APDs are operated justbelow this breakdown voltage where a multiplication on the order of 100-1000occurs. A drawback for APDs is that fluctuations in this multiplication processresult in an excess noise factor that increases exponentially with gain [21] imping-ing upon the photon counting accuracy. An APD operated above this breakdownvoltage is will continue to flow current once the avalanche has been initiated, ef-fectively acting as a light switch if the current flow is not quenched with a resistor.With a quenching resistor the avalanche process is halted producing a current pulsewith a distinct shape and charge [21]. An APD operated above breakdown voltagewith a quenching resistor is described as operating in Geiger mode and is referredto as a Geiger avalanche photo-diode (GAPD).Figure 5.2: (Left) A PN junction with a small reverse bias, showing the pho-ton absorption creating 1 electron-hole pair. (Right) A PN junction operatingas an APD in the linear region. The lower diagram shows the IV curve fora junction, with the kink at large negative voltage showing the breakdownvoltage where a small increase in voltage produces a large change in current.Images taken from [1].45In a GAPD the quenching resistor Rq is added in series with the diode; whenthe avalanche occurs a large current begins to flow from the junction. The currentflowing through the quenching resistor creates a voltage drop, reducing the voltageacross the diode exponentially down to breakdown (it behaves like an RC circuit)and the avalanche process stops. If the quenching resistor is too small the biasvoltage will be able to maintain the diode above breakdown while pushing currentthrough Rq and current will continue to flow.5.1.3 Silicon PhotoMultiplierA Silicon Photo-Multiplier (SiPM) is also known as a multi-pixel photon counter(MPPC), which provides more insight into their structure. One SiPM is composedof hundreds or thousands of GAPD all attached in parallel. Each GAPD is referredto as a pixel, microcell, or single-photon avalanche photodiode (SPAD). An equiv-alent circuit for an entire SiPM is shown in Figure 5.3 with the circuit elementsdefined therein.Before avalanche occurs charge is stored on the junction. Upon avalanche thischarge is released quickly and the quenching reduces the voltage to the breakdownvalue with zero charge remaining on the diode. This corresponds to the peak ofthe waveform (see V(vp) in Figure 5.4), and the fall corresponds to the rechargingof the SPAD where it slowly returns to the bias voltage. In the SPICE simulationthe capacitor Cd represents the charge available from the diode, with the capacitorcharged by closing and switch, and the avalanche emulated by the switch openingand Cd discharging.In the diode the avalanche process is fast, in comparison to the abilities of read-out electronics, and the rise time τr of the pulse is dominated by the diode’s capac-itance and internal resistance with a small contribution from Cq; τr ≈ Rd(Cd+Cq)[52]. In the equivalent circuit, this corresponds to Cd being charged while currentalso flows through Rq to the output. The small parasitic capacitances C3 and C4are also charged in the avalanche process (spikes in middle plot of Figure 5.4). Theswitch disconnecting emulates the charge being quenched and the diode capacitorCd discharges slowly with time constant Cd×Rq. However the voltage seen atthe output (V(vp))does not match the smooth voltage across the diode (V(spad))46Figure 5.3: The equivalent circuit in SPICE for one firing SPAD outlined inthe red box. A 200ps pulse is produced in V3 to close the switch simulatingthe avalanche in the PN junction. Cd and Rd emulate the diode’s capacitanceand internal resistance, and V2 is the overvoltage. C4,Rq1 and C3 represent-ing the parasitic capacitance due to the other microcells and silicon substraterespectively [23]. Equivalently the quenching resistor Rq has a parasitic ca-pacitance Cq. The output load is R5. Circuit simulation and analysis in SPICEby Peter Margetak.because the other parasitic capacitors (C4) starts discharging. This causes a sharpdrop on the output in the first few ns(see negative current on I(C4) in Figure 5.4).The fall time of the voltage V(vp) is also slower than Vspad due to the parasiticcapacitors which act as a voltage source at a later time (this can be seen via longvoltage tail of V(vn) in Figure 5.4). As summarized by Marano et al., the risetime is given by the time for the charge to be transferred the the output load, thefirst sharper drop is due to the voltage that remains across Rq while the parasiticsdischarge, and the long time constant is due to recharging and is dominated byRq(Cd+Cq).With the microcells connected in parallel the output signal is approximatelythe linear sum from all the SPADs that avalanche [52]. At high pixel occupancynon-linear saturation effects can occur [63] but most low energy particle detectors47Figure 5.4: Voltage and current pulses from SPICE simulation of SiPMequivalent circuit. Blue is voltage on SPAD, red the output voltage, greenthe parasitic voltage. See text for detailed description.should operate far from this region. The pixels are fabricated on one monolithicpiece of silicon[11], with trenches, made of IR frequency attenuating materials,placed between pixels to decrease internal cross-talk between (see Section 5.2 formore on cross-talk). The trenches and quenching resistors (when placed on theactive surface) decrease the photosensitive area of the SiPM. A well manufacturedSiPM will have fairly uniform pulses from alll SPADs, with respect to charge andshape. Some example pulses shown in Figure 5.6.The charge produced from a SPAD avalanche has small fluctuations such thatas long as the electronic noise is small single photon resolution can be achieved.This means that the distribution of single photo electron (SPE) charges does notoverlap with the signal from two SPADs firing. If a pulse is too large to countindividual peaks, the number of SPADs fired can be extract by dividing the totalpulse charge by the average SPE charge. An example charge histogram is shownin Figure 5.7 showing good separation between the one and two PE peaks.48Figure 5.5: Close up image of two SiPM pixels with a different pitch. Thequencing resistor is the rectangle wrapping around each pixel. Left image has25µm pitch (SPAD spacing), while right has 50µm pitch. Image taken from[11]Figure 5.6: (clockwise from top left) A ‘standard’ single photo electron (SPE)pulse, a two photo-electron (PE) pulse (likely delayed cross-talk (XT)), de-layed correlated avalanche, delayed correlated avalanche suffering from XTon the second pulse. Pulses from a VUV4 device cooled to -40C at roughly4V overvoltage, measured using preliminary LoLX amplifiers with a highergain than the final electronics.49Figure 5.7: Histogram of pulse charges showing the one and two PE distri-butions. The shoulder on the right of each distribution is attributed to after-pulsing creating slightly larger charges. Pulses from a VUV4 device at ∼4Vovervoltage, cooled to -40C, measured using preliminary LoLX amplifiers.5.2 Sources of NoiseThere is both random and correlated noise in SiPMs. The random noise is referredto as dark noise (DN) as these events occur in the absence of light. DN occurswhen an avalanche is triggered by an electron-hole pair produced in the junctionby thermionic emission or tunnelling enhanced via the electric field [34]. For mostSiPMs at room temperature the DN rate is extremely high so cooling is requiredto attain waveforms with resolvable pulses, with LXe temperatures giving low DNrates below 1 Hz/mm2 for the Hamamatsu devices used in LoLX. The dependenceof DN rate with applied voltage is due to increased field enhanced emission, whichchanges the rate less than the temperature as evident by Figure 5.8.The distribution of dark noise events in a given time window follows a poissondistribution, so for a rate RDN the poisson mean Λ for number of pulses in a timewindow δ t is Λ= δ tRDN . Therefore the probability of having atleast one DN event50Figure 5.8: The dark noise rate normalized by SiPM surface area for a VUV4,measured at TRIUMF for various temperatures and overvoltages. The gaseounitrogen (GN2) data taken in LoLX is in the temperature range from 193K to163K. Plot from [27]in a given window is the compliment of having zero pulses:P(N > 0) = 1−P(N = 0) = 1− eδ tRDN (5.1)For the entire LoLX detector1 operating at LXe temperatures and overvoltage of4V, the probability of a DN coincidence event within 100 ns is less than 10−4. Forcorrections to scintillation yields this is negligible, but may be relevant to otherstudies (see External XT Framework).Correlated noise or correlated avalanche (CA) has a greater effect than DN inbiasing photon counting. There are two distinct sources of CAs, namely cross-talk (XT) and after-pulsing (AP). XT occurs when IR photons produced duringa charge avalanche trigger an avalanche in a nearby SPAD. If the electron-holepair created by the XT photon must diffuse to the depletion region this will be adelayed XT event while if the photon is absorbed in the depletion region the XTwill be prompt. The larger prompt populations in Figure 5.10 indicate that prompt1surface area SA ≈ 24sipms×4 per package×36mm2 per sipm≈ 3500 mm251Figure 5.9: The total number of correlated avalanches for the VUV4 SiPMsand for two Fondazione Bruno Kessler (FBK) devices at ∼170K, taken from[36]. At 4V the effect is ∼20% meaning if a 100PE signal is measured, 80photons were absorbed by the device.XT likely dominates over delayed XT. After-pulsing occurs when a mobile chargecarrier produced during an avalanche is temporarily trapped and then later released,triggering another avalanche. The trapping can occur on impurities or lattice im-perfections. This process occurs in the same SPAD as the first avalanche, so thesecond avalanche may be initiated before the SPAD is fully recharged resulting ina larger spread of charge for AP events. The shoulders of the PE distribution inFigure 5.7 are attributed to this. The correction for these correlated processes canbe made for the total number of correlated avalanches in a given time window, asmeasured in Figure 5.9. For more detailed corrections, relevant when looking atphoton signal vs time, the correction is done in terms of delayed or prompt cor-related avalanches. This distinction between delayed and prompt noise is donebecause the delayed XT and AP events can be difficult to distinguish and their ef-fect is similar. In a 1µs window the ratio of prompt over delayed correlated eventsis about 10%, meaning AP dominates [27].These different pulse types are labelled in Figure 5.10 (taken from [36]), whichshows the different populations by plotting charge and time between pulses. The52Figure 5.10: The 2d histogram of charge and time between pulses for an FBK‘low field E’ device, which shows distinctly the different noise populations.The purple dotted line is an artifact from the analysis. Taken from [36]populations labelled ‘prompt’ are the initial pulses, with the two and three PEevents being caused by prompt XT. The delayed XT in purple is a small popu-lation as this process is more rare. The AP bands in orange have a repeating 2and 3PE structure as they also have prompt XT. The orange AP band is smearedover a larger PE range due to the avalanching occuring before the cell has fullyrecharged resulting in the correlation between AP’s charge and time after trigger.The green highlights both random noise and AP which occurs once the SPAD isfully recharged.5.3 Photon Detection EfficiencyThe previous sections have outlined how a SPAD will behave once an electron orhole triggers an avalanche in the depletion region. This section will device effi-ciency for different wavelengths, the SiPM parameter known as photon detectionefficiency (PDE). The PDE is defined as the number of photons producing a mea-surable avalanche divided by the total number of photons hitting the SiPM surface.It is commonly described with three terms [28]:53PDE = FF · ε(θ ,λ ) ·TP(V ) (5.2)The geometric fill factor FF is given by the fraction of active surface area. εis the quantum efficiency, which includes the photon transmission and probabil-ity of absorption creating an electron-hole pair. Finally TP is the probability ofone of these e-h pairs triggering an avalanche. θ is the angle of incidence, V theovervoltage and λ the wavelength of the light. A more thorough but physicallyaccurate approach can be taken where the PDE has separate contributions from theprobability of a hole or electron triggering the avalanche [28]:PDE = PDEmax(f ∗e ·Pe(dP)+(1− f ∗e ) ·Ph(dW ))(5.3)PDEmax is defined with respect to the junction size, electron-hole diffusion proper-ties, optical transport into the bulk and the attenuation length[28]. Pe and Ph are theprobabilities of an electron or hole triggering an avalanche, with f ∗e the fraction ofelectron driven avalanches. The benefit of this equation is that PDEmax and f ∗e canbe treated as voltage independent, with Pe and Ph being voltage dependent. BecausePDE is defined with respect to PDEmax, PDE can be more easily extended over un-measured phase spaces of incidence angle or wavelength if the voltage dependenceof Pe and Ph are known.For the photon to create an electron-hole pair in the depletion region, it must notbe reflected and also penetrate sufficiently far into the silicon. The silicon typicallyhas a passivation layer of SiO2 which will form naturally, while other passivationlayers can be manufactured. Therefore reflectance of this passivation layer on bulkSi is the relevant quantity to be measured. Interference between the two layers cancreate an oscillatory signal when scanning through angles or wavelength which isvisible in Figure 5.11. If the SiPM has a window on it, like the devices in LoLX, theoptics of this window are also important. For VUV light detection certain glassescannot be used as they absorb VUV light, and specific VUV transparent materialssuch as fused silica, magnesium fluoride or calcium fluoride must be used.Once the photon has entered the silicon bulk the absorption length is the rele-vant parameter for understanding PDE [28]. The majority of short wavelength light54Figure 5.11: Reflectivity measurements of 1.5µmSiO2 on bulk silicon. Thisis for an incidence angle of 45 degrees. The oscillation due to the thin-filminterference is evident. The red line is an average of the data. This is prelimi-nary data taken with the VERA setup at TRIUMF by Mark Ward.will be attenuated before reaching the depletion region, while long wavelength IRlight will fail to be stopped in the SiPM. This results in visible wavelength light of-ten having the highest PDE, with VUV specific sensors requiring specialized dop-ing profiles to minimize the silicon thickness between the SiPM surface and thedepletion region. For VUV photons some devices have had reported PDE as highas 25%, although there is disagreement between measurements. This disagreementis possibly due to surface contamination from improper SiPM storage. The PDEfor various SiPMs, including those used in LoLX, is shown in Figure 5.13. Forvisible light the PDE can be as high as 60-70% and becomes dominated by thephotosensitive surface area.55Figure 5.12: The attenuation length of magnesium fluoride and calcium fluo-ride. Data taken from [58]5.4 Hamamatsu VUV4The 24 SiPMs used in the LoLX detector are the Hamamatsu VUV42 (4th gener-ation) originally designed for the MEGII experiment. Each package has four indi-vidual SiPMs, each with 13,923 pixels and a surface area of 5.95mm x 5.85mm.Their pixel pitch is 50µm with a fill factor of 60%. They have a non-hermeticallysealed quartz window with a transmission allowing 175 nm light but light below150 nm will be attenuated. Some device testing was done and the measured gainand breakdown voltages agreed with the detailed study by Gallina et al..2model number: S13371-6050CQ-0256Figure 5.13: PDE values measured for the Hamamatsu VUV4 devices andsome devices from FBK, as reported in [27]. Measued for ∼180nm light.Orange and yellow data points taken from reference [7] in [27].Figure 5.14: An image of two of the VUV4 devices used in LoLX.57Chapter 6The LoLX DetectorThe LoLX experiment is a small multipurpose detector designed to further inves-tigate light production in single phase LXe, test the reliability of photon transportsimulations and provide experience operating close to 100 SiPMs in liquid xenon.It operates in single phase liquid xenon with zero applied electric field. Three dis-tinct experimental phases with varying physics goals are planned for the detector,with phase 1 construction completed and commissioning ongoing.Phase 1 of LoLX utilizes custom analog electronics built at TRIUMF and aCAEN V1740 digitizer with a 16 ns sampling rate. The detector utilizes opticalfilters covering Hamamatsu SiPMs to differentiate between VUV scintillation lightand broad wavelength cherenkov photons. This will allow measurement of thescintillation and cherenkov light yields, as well as investigate sipm to sipm cross-talk and validate photon transport simulations. The radioactive source is either oftwo needles tipped with a strontium 90 beta or polonium 210 alpha source, placedat the center of the detector. Figure 6.1 provides a simple view of the cross sectionof the detector, illustrating a beta decay producing scintillation and cherenkov light.Phase 2 includes upgrading to FBK SiPMs with a faster rise time and elec-tronics from the MEGII experiment, aiming to attain ∼100 ps timing resolution.With this improved resolution the temporal structure of the scintillation light canbe used to investigate electron-ion recombination dynamics and possibly the risetime of the scintillation signal. Phase 3 of LoLX will switch to digital SiPMs andaims to reach ∼10 ps timing resolution to perform the temporal separation of the58Figure 6.1: Illustration of the LoLX detector, showing a beta decay fromneedle producing the scintillation and cherenkov light. This cross-section isdown the middle, so the left and ride side are two side of the octagonal barrel.cherenkov and scintillation signal, for applications to Time of flight (TOF) PETimaging.This chapter will provide the motivation for the LoLX experiment and detailphase 1 of the detector, specifically the electronics and data acquisition system(DAQ) which were a central focus of this thesis.6.1 Motivation and relation to nEXOThe original inspiration for LoLX was to measure the cherenkov yield in liquidxenon, motivated by its possible application in background rejection for nEXOas discussed in Section 3.2.2. The two papers cited therein have differing resultsfor their cherenkov yields; Brodsky et al. simulated the 0νββ having 15% fewerphotons than the background events while Signorelli and Dussoni simulated thedifference to be ∼20%. LoLX can provide empirical measurements of this yield andhelp reduce uncertainty for future simulations. Although the immediate applicationof cherenkov light in nEXO is infeasible due to the low photon yield, the novelmeasurement has applications in other fields such as TOF PET. With suitable high59speed electronics the very prompt cherenkov light could be used to attain 10pstiming resolution. Applying this to PET allows for the localization of the emissionpoint to the mm scale. This removes the need for tomographic image reconstructionwhich will greatly improve the capabilities of PET imaging; improving the imageresolution and reducing the required radiation dose, among other benefits [19] [22][43].As outline in Section 3.2.1, the light collection efficiency in nEXO plays acritical role in reaching the energy resolution goal of ∼1% at Q0νββ . Therefore innEXO the photon transport must be well understood and simulated. Agreementbetween GEANT4 simulations and experimental data can validate the simulationof photon transport and reliability of optical data, helping attain accuracy in futurenEXO simulations.Although all of the light readout electronics in LoLX are external to the cryo-system, different from nEXO, LoLX can provide valuable experience with operat-ing 96 SiPMs simultaneously in liquid xenon. The detector can test SiPM stabilityover time, electronics response and the use of SiPMs to monitor temperature, aswell as investigate the usefulness of in-situ IV curves.6.2 Detector Body and CryostatThe detector body is an octogonal prism which holds the 24 Hammamatsu VUV4SiPM packages, which are each composed of 4 individual 5.96 mm x 5.85mmSiPMs for a total of 96 channels. There are 4 VUV4 packages on the top and bot-tom of the cylinder, and two rows wrapping around the 8 sided barrel. The detectorbody is 3d printed using the Formlabs Durable TM resin which was selected for itsdurability to thermal shock and vacuum compatibility. Tests done at McGill in-cluded cryogenic shock testing various printed forms by quickly submerging themin liquid nitrogen (LN2) and afterwards impact testing them; of the various testedonly the DurableTM resin did not break. A printed form slightly bulkier than thefinal LoLX design was slowly cooled in gaseou nitrogen followed by a full sub-mersion in liquid nitrogen; no damage was observed and a 1.5% shrinking wasmeasured. Using the same form after a 60◦C bakeout a pressure of 10−8torr wasreached using an 80L/s turbo pump, satisfying the vacuum requirement of 10−8torr.60Figure 6.2: The 3D printed detector body without the top cap and the farSiPM installed. Resting on the bottom plate and springs which separate thedetector from the cooling chuck. The four support rods are wrapped in kaptontape.The detector body and cryostat were designed and built at McGill University pri-marily by Dr.Thomas McElroy, with M.Sc.student Tsvetlin Totev assisting withdetector geometry design and cryo-testing.The inner detector body is placed between two hexagonal aluminum plateswith 4 kapton wrapped screws used to hold it together. The SiPMs are held inplace via clips (aluminum bars being SiPM package in left image, Figure 6.3).Springs separate the bottom of the detector from the cooling plate and also helpingto dampen vibrations from the external components. Additional plates are usedto assist with routing the 96 cables up the metal rod which holds the detector inthe vacuum vessel. The rod extends downwards from the bottom of a six wayvacuum flange, visible in Figure 6.4. A custom feedthrough was built by pouringSTYCAST 2850FT Black TM epoxy around eleven circuit boards, each with 10micro coaxial connector (MCX) terminated channels. This strategy was success-ful for giving a relatively low cost, vacuum compatible flange with 110 electrical61Figure 6.3: The fully assembled detector with and without SiPM wiring. Thesmall gold nipples pointing out from the bottom are the needle holders, andthe hexagonal aluminum plates are for cable routing. The white backsides ofthe SiPM packages can be seen with their inputs being the small gold needlessticking out. The rod exiting from the top of the photo holds the detector inthe main vacuum vessel.feedthroughs.The entire system shown in Figure 6.4 is enclosed in a vacuum chamber, withthe bottom portion that houses the detector body having additional flanges to at-tach the vacuum pump and LN2 feedthroughs required for the cooling chuck. Thedetector sits above the cooling chuck (Figure 6.5) which LN2 circulates through,using thermocouples placed throughout the detector to modulate the flow rate andachieve a stable temperature.6.3 Radioactive SourcesTwo main sources are used for phase 1 of LoLX, a strontium 90 (90Sr) beta sourceand a polonium 210 (210Po) alpha source. The beta source produces the Cherenkovlight while the alpha does not, providing two contrasting data sets. The expectationbeing the beta signal has a correlation between cherenkov light and energy whilethe alpha produces bright scintillation events. The 90Sr source has a half-life of 28.8years with a low energy endpoint of 546 keV, while the daughter yttrium 90 (90Y)beta decays with a higher endpoint energy of 2.2 MeV. The 90Y also has a much62Figure 6.4: (Left) The wired detector held in the six way vacuum T. Thewires are fed into the custom made feedthrough, which is shown close-up onthe right.Figure 6.5: (Left) The lower plate of the copper cooling chuck, showing thepath the LN2 is pumped through. (Right) The lower portion of the vacuumchamber, where the detector rests upon the assembled cooling chuck.63Figure 6.6: (Left) The decay chain of strontium 90, including the secondmost intense transition of 90Y labelled E0. A third even less intense transitionis not shown. (Right) The energy spectrum of the 90Sr and 90Y decays, over-lapped. EC is the experimental cutoff energy, with E02 and E02 giving the 90Srand 90Y endpoints, respectively. Both figures taken from [32].shorter half-life of 3.2 hours, such that it will remain in stochastic equilibrium with90Sr meaning the activity of yttrium will remain equal to that of the strontium. The90Y daughter, zirconium 90, is stable.As can be seen in Figure 6.6, both beta decays have a net angular momentumchange ∆J = 2 and a parity flip, making them both a ‘unique first forbidden’ tran-sition [65]. These forbidden, pure Gamow-Teller transitions [6] are a reason fortheir relatively long half-lives. The branching ratio for decays from the 90Y groundstate to any zirconium 90 (90Zr) excited states are less than 0.1% and should benegligible in the detector [65].The 210Po alpha source has a half-life of 138 days, with a much higher decayof 5.4 MeV. This is the polonium’s only decay mode, and the daughter lead-206is stable. The radioactive sources are placed on a needle tip for insertion into thedetector, such that the sources sit at the center of the detector. The needles werepurchased from the company Spectrum Techniques. The alpha source appeared tobe flaking off the needle, so only the strontium source was installed in LoLX forfear of otherwise contaminating the detector or xenon. Upon purchase in fall 201864the strontium needle had an activity of 0.37±0.07 Bq, as reported by the supplier.6.4 Optical FiltersThe output from a SiPM provides no information about the wavelength of incidentphoton, therefore LoLX uses optical filters to decouple wavelengths. The filtersnot only allow the separation of scintillation and cherenkov light but also help toconstrain detector effects such as amplifier linearity as some signals are scaled bythe transparency of their given filters.Longpass optical filters are used to select the Cherenkov signal, and are placedabove 22 of the 24 SiPMs packages1. The majority of SiPMs use longpass filtersbecause in LXe the Cherenkov signal is less intense than the scintillation light,their relative intensities are roughly 1/150. The longpass filters are the 10CGA-225model manufactured by Newport Optics, which have a transmission close to 90%at 0◦ incidence angle for wavelengths longer than 240 nm. The longpass filtersare expected to transmit the IR photons produced in a SPAD avalanche makingthe 22 SiPMs they are covering available for external cross-talk (see Chapter 7).The separation of Cherenkov from scintillation light may also allows the longpassfiltered SiPMs to observe the weak IR emission in gaseous and liquid xenon, whichwas previously reported in [17].One SiPM package is left bare allowing sensitivity to all light, and a VUVbandpass filter is placed on the last SiPM package. These two scintillation sensi-tive SiPMs packages are side-by-side on the top face of the detector. The VUVfilter is the 14S172FNB model from eSource Optics. It transmits light centredaround 172 nm with a gaussian FWHM of 20 nm, sufficient to pass the scintilla-tion signal which is centred at 175-178 nm with a FWHM of ∼10 nm [26][37] [14].The VUV SiPM is expected to be unaffected by external cross-talk as this processwon’t produce VUV photons (see 7). The VUV filter has a peak transmission closeto 20% which my be useful for analyzing very bright events; signal saturation mayoccur in the bare SiPM but the VUV channel should see roughly 5 time fewer pho-tons. Additionally comparing the VUV and bare channels may be used to assessnon-linear responses in the bright events. For example if the electronic’s response1recall there are 4 SiPM per package65Figure 6.7: Preliminary optical data for the longpass filters, taken with theVERA setup at TRIUMF by Shirin Edalatfar. Data taken at 0◦ equal for the bare and VUV channels the signal sizes should differ only by theVUV filter transmission2. The Cherenkov and scintillation spectra are overlayedwith filter data in Figure ElectronicsPhase 1 of LoLX uses custom analog electronics designed at TRIUMF to controlthe SiPMs, sum and amplify their outputs. The electronics of LoLX were a col-laborative effort with design and construction done by Peter Margetak (TRIUMF),and testing with SiPMs attached done by the author. There were multiple elementsto testing the electronics; ensuring proper pulse shapes (requiring proper termina-tion), measuring timing jitter, signal resolution and gain tuning.The amplifier boards can be built to sum channels in groups of 4 or leave thegroup unsummed. As the Cherenkov signal is very weak, with expectations onthe order of one signal per 4 SiPMs, all the longpass SiPMs are summed while2This example assumes the filter transmission is the only contribution to the light collection dif-ferences between the bare and VUV-filtered SiPMs.66Figure 6.8: Scaled scintillation and Cherenkov spectra overlayed with filterdata taken at normal incidence. VUV filter data taken from manufacturer,longpass filter same data as Figure 6.7. Cherenkov spectra should be taken asapproximate, and scintillation spectrum taken from [26].the bare and VUV SiPMs are left unsummed. The summing results in 22 output‘Cherenkov’ channels and 4 channels for both the bare and VUV SiPMs, giving 30channels in total. The summing is evident by the difference in dark noise shownin Figure 6.10. The first stage of the two stage amplifier is an AC coupled RFamplifier, part number MAR-6SM+ from Mini Circuits. It provides a voltage gainof approximately 12 its specific implementation and has a bandwidth from DC to 2GHz. The output from the 4 RF amplifiers are summed and passed to an operationalamplifier, which provides easy gain tuning by changing the R4 resistor shown inFigure 6.9.The electronics were tested using a VUV4 SiPM cooled to -40 ◦C with a sim-ilar apparatus to used in [27]. Extra gasesous nitrogen was used to purge the boxcontaining the SiPMs. The gain of the second stage was tuned to 5.4 to achieve anSPE pulse height of 10 mV at a 4 V overvoltage. This was done to allow for suffi-cient dynamic range in the scintillation channels while still retaining a good signalto noise ratio (SNR). The chosen operating voltage is ∼4 V because at this voltagethe PDE begins to saturate. Going to higher voltage increases the correlated noise67Figure 6.9: The second stage of the amplifer. The RF amplifier input comesfrom ‘AmpOut’. By changing the ratio of R4 and R15 the gain can be tuned.Figure 6.10: Example pulses taken from the installed LoLX detector ataround 10◦C. Channel 2 and 3 are unsummed while channel 4 has the contri-butions from an entire package (4 SiPMs).which has adverse affects on the photon counting accuracy. The SNR is definedas the SPE mean divided by the SPE standard deviation, which was above 25 forthe electronics tested with the oscilloscope instead of the digitizer. This SNR iswell above the required SNR of 10, which is set by the baseline nEXO design [57].This SNR also allows for efficient triggering on photon pulses without triggeringon noise events. Figure 6.11 shows the distribution of peak heights which alsoshows good separation between the induced noise, 1 and 2 PE events.68Figure 6.11: Histogram of the baseline subtracted peak height for an over-voltage slightly higher than 4V. At 4V overvoltage the peak height is 40ADCunits. The noise peak at ∼10 ADC is due to induced noise from the digitizerpower crate. Data taken amplifier with gain factor of 2 too high.The kapton coated coaxial cables that were used in the construction of LoLX(see Figure 6.3) were tested using a waveform generator to produce sharp currentpulses. The jitter and rise time were compared for the kapton cable, a referencecoaxial cable, and the reference cable combined with the PCB used in the cryostatfeedthrough. The jitter was measured to be 24 ps for a 50 mV square pulse withno measurable change for the different cabling types. For large pulses the rise timewas constrained by the waveform generator at 2.6 ns with no measurable differencefor the various cables.All of the previous studies were done using DN data or a waveform generator.To test using larger pulses a Hamamatsu PLP-10 laser was used, with small pin-holes placed in the top of the box containing the VUV4 devices. The laser headhas a nominal wavelength of 444 nm and typical pulse width of ∼70 ps. Usingan oscilloscope with 1 GHz bandwidth it was observed that the pulse shape was69Figure 6.12: Example pulse taken on the oscilloscope with 1GHz bandwidth,showing the distorted pulse shape. Taken for a VUV4 device at 4 V overvolt-age, large pulse generated with a 444 nm pulse laser. The peak height shownhere is ∼1.72 V.distorted due to an impedance mismatch. The distance from the pulse rising edgeto the second peak (see Figure 6.12) changed in agreement with changing cablelengths indicating signal reflection. The termination on the amplifier was correctedwhich successfully corrected the distorted shape see in Figure 6.12. It was mea-sured by Peter Margetak that the first stage RF amplifier still has a small impedancemismatch for larger pulses. The effect would be important for the large pulses ex-pected on the bare and VUV SiPM. To circumvent this a 6 dB attenuator wasplaced in front of the RF amplifier with the gain of the second stage doubled en-suring that the output pulse height is still 10 mV at 4 V overvoltage. The baselineRMS noise increased from 590 µV to 885 µV. Using a 10 mV peak to peak pulse,the measured rise time increased from 3.3 ns for the reference channel to 4.1 ns onthe 6 dB attenuated channel.The preliminary amplifier design was then incorporated into a more completeboard which holds 4 copies of the amplifier shown in Figure 6.9, giving 16 inputsand 4 outputs if maximal summing is done. This board has a charge pump andwhich provides a global bias voltage to the inputs on the board. The voltage fromeach input can then be individually set from +0.5 V to +4 V allowing for specific70Figure 6.13: IV curves taken for the LoLX detector installed at McGill.Taken at room temperature in december 2019 with the system under vacuum.Three of the dead channels are due to a wiring issue in the detector and afourth due to a blown amplifier.bias voltages to be set for each attached SiPM. The output of the charge pump,global HV and individual 0.5-4 V are set via a digital to analog converters (DACs).The readback for the charge pump and voltage output are done via an analog todigital converter (ADC). The current from each channel can also be readout viaan ADC with sensitivity down the micro amp scale. Both the DAC and ADC arecontrolled via an Serial Peripheral Interface (SPI) communication with a onboardmini computer (Nanopi), which in turn is connected to the DAQ system (see Sec-tion 6.7). This board was designed and built by Peter Margetak at TRIUMF andthe Nanopi setup and SPI communication code written by Dr. Lars Martin of theTRIUMF DAQ group. IV curves can be taken for all SiPMs using a python script,with warm IV curves taken for all LoLX channels shown in Figure 6.13. In total6 of these boards are used, 5 having complete summing and the board with the 2unsummed and 2 summed SiPM packages having 10 outputs.716.6 Linearity CorrectionFor events with high photon fluxes, the electronics are not expected to behave ide-ally as they were designed to operate in the single photon counting regime. Non-linearity means the measured charge from an N photon event will be less than Nmultiplied by the SPE charge, where the SPE charge is that produced by a singleSPAD avalanche. This effect can occur due to non linear affects in the SiPM, atten-uation from the cabling or a non-linear amplifier response. Instead of decouplingthese individual effects the response of the complete system is characterized usingthe setup mentioned in the previous section. The output intensity of the laser istuned using an optical attenuator, first taking data at in the single PE regime. Thenthe laser intensity is increased and the light intensity calculated using the low PEdata. A non-linearity is given by a deviation between the expected photon yieldand that measured with the SiPM, which is shown at the end of this section.Figure 6.14: The charge distributions for four largest attenuations. The left-most peak from 0 to 1000 ADC x ns is the zero count population, which hasvarious charges due to baseline noise. As expected the zero count populationdecreases with the optical attenuation.The measurements were performed on amplifier channels with the 6 dB atten-uation, 3 dB attenuation and zero added attenuation. Because the channels withthe VUV and bare SiPM have the 6 dB attenuation only those results are shown.72It should be noted that the laser light is very prompt due to its ∼70 ps pulse width,while the scintillation light is distributed over several nanoseconds. Therefore thethe non-linearity measured in this section is likely to be larger than that measuredfor actual scintillation light, as any bandwidth limited effects will be more signifi-cant for events with a more prompt pulse edge.Figure 6.15: An example large pulse showing the different integral windows.The horizontal red line represents the baseline, the dotted black line the be-ginning of the integration window and also the peak height. The green line isthe variable window size, the dark blue the fixed 500 ns window and the pinkthe large window. The small purple line represent the magnitude of the pulseovershoot.Λ(dB) = Λ010−dB/10 (6.1)Because the input signal is connected via a capacitor (AC coupled), for ideal elec-tronics the total pulse charge over an infinitely long time window will evaluate tozero. This manifests in the signal as overshoot, where the pulse will return to abovethe baseline (see purple marking in Figure 6.15). The pulse charge was computed73via three integrals after baseline subtraction, with no pulse fitting performed. Onewith a long integral window of 1.75µs, another with a shorter window of 500 nsand a third with a variable window size, integrating from the beginning of the pulseuntil the average of three bins are above the baseline value. The difference betweenthe 500 ns and variable window was negligible, but for pulses greater than a fewPE the long time window underestimates the charge due to the integral includingthe overshoot.Figure 6.16: The x-axis gives the expected PE while the y-axis the measuredPE. The first 3 data points used to fit Equation 6.1 used the 500 ns integrationwindow. The blue dots shows the error induced by overshoot for a large in-tegration window. The green and black data points show a better estimate forthe non-linear response of the electronics for large pulses.A zero count event is defined as the laser firing and no measurable avalancheoccuring in the SiPM. As photon counting is poisson process [20], the number ofzero counts can be used to calculate the average number of photons detected. SeeFigure 6.14 which shows the zero, one and two PE charge distributions for the four74largest optical attenuations. For an average number of photons Λ the probabilityP(n) of detecting n photons is given by the poisson distribution:P(n) =Λnn!e−Λ (6.2)If the total number of laser pulses is N and the number of zero counts is N0 theprobability of detecting zero photons is N0N , which gives the average photon rate Λ:P(n= 0) =N0N= e−Λ → Λ= ln(NN0)(6.3)Λ is measured for the three lowest photon fluxes (28, 25 and 23 dB) and fit toequation 6.1 to find Λ0, the average photon flux for zero attenuation. Equation 6.1is used to calculate the photon flux for data taken with less attenuation, where thethere are very few or no zero count events. dB is the optical attenuation. For thehigh PE events, where the attenuation was weak, the charge is computed using thethree integrals outlined above. The average of this charge is divided by the meanSPE charge to get the estimated mean PE for each attenuator setting. This is plottedversus the expected photon flux found using equation Equation 6.1.The peak height and overshoot show a good correlation with measured chargeas seen in Figure 6.17. This shows that with a constant scaling factor the peakheight distributions match the charge distributions. This relationship may only holdfor prompt light where the pulses arrive within the SiPM rise time, but is helpfulto asses the quality of noise cuts for commissioning data (see Chapter 8). Thecorrelation between measured charge and overshoot, shown in figure Figure 6.18may be helpful to estimate the charge of very bright events where the digitizedsignal is completely saturated.6.7 Data Acquisition SystemThe data acquisition system serves the purpose of controlling the hardware andmore importantly saving all of the needed information. The DAQ system runson Maximally Integrated Data Acquisition System (MIDAS) which has been de-signed by TRIUMF and Paul Scherrer Institut (PSI). MIDAS hosts front-end (FE)75Figure 6.17: The variable window length charge histograms in pink and red,scaled by 22.98 ± 0.017 mV/(ADC x ns) to match the baseline subtractedpeak height distributions. The rightmost pulses exceed the dynamic range ofthe digitizer resulting in the populated bin and shape mismatch.programs which control equipment and saves any requested variables, either in theMIDAS database or in separate data files. The programs that control the cryostattemperature run independently from MIDAS and was written by Thomas McElroyof McGill.The 30 outputs from the amplifier are digitized by a CAEN V1740 digitizer,with a 16 ns sampling rate and 2 V dynamic range with 12 bits of resolution dy-namic range. This means the least significant bit (LSB) corresponds to a voltage of0.48 mV3, and the 10 mV SPE peak height is ∼20 ADC units4. There is intrinsicmisalignment of the baselines, which changes depending upon the temperature ofthe V1740 board. The self-trigger logic is organized in groups of 8 channels, thisrequires the baselines to be aligned for the trigger threshold to be equal for all 8channels in a group. In addition to triggering for any channel above a threshold,coincidence triggers can also be set between different channel groups. This allowsthe detector to trigger on only events where many SiPM see light. The V1740 can32000mV/212 = 0.48 mV4the terrm ADC units will be used synonymously with LSB76Figure 6.18: The overshoot (measured in ADC units) on the x-axis and themeasured charge on the y axis. The second less intense linear population islikely an artifact of the analysis, as the overshoot value is found by taking themaximum value of the waveform without performing any averaging of nearbybins.also be triggered via a software trigger, or external signal as was used for the mea-surements in section Section 6.6. The FE to control the V1740 was similar to thatused by the DEAP-3600 experiment [8] with modifications done by the author.The FE for the Nanopis allows control of the applied voltages for each chan-nel. A script was written by the author to set all of the voltages across the de-tector within an accuracy selected by the user. Additionally, FEs were written tostore the environmental variables such a temperature and pressure in MIDAS. TheNanopi FE was supplied by Dr. Lars Martin and Dr. Pierre-Andre´ Amaudruz ofthe TRIUMF DAQ group, with modifications done by the author. The Nanopis areconnected to the LoLX-DAQ computer via a Network File System mount and theV1740 data transfer via an optical link.The mapping of the DAQ system is outlined in figure Figure 6.20, with thevariables describing all the connections for a single SiPM listed in the bottomright corner. The SiPM ID denotes the physical location inside the detector, thefeedthrough the input/output on the cryostat feedthrough. The Nanopi number de-77Figure 6.19: A image of the outputs from the cryostat to the six amplifierboards on the rack. This rack also holds the amplifier board’s power source(top), V1740 in a power crate and LoLX-DAQ computer.scribes which amplifier the SiPM is connected to and the Nanopi input describingwhich of the 16 inputs is used. Finally the Digitizer Channel describes which chan-nel on the V1740 the SiPM is attached. The full documentation of the DAQ systemis available on the experiment’s internal webpage.78Figure 6.20: Diagram of the major components of the DAQ system, with allthe connections relevant to one SiPM given in the bottom right corner. Thenumber of wires or channels is given above each line.79Chapter 7External XT FrameworkThe high number of SiPMs in close proximity to one another in LoLX may allowthe study of external cross-talk (eXT), where photons produced by an avalanchein one SiPM triggers an avalanche in a different SiPM. This is different fromXT described in Section 5.2 where a different SPAD in the same device is trig-gered. The ability of LoLX depends on the strength of this effect, which is not wellknown.external cross-talk can be relevant to precision physics searches which, forexample, may use a two PE threshold to trigger the detector. External cross-talkcan falsely create this signal so the magnitude of this effect should be measured,especially as excesses in low energy trigger rates have recently been investigated asa possible dark matter signal [41]. External cross-talk can also bias photon count-ing measurements by triggering extra SPADs, although this effect is expected tobe small as the probability of eXT is expected to be less than 1%. The varietyof geometries between SiPMs in LoLX can be used to constrain the probability ofeXT. The VUV covered filter will act as a reference SiPM insensitive to eXT as theemission spectrum is peaked in the IR and does not extend to VUV wavelengths[4] [54] [2].The eXT observable is the quantity Pi, j, defined as the probability that the‘source’ SiPM i triggers the ‘target’ SiPM j. Unless the photon emission is highlydirectional, it is expected that Pi, j ≈ Pj,i (see Section A.2 for more). This probabil-80Figure 7.1: The total, random and eXT DN rates for two SiPMs at either 4Vor 7V overvoltage. Random coincidences are computed using a 16ns timewindow. A colder detector improves the signal to noise ratio.ity will have three main contributions:Pi, j(r,V ) = Yi(V ) ·F(r) ·Φ j(θ ,V ) (7.1)Yi is the photon yield for the SPAD avalanche from the source SiPM, which willhave a geometric contribution F(r) to describe the photon transport to the targetSiPM. Φ j is target SiPM PDE averaged over expected emission spectrum, at in-cidence angle θ given by r. Performing this measurement by only analyzing theincrease in DN rates due to eXT is not feasible (see Section A.3).Instead, using the coincidence between devices can help to tag eXT eventsbecause the two pulses should occur simultaneously. This effect requires that therate of a random coincidences Rrand in time window δ t has to be less than the eXTrate ReXT . This random rate is given using poisson statistics with Ri being the rateof one SiPM and R j the other.Rrand = Ri · (1− e−R jδ t) (7.2)81Figure 7.2: The expected ratio between signal NX and random coincidencefluctuations√NR, assuming the Pi, j is Pi, j = 10−5. The line drawn is for 4Vovervoltage and a temperature of -110C.The expected eXT rate is simply the DN rate of both SiPMs multiplied by theprobability of eXT assuming Pi j = PjiRext = Pi, j(Ri+R j) (7.3)Using the DN rates measured in [27] folded to give a temperature dependence, therate of eXT events can be compared to the random coincidence rate where a valuefor Pi, j = 10−5 is assumed. A statistically significant measurement requires the thatthe number of eXT events NX is larger than the fluctuation of random coincidences,given by√NR1. The ratio NX/√NR represents the signal strength and is plotted inFigure 7.2 for four or one target SiPM packages (denoted with T ) and one sourcepackage (denoted with S).There are a total of 120 different geometric configurations between SiPMs onthe barrel with 9 unique angles between SiPM surfaces, with many more arrange-ments coming from the cylinder top to bottom and cylinder top/bottom to the bar-rel. This variety of spatial arrangements in the LoLX detector, which can help1Number of counts must be high enough to allow for poisson statistics82Figure 7.3: The LoLX detector unfolded, with dotted lines showing onlythe geometric orientation between 1 layer with a 45 degree incidence angle(giving a degeneracy of 8 for 45◦ incidences on one layer). The notation onthe right describes the angle between SiPM surfacenormal vectors and thedegeneracy in bold, with the + sign indicating moving one layer up the barrelslightly decreasing the angle between SiPM normal vectors. The squares arethe SiPM packages, with the pink and gray being the bandpass and bare SiPMsrespectively.constrain the spatial emission of eXT photons. For further studies the bias voltagecan be scaled to build a dependence of eXT photon yield with overvoltage.83Chapter 8Commissioning and First ResultsThis chapter will discuss the data taken in the first two cool downs of the LoLXdetector where the volume was filled with gaseous nitrogen. The pressure in thechamber was around 1.25 bar with fluctuations of 0.01 bar. The temperature mea-sured via a thermocouple near the bottom of the detector read 169 K (-104 ◦C) andthe thermocouple at the top reading 185 K (-88 ◦C), giving a thermal gradient ofroughly 15 K. Other than occasional large fluctuations due to process system errorsor changing of LN2 dewars the temperature stability was with ± 1 K.The electronic noise was characterized followed by the trigger rates for eachof the 96 SiPMs biased around 4 V overvoltage. The breakdown voltage was thenestimated by extrapolating data for the SPE charge versus voltage. After applyingcuts to remove noise induced events some preliminary detector occupancy and PEspectrum plots are shown. The timing structure of fluorescence in GN2 is analyzedand finally some possible evidence for eXT is given.8.1 Electronics NoiseBefore biasing SiPMs the trigger rate due to electronic noise was measured toensure that thresholds are set sufficiently high above the electronic noise. TheSiPM voltage was set to 20 V to engage the HV output from the amplifier boards.After baseline alignment was completed, low trigger thresholds were set for eachchannel group of 8. At a threshold of 5 ADC channel groups had trigger rates of84over 100Hz, at 7 ADC it improved to around 5 Hz while moving to a 10 ADCthreshold gave trigger rates less than 1 Hz. This was deemed an acceptable levelof noise as 10 ADC is half of the SPE pulse height at 4 V overvoltage, and thedistribution of SPE peak height distribution is not broad enough for a significantamount of pulses to fall below the threshold.8.2 SiPM Trigger Rates: S-Curve AnalysisTo find the voltage corresponding to a given peak height, the trigger rate was mea-sured at a fixed threshold over range of voltages. The trigger threshold was set to 20ADC which corresponds SPE peak height at the target overvoltage of 4 V. As thevoltage is increased a larger fraction of the pulse heights will be above threshold.Thus the trigger rate will increase, with the largest increase in trigger rate occurringas the distribution of peak heights becomes centred around the threshold. Effec-tively the trigger threshold acts as an integral of the peak height distribution, withthe voltage shifting the distribution so more or less of the curve is integrated.If the dark noise rate was constant with respect to voltage, the trigger rateversus voltage would yield the error function (erf) with the inflection point at 4 Vovervoltage. Because the DN rate increases approximately linearly with voltage,the trigger rate vs voltage or ‘S-Curve’, is scaled by a constant factor1. To accountfor the constant electronic noise a constant offset was also added. The S-Curvefunction is given below, with T the trigger rate, V the voltage, µ the inflectionpoint or 4 V overvoltage, σ representing the curve width, R the DN rate scalingfactor and C the constant offset to account for the electronic noise. The 12 factor isto scale the function and +1 in(erf(V−µσ)+ 1)is to shift and the the function toabove the x-axis. The 4 V added in the linear term (multiplied by R) is to scale theDN rate from breakdown voltage and not from the 4 V overvoltage. An exampleof data fit is shown in Figure 8.1 along with fits for some less complete functions,motivating the functional form just described.T (V ) = R(V −µ+4V ) · 12·(erf(V −µσ)+1)+C (8.1)1The DN measurements from [27] show a power relation between DN rate and voltage but forthe small voltage range used here a linear approximation is made85This analysis yielded overvoltages of 4 V between 48.7 V and 50.11 V with anFigure 8.1: An example S-curve fit, showing several different fits; f2 is anerror function shifted and scaled, f3 is Equation 8.1 withoutC and finally f4 isthe complete Equation 8.1. The fit for f4 is much better than the others givenby it’s low chi2 value, indicating the model is accurate.average of 49.3 V. The trigger rate across channels at the 20 ADC threshold wasfairly uniform with rates between 50 and 100 Hz, with the exception of SiPMnumber 61 2, which had a rate of over 500 Hz. The voltages extracted from thisS-Curve analysis was used to set the voltages for the remainder of the data taking.8.3 SPE Charge versus VoltageThe detector sums the signals from for devices into a single output channel. Toseparate the contributions from each of these SiPMs the devices were individuallybiased +4 V above one another. Thus at near 4 V overvoltage, 3 of the SiPMs onone package are approximately at 0 V overvoltage and don’t contribute to the out-put signal. This measurement was done at two voltages, thus requiring 8 differentvoltage settings. For each of the 96 SiPMs the breakdown voltage was calculatedby extrapolating between the two SPE charges to find the breakdown voltage. A2sipm 61, counting from zero, is located on the barrel of the detector and output on digitizerchannel 1786different study, which measured the SPE charge versus voltage for the entire groupof 4 SiPMs, showed excellent linearity between SPE and voltage. That data can beseen in Figure 8.3 and Figure 8.2, and provided confidence that using only two datapoints to extract the breakdown voltage for a single SiPM may not be so innacurate.Figure 8.2: Charge histograms and their gaussian fits in red, for three volt-ages. The signal is from all 4 SiPMs on the channel. The charge on the x-axisis the charge returned from the pulse fitting algorithm. The charges from thesehistograms are used in Figure 8.3.The breakdown voltages measured for all devices, extracted using two voltages,showed a slightly wider distribution than the voltages measured using the S-curveanalysis, with the mean of 49.7 V being 0.4 V higher. A temperature differenceof 8 K between runs could explain this discrepancy, although the cryostat temper-ature was stable so this explanation is unlikely. The disagreement is likely dueto the measurement method, biassing due to noise or triggering. Using the linearrelationship between temperature and voltage reported in [27], these voltages weretransformed to a temperature. Although the absolute temperature scale is muchlower than given from the thermocouples, the difference between the SiPMs on thetop and bottom of the detector agree qualitatively with the measured temperaturegradient, as can be seen in Figure 8.4. Overall this method can be used in futurecooldowns of LoLX when the voltage for each SiPM is required, with more than87Figure 8.3: The data from Figure 8.2 fit with a line. The y error bars are theFWHM of the charge distributions Other channels had a similar good linearitybetween the three data points.two voltages being used to improve the accuracy of the method.8.4 Induced NoiseCuts were implemented to remove events caused by induced noise. Three cutswere used, and were devised by assessing data with a trigger threshold of a halfSPE (referred to as low threshold trigger) and requiring coincidence between threechannel groups. This dataset was used as it is most sensitive to induced electronicnoise which affects the entire detector.When there is a large induced noise signal many channels are above thresholdmultiple times in a given event, leading to new trigger generation resulting in otherevents having a shorter time window3. Thus the first cut applied was to removeany events with a length shorter than that set by the DAQ. This cut removed about10-15 % of the events. The next two cuts were to ignore any event where a pulse isreconstructed with PE less than 0.5, as this is likely the pulse finder mis-identifyingnoise as a peak. The half PE cut removed about 2% of the events. The last cut wason the width of the pulse. As can be seen in Figure 8.5, which is a plot made with3It is unclear if this is due to an error in the system’s buffer or expected behaviour.88Figure 8.4: The distribution of voltages for each SiPM, transformed to tem-perature. SiPMs locations in the detector are given in the legend. The absolutescale much colder than the coldest thermocouple but the gradient from top tobottom agrees qualitatively with the thermocouple applied cuts, there is a large population of events with a width less than sixADC samples 4. The narrow events are attributed to a pulse being mis-identified ina sharp noise spikes. The width cut removed an additional ∼ 1% of events after theprevious two cuts.As was shown Figure 6.17, for prompt pulses there is a linear relationshipbetween charge and pulse height. As will be discussed in the following section, itis suspected that observed large light pulses are due to GN2 fluorescence causedby the 90Sr source. The lifetime for the excited states is very fast [45] so the lightsignal is still expected to be prompt, and the linear relationship between charge andpulse height approximately valid. Figure 8.6 shows the distribution of the ratio ofthe pulse height divided by fit charge. The applied cuts reduce the population to anarrow set of values as expected for clean data.4The width is defined for the raw data length from the rising edge at 20% of the maximum heightto 20% on the falling edge89Figure 8.5: The 2d distribution of pulse width (in ADC samples of 16ns each)on the y-axis and raw charge on the x-axis. The different PE populations arevisible as the yellow populations centered around the y-value of 10. The smallwidth events also have a low charge, further indication that they are not SiPMpulses.8.5 Large Pulses and OccupancyThe detector activity was noticeably higher than would be expected for only darknoise. Pulses were observed in the detector in multiple channels and coincident intime, with some pulses being larger than 10 or 15 PE. It is possible that the installed90Sr is causing fluorescence in the GN2, but it could also be fluorescence in theplastic or some other currently unknown mechanism. Gaseous nitrogen fluorescesat a variety of wavelengths, most strongly in the 300-400 nm region and at 630 nm[38] [44] so this light will be transmitted by the longpass filters. The literature hasnot reported any light emission in the VUV region, although this spectral region isnot typically of interest for light emission in air because it is quickly attenuated.To select this activity, the low threshold trigger data with coincidence between twoand three groups was analyzed. Figure 8.7 shows the number of photons (NPE)measured in a single channel per event on the y axis with the corresponding channelon the x-axis. NPE is calculated by dividing the summed charge of each pulse bythat SiPM’s average SPE charge. All channels see light, with slightly less in thebare SiPMs (channels 26 - 29) and much less light in the VUV bandpass coveredSiPMs (channels 0-4). This isotropy is indicative of fluorescence, or at least a90Figure 8.6: The distribution of the ratio of peak height divided by fit charge,both before and after the three cuts listed.non-directional light signal.Nhit is defined as the number of channels that see a pulse larger than 0.5 SPE.This variable is used to plot the spectrum of total PE for all channels versus Nhitin Figure 8.8. The Nhit spectrum has a large Nhit=2 population which is possiblyeXT and is investigated in the following section. The PE spectrum shows a knee ataround 60 PE. It is doubtful that the spectral shape is related to the beta spectrumas the large majority of betas produced by the 90Sr source are energetic enough tohave a range much larger than the dimensions of the detector [16]. If the light isdue to nitrogen fluorescence, this spectrum may be due to fluctuations in energydeposited in the GN2, partially due to hard scatters which occur infrequently [7].The majority of literature for fluorescence in GN2 is focused on measuringthe emission spectrum in air, as this pertains to cosmic ray experiments and ap-plications such as LIDAR [44] [38] [24] [12] [47] [71]. In atmospheric air oxy-gen plays a major role in the light production process by quenching many excitedspecies, reducing the light yield [12]. The longer the lifetime of a species, the morethe quenching will reduce the light output. A higher temperature also increases91Figure 8.7: Number of PE per channel versus channel ID, for the three groupcoincidence data. This shows the light is seen isotropically throughout thedetector. The populated zero NPE bin is not understood as the 0.5 PE cutshould prevent this. The VUV filtered channels are ch 0 to 4 and the bareSiPM channels 26-29.the amount of quenching due to an increased number of collisions of the excitedspecies with nearby atoms. The light yields for keV-MeV scale electrons in air arereported in the previously mentioned paper, and the values are quite low. Lefeuvreet al. ([44]) reported 4.23±0.20 photons/m when using a 90Sr source. The authorof this dissertation was only able to find one paper measuring both a yield and tem-poral structure for relativistic charged particles in pure nitrogen, which reported ayield of 24 photons/MeV with a decay time of 2.5±0.5 ns. This was for fissionfragments in GN2 at 1 atm pressure and measured by Lehaut et al. [45]. It is notstated what temperature the measurement is performed at but room temperature isinferred as their apparatus has no cryogenic system. The integration window usedwas also only 30 ns, making the measurement of a longer time constant difficult orimpossible for their analysis.The activity in the VUV covered channels could have two possible causes;leakage of light behind the optical filter or the signals are is not strictly due to92Figure 8.8: The total PE detector per event on the y-axis, and the number ofchannels with pulse larger than 0.5 SPE on the x-axis. Data is from the 2 groupcoincident trigger data. The x axis projection is shown above (Nhit spectrum)and the y axis projection to the right (NPE spectrum). The spectrum for the3 group coincident is similar but with less of a knee in the PE spectrum, andless Nhit = 3 events.fluorescence in the GN2. If the former is true then this will be problematic for thecherenkov measurements, if light also can leak behind the longpass filters. If thelatter is the case, there is a different source of light, this may be attributed to cosmicmuons, fluorescence in the plastic or another unknown effect.The author suggests that if the light is indeed primarily due to fluorescence in93the GN2, the lack of oxygen to quench the light production gives a yield in theLoLX detector much greater than the 4.23±0.20 photons/m reported in [44]. Aproper GEANT4 based study will allow for the energy deposition in the gaseousvolume to be scaled to a light yield, to see if there is agreement with the value of24 photons/MeV reported in [44] for pure GN2. A correction for the increase inyield due to temperature may also be required for the values in cold gas to agreewith 24 photons/MeV measured at room temperature. The measurements may stilldiffer due to a difference in purities of the GN2 used in both experiments. Alsothe high stopping power of the fission fragments used in [44] may change the yieldcompared to a beta, if quenching processes similar what occurs in LXe [25] alsooccurs in gaseous nitrogen.8.6 External SiPM Cross-TalkThe same data analyzed in the previous section (Nhit = 2) was investigated toattempt and observe eXT. The channel occupancy for channels 24 and 25, locatedon the bottom of the detector, was plotted for pulses within 8 ns of one another (seeFigure 8.9). These two SiPMs were selected for various reasons; they are colder soless dark noise to affect the eXT signal, they can be triggered on their own channelgroup independent from the barrel SiPMs, and they each have various SiPMs onthe barrel with which eXT can occur. When first comparing the two signals inFigure 8.9 it looks as though there is evidence for eXT. The two devices both showa structure for the odd numbered channels, and the odd channels correspond to theSiPMs on the bottom of the barrel closer to channel 24 and 25. The peaks also shiftfor each SiPM which indicates channel 24 and 25’s different positions with respectto the barrel SiPMs; channel 24 is closer to SiPMs 13, 15 and 17 while channel 25is closer to the SiPMs on channels 9, 11 and 13.A simulation was performed by Kevin Sohn, a summer student at McGill,where photons were shot isotropically from one SiPM and detected at others, em-ulating eXT for isotropic spatial emission. The overlay of this simulation withchannel 24 data is shown in Figure 8.10, where both distributions were normalizedexcluding channel 24. This normalization skipped channel 24 as it has an non-physically high population, which is an artifact from the analysis as channel 24 is94Figure 8.9: The time to next pulse spectrum for the Nhit = 2 population of thelow threshold 2 group coincidence data. The fit is for the two term exponentialfunction with parameters [1] and [2] being the slow and fast time constants.selected for every event. The comparison of data and simulation shows qualitativeagreement in their peak structures.However when doing the same comparison with data and simulation for a SiPMlocated on the top of the detector (channel 4, see Figure 8.11) the results are not aspromising. There is no clear structure in the data and the peaks from the simulationdo not align well with the data. Furthermore Figure 8.9 is reproduced in Figure 8.12for pulses within various time windows of one another, not only pulses with 8 nsof one another. In Figure 8.12 the first two smaller time windows seem to havesimilar distributions, with a larger change occurring in the populated channel 11for pulse separation greater than 32 ns. The relationship between between thesedistributions may give an estimate for the amount of cross-talk occurring.It is suggested that the majority of the structure seen in Figure 8.9 is due to lightcollection and the beta interacting near the edge of the detector; if a beta interactionoccurs close to channel 25 and a small amount of light is produced, the channelsthat are most likely to see the scintillation signals are also those most likely to seean eXT photon from channel 25. This could be tested by investigating the energy95Figure 8.10: The simulation of isotropic eXT overlayed with the data forchannel 24. The normalization for the raw data skips channel 24 as it has avery high count due to bias from the analysis; every event includes channe 24.The raw data still enforces time between pulses to be less than 8ns.deposition versus distance travelled for a beta in GN2, if it has an interaction lengthon the order of cm a first scatter may occur near the detector’s edge. This effectcould also occur from fluorescence in the plastic, as fluorescence in the plasticwill be localized to nearby SiPMs. Regardless of the validity of this hypothesis,to continue the eXT investigation the timing resolution of the detector and pulsefitter must be assessed to attain the correct time window for separating eXT; theresults from Figure 8.12 indicates that if the signal is due to eXT the 8 ns timewindow is not the correct one to use. The fluorescence spectrum due to GN2 mayneed to be better understood so it can be subtracted. In general much more analysisis required to reliably extract eXT probabilities, and the possibility of nitrogen orplastic fluorescence makes the measurement more challenging.96Figure 8.11: The simulation of isotropic eXT overlayed with the data forchannel 4. The normalization skips channel 4 for the reason mentioned previ-ously. The low count rate in channels 5, 6 and 7 is due to trigger bias; channel4, 5, 6 and 7 are on the same trigger group. The raw data still enforces timebetween pulses to be less than 8ns.97Figure 8.12: The same data for Nhit = 2 and including channel 25, now withdistributions for multiple time between pulses. The distributions are againnormalized within channels 4 and 23.98Chapter 9Conclusion and OutlookThe work presented in this thesis provides a starting point for much future physicsto be completed. With the LoLX detector constructed and DAQ operational anabundance measurements can be done, namely operating the detector in gaseousand liquid xenon. The various methods described for extracting the breakdownvoltage for the detector were successful, providing well understood methods tocharacterize the detector in future cooldowns of LoLX. When LXe data is taken,the electronics linearity correction can be used to correct the signal on the bareSiPMs for very bright events. The analytic framework for temporal signaturesmay also be applied to the LXe data. More work can be done to understand thenitrogen data; the evidence for eXT was not definite. The eXT simulation datacan be repeated for a non-isotropic distribution, and by performing a dark noisecorrection the eXT signals can be improved. If the suspected GN2 fluorescencewaveforms can be produced their time structure should be investigated for the 2.5ns time constant reported in the literature. Observation of this would help to clarifywhat contribution of the light signal is due to is from light production in GN2.The GEANT4 study of the energy deposition in the gaseous volume may help tounderstand if the observed light is strictly from the nitrogen, or if there is anothereffect such as fluorescence in the detector plastic. 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The phase velocity isstill the relevant quantity for calculating light propagation in large detectors.The simplest form of a single frequency propagating with wavelength λ and fre-quency f = 1/T is a sin or cosine:f (x, t) = cos(2piλ x− 2piT t) = cos(kx−ωt)k ≡ 2piλ ω ≡ 2piT ≡ 2pi fThe velocity for a wave is given by fλ , and for a single frequency is called thephase velocity vp = fλ = ωk . For information to be conveyed the signal intensitymust be modulated by having two waves with different frequencies, offset by ∆kand ∆ω = vp(k+∆k). The two frequency modulated wave has the form:g(x, t) = cos[(k−∆k)x− (ω−∆ω)t]+ cos[(k+∆k)x− (ω+∆ω)t]cosA+ cosB= 2cos(A+B2 )cos(A−B2 )g(x, t) = 2cos(∆kx−∆ωt)cos(kx−ωt)This is just a single frequency who’s amplitude is modulated by the first cosine.111The velocity of this amplitude modulation, or group velocity vg = ∆ω∆k =dωdk . In dis-persive material (ie almost all matter except the best camera lenses) the frequencychanges with wavelength. For light this defines the index of refraction n= cvp . Thisleads to ω(k) = kcn . Taking the total derivativevg =dωdk=∂ω∂k+∂ω∂n∂n∂k(A.1)=cn− kcn2∂n∂k=cn− ωn∂n∂k(A.2)vg =cn+cλn∂n∂λ(A.3)In xenon as the wavelength increases n decreases, giving vg < vp, as expected fora medium with normal dispersion.A.2 External Cross-Talk: DegeneracyThe notation in this section is changed from Pi, j to PST . Below it is shown howeven turning up one device to a higher voltage than another the probability Pi, j willbe close to Pj,i.It is expected that the photon yield will have a primarily linear relation to gain,and it has been measured that gain is linear with V .YS ≈ k′Gain+ k2V 2 (A.4)YS ≈ kV + k2V 2 (A.5)Assuming second order effects are small, then the yield from a target SiPM will beroughly half the yield from a single SiPM at twice the overvoltage:2 ·YT (VOv = 4)≈ ·YS(VOv = 8)If the emission is isotropic the solid angle contribution for each probability willbe equal. The only situation where the FST factors won’t cancel one another out isif the photon emission is highly anisotropic, for example all the photons are emittednear perpendicular to the normal. Then if two devices are close to 90 degrees fromone another, one will see many XT photons while the other sees very few.112With a target SiPM and one source SiPM, with PDE values taken from avalanchetriggering paper at IR wavelengths, we can look at the following approximation.The probabilities are the same order of magnitude and therefore will be hard todissociate in analysis, unless the anisotropy mentioned above is real and can beexploited.PSTPTS≈ YSYTFSTFTSPDESPDET≈ 21·1 · 0.70.5= 2.8A.3 External Cross-Talk: Dark Noise methodThe notation in this section is changed from Pi, j to PST . This investigates how theDN rate will change with the effect of external cross-talk for only two sipms. TheSiPM dark noise rates will be increased due to external cross-talk from the otherSiPMs:RT = Ro,T +PSTRS (A.6)RS = Ro,S+PTSRT (A.7)RT = Ro,T +PST(Ro,S+PTSRT)RT =11−PSTPTS(Ro,T +PSTRo,S)(A.8)RS =11−PSTPTS(Ro,S+PTSRo,T)(A.9)The non-linearity of the target SiPM triggering the source SiPM is reflected by the1/(1− x) prefactor. If PSTPTS is small (as expected) this can be expanded to theconverging geometric functional form we originally expected:RT ≈(Ro,T +PSTRo,S)[1+PSTPTS+(PSTPTS)2+(PSTPTS)3+ ...](A.10)RS ≈(Ro,S+PTSRo,T)[1+PTSPST + ...](A.11)If the data suggests second order effects (meaning RS > R0,S), we can solveanalytically for PST . Two equations RS and RT and two variables PST and PTS.113Using equation A.8 to isolate for PTS:RT(1−PSTPTS) = Ro,T +PSTRo,SRT −Ro,T −PSTRo,S = RTPSTPTSPTS =RT −Ro,T −PSTRo,SRTPST(A.12)Now we sub this into equation A.9 and do lots of algebra:RS =Ro,S+Ro,TRTPST(RT −Ro,T −PSTRo,S)1− RT−Ro,T−PSTRo,SRTRS =RTPSTR0,S+Ro,T(RT −Ro,T −PSTRo,S)PST(Ro,T +PSTRo,S)RS =(Ro,T +PSTRo,S)(RT −Ro,T)PST(Ro,T +PSTRo,S)RS =RT −Ro,TPSTPST =RT −Ro,TRSand PTS =RS−Ro,SRT(A.13)And conversely for the target SiPMs triggering the hot SiPM. This is perhaps a sur-prising result, but this means we can easily include all order effects in our analysis.Dark Noise Signal StrengthFor having a reliable measurement, we need the change in target dark rate to begreater than the error on the dark rate measurement.At VS = 8V and VT = 4V , both with 1 full SiPM package (4 quadrants) on, anda very high PST = 0.001 = 0.1% the fraction of increase in DN can be calculatedusing the equations outlined above:RT −Ro,TRo,T=PSTRSRo,T= 0.003 = 0.3% (A.14)In the the VUV4 Paper, Giacomo [27] was able to measure the DN with anerror of 1.5%. Our expected change is one order of magnitude less than this for our114generous PST value. We could try turning on many SiPMs, so we increase RS by afactor of 10, but that only puts us at the measurement limit.A.4 Analytic Dimer PopulationsThis calculation is performed for the case of no escaping electrons: η = 0. Thedecay time constants are comparable to the recombination time for minimum ion-izing particles, so a transient equilibrium type of simplification cannot be made.The rate of dimer formation will depend on their recombination (first term) andthe two decay modes (last two terms), taking the excitation to exciton relaxation asinstantaneous:dNdt=Noτr(1+ t/τr)2− N(t)τsβ − N(t)τt(1−β ) (A.15)=Noτr(1+ t/τr)2−N(t)A (A.16)A≡ [τs+β (τt − τs)τsτt] (A.17)β indicates the total ratios of singlet/total ionizations, so β = ρi1+ρi can be sub-stituted later. The analytic solution to equation A.15 is given below (thanks towolfram):N(t) =Ce−At +ANoτre−A(τr+t)Ei(A(τr+ t))− Noτrτr+ t (A.18)Where Ei(x) is the exponential integral1. The boundary condition N(t = ∞) = 0 issatisfied, and for N(t = 0) = 0 the condition below is required:C = No(1−Aτre−AτrEi(Aτr)) (A.19)This gives the dimer population as a function of time but as justified in Section 4.2.4its derivative does not give the correct photon intensity.1See appendix for info on exponential integral115Figure A.1: Equation A.18 with the correct constantC plotted for a 1MeV electronwith given parameters.116


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