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\author{Giacomo Petrillo\\
Supervisors: Eugenio Paoloni, Simone Stracka\\
University of Pisa}

\title{Thesis abstract: Online processing of the large area SiPM detector
signals for the DarkSide20k experiment}

\begin{document}
    
    \maketitle

    DarkSide20k is a planned dual-phase liquid argon (LAr) time projection
    chamber (TPC) designed to detect dark matter, the successor to DarkSide-50.
    It will be the largest detector of its kind, with 20~metric tons of argon
    in the fiducial volume. The predicted resulting upper bound on the
    spin-independent WIMP-nucleon scattering cross-section, in case of no
    discovery, is $\approx\SI{1e-47}{cm^2}$ at \SI{1}{TeV/c^2} WIMP mass, to be
    compared with the current best limit $\approx\SI{1e-45}{cm^2}$ by XENON1T.
    
    In this thesis we present reconstruction and characterization studies on
    the photodetector modules (PDMs) that will be used in the TPC. These
    studies are primarily meant as a support to the definition of the first
    stages of the online processing chain.
    
    Each PDM has a \SI{25}{cm^2} matrix of silicon photomultipliers (SiPMs),
    instead of the usual photomultiplier tube (PMT). The SiPM has Geiger-mode
    single photon response, i.e., each detected photon produces one fixed
    amplitude pulse. Compared to a PMT, the photodetection efficiency is
    expected to be higher, reaching \SI{50}\% at room temperature, with also a
    better filling factor, which should be greater than \SI{85}\% in
    DarkSide20k, compared to \SI{80}\% in DarkSide-50, and a much better single
    photon resolution. The pulse looks like a sharp peak followed by a rather
    long exponential tail, which is a disadvantage because pulses can pile-up
    leading to saturation.
    
    SiPMs have three kinds of noise: 1) stationary electric noise, which scales
    with the square root of the area; 2) a ``dark count rate'' (DCR) of pulses
    independent of incident light that scales with the area; 3) ``correlated
    noise'' produced by primary pulses, which contributes a factor proportional
    to the DCR and photon pulses.
    
    The first two stages in the readout chain will be the digitizers and the
    front end processors (FEP). The digitizers find candidate pulses, and for
    each one send a slice of waveform to the FEP, where the final
    identification of pulses is decided. The performance of these stages is
    mainly determined by the electric noise, characterized with the signal to
    noise ratio (SNR), which is the ratio of the amplitude of pulses over the
    noise standard deviation. It influences the fake rate, i.e., the rate of
    random oscillations high enough to be mistakenly identified as pulses, and
    the temporal resolution of pulse detection.
    
    By applying linear filters to digitized waveforms acquired from the PDMs
    illuminated by a pulsed laser, both in a testing setup at Laboratori
    Nazionali del Gran Sasso (LNGS) and in the small prototype TPC ``Proto0'',
    we study the noise parameters of single pulse detection: SNR, temporal
    resolution, fake rate.
    
    We consider 1)~an autoregressive filter, which uses the least possible
    computational resources, 2)~a matched filter without spectrum correction,
    which gives almost optimal performance, 3)~a moving average, which is a
    compromise between simplicity and performance. Simple filters are needed on
    the digitizers, which must process all the incoming data, while the FEP
    will probably use the optimal filter. We also study the baseline
    computation and the filter length.
    
    Then using a custom peak finder algorithm we measure the DCR and study the
    correlated noise, which consists in additional pulses produced recursively
    by each pulse, divided in two main categories: afterpulses (AP), which
    arrive with some delay from the parent pulse, and have smaller amplitude as
    the delay goes to zero, and direct cross talk (DiCT), which manifests as a
    integer multiplication of the amplitude of pulses because the children
    pulses are overlapped with the parent.
    
    The results follow.
    
    While with an ideal filtering procedure the post-filter SNR reaches~20, it
    may realistically be~13 with the resources of the digitizers, i.e., using a
    moving average \SI{1}{\micro s} long for both the pulse and the baseline.
    
    With the moving average as just described, the fake rate is \SI{10}{cps}
    when the threshold is set to 5~standard deviations of the filtered noise,
    where the filter includes the subtraction of the baseline. Since the
    filtering procedure is not actually decided yet, we describe and test a
    general procedure to measure low fake rates without actually counting the
    threshold crossings with only \SI{1}{ms} of recorded data. Of the 25~PDMs
    we looked at, all are within specifications but a single one which has an
    anomalous fake rate whose origin is still under investigation.

    The temporal resolution mostly matters on the FEP, so we summarize the
    results with the matched filter: 1)~upsampling is not necessary; 2)~at low
    SNR the resolution diverges and how fast heavily depends on the noise
    spectrum, with the Proto0 noise the maximum allowed by specs, \SI{10}{ns},
    is reached at pre-filter SNR~2.6; 3)~it is sufficient to have \SI{1}{\micro
    s} of waveform per pulse sent to the FEP; 4)~it is possible to lower the
    sampling frequency from \SI{125}{MSa/s} to \SI{62.5}{MSa/s}. In the thesis
    we show detailed curves for all the filter, filter length, SNR and sampling
    frequency choices.
    
    We give upper bounds for the DCR of a \SI{25}{cm^2} SiPMs Tile at three
    overvoltages, \SI{5.5}{V}, \SI{7.5}{V}, \SI{9.5}{V} (the overvoltage is the
    difference between the bias put on the SiPM and the breakdown voltage of
    the junction), which are respectively \SI{50}{cps}, \SI{170}{cps},
    and~\SI{120}{cps}, to be compared with the DarkSide20k requirement of
    \SI{250}{cps}. \SI{5.5}{V} is a somewhat usual operating overvoltage while
    \SI{9.5}{V} is considered high. Increasing the overvoltage increases both
    the SNR, the DCR and the correlated noise.
    
    The analysis of correlated noise, done on the same data, gives upper bounds
    for AP probabilities of \SI{2.5}\%, \SI{3.5}\% and \SI{6.5}\%, and DiCT
    probabilities \SI{20}\%, \SI{30}\% and~\SI{50}\%. These are the
    probabilities of said noises being generated by any given single pulse,
    i.e., the stacked pulses produced by DiCT count separately. The DarkSide20k
    specifications require the sum of correlated noise probabilities to be less
    than \SI{60}\% in order to avoid performance degradation, e.g., dynamic
    range reduction on ionization signals, where there is a lot of pile-up. For
    this analysis we employ the common procedures used to fit histograms with
    least squares, which we rederive in the Bayesian framework in an appendix.
    
    Measuring AP and DiCT requires models. We try the models we find in the
    literature and in the DarkSide20k simulation and bring them into question,
    but we do not search for better alternatives, since their level of accuracy
    should be enough for the simulation requirements. We find that the AP
    temporal distribution is well described by two exponential decays with
    constants \SI{200}{ns} and \SI{1}{\micro s}, but not by a single one.
    
    Finally, based on the peak finding algorithm we used in the correlated
    noise analysis, we suggest but do not test the following procedure to
    better resolve multiple pulses: do a first pass with a short filter, pick
    candidate peaks, do a second pass with a long filter, eventually pick
    additional candidates, compute the amplitude of pulses solving the linear
    system for the superposition of pulses using only the long filter peak
    amplitudes, curb peaks with low amplitude and compute it again. We sketch
    an argument to justify this procedure.

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