-
xe
ral R
Avalanche photodiode
GPD
rs (
d f
erfo
eld
g m
me
n a
era
time constants of 15 and 82ns. The cross-talk probability is a
factor of 3 smaller than the after-
puling probability. Simulating the MPPC response, we nd that
after-pulsing and cross-talk do not
t
desigARC acdetec
tromagdetecto
detection efciency, and being insensitive to magnetic eld.
While
characterized in depth. The aim of this paper is to
investigate
ableon as [4].
peaking time. Both electronics are expected to achieve the
ARTICLE IN PRESS
Contents lists availab
.e
te
Nuclear Instruments and Methods in Physics Research A 596 (2008)
396401do not affect the energy resolution and the timing
resolution,quantitatively two possible drawbacks: after-pulsing and
cross-talk, in order to determine to which extent they affect the
detectorperformance.
required timing resolution of 3 ns or better. The energy
resolutionrequirement is modest. The energy information will be
usedmostly to identify muons from protons. The requirement for
thePPD is that effects such as dark noise, cross-talk or
after-pulsing
which should both be driven by the statistics of the number
ofphoto-electrons.
Corresponding author. Tel.: +1604 2227572; fax: +1604
2221074.
E-mail address: [email protected] (F. Retie`re).0168-90
doi:10.1PPDs appear to be a perfect solution for experiments
such as T2KND280, being newly developed devices, they have not
been
In order to achieve the required timing resolution, the PPD
pulsesare stretched by a RC-CR2 preamplier shaper with a
120nsIndeed, they provide a much larger gain than standard
avalanchephotodiodes, while matching or surpassing the photo-tube
photo-
signal that is subsequently time stamped by a eld programmgate
array. The ne grain detector electronics is basedwaveform
digitization scheme sampling at 50MHz for 10mwavelength shifting
(WLS) ber threaded through a plasticscintillator bar and readout on
one or both ends by a photosensor.Most of the photosensors are
enclosed within a 0.2 T magnet,which rules out using simple
photo-tubes. The recently developedpixelated Geiger-mode avalanche
photon detectors (PPD) havebeen chosen in place of photo-tubes or
avalanche photodiodes.
50ns. In practice, the integration time will follow the
beamspill structure to be about 500ns depending on the
acceleratoroperation mode. Most ND280 elements will use such
electronicsbased on the TRIP-t ASIC that also provides a
discriminatoroutput per channel [3]. The discriminator triggers
when theintegrated charge exceeds a programmable threshold,
providing a1. Introduction
1.1. The T2K near detector experimen
The T2K near detector (ND280) isof the neutrinos produced by the
J-PThe building block of most ND280detector, ne grain detector,
elecdetector, and side muon range02/$ - see front matter Crown
Copyright & 20
016/j.nima.2008.08.130near detector.
Crown Copyright & 2008 Published by Elsevier B.V. All rights
reserved.
ned to detect a fractioncelerator complex [1,2].tor elements (on
axisnetic calorimeter, pi0r) is a Kuraray Y11
The most important detector performance that must beachieved is
a detection efciency of 100% for minimum ionizingparticles (MIPs).
Accounting for channel-to-channel variation andthe low-energy tail
of the energy loss, this translates to requiringthe average number
of photo-electrons produced by a MIP to be atleast 15. The light
coming out of the WLS ber is not emittedinstantaneously but is
fully collected in about 50ns, mostly due tothe WLS ber decay time
constant of 9 ns. The T2K ND280electronics hence has to integrate
the PPD current for at leastMPPC degrade the detector performance
signicantly within the expected operating conditions of the
T2KAfter-pulsing and cross-talk in multi-pi
Y. Du a, F. Retie`re b,
a Department of Physics and Astronomy, University of British
Columbia, 6224 Agricultub TRIUMF, Science, 4004 Wesbrook Mall,
Vancouver, BC, Canada V6T 2A3
a r t i c l e i n f o
Article history:
Received 17 January 2008
Received in revised form
18 July 2008
Accepted 12 August 2008Available online 28 August 2008
Keywords:
Photo-detector
Scintillator
a b s t r a c t
Multi-pixel photon counte
photonics. They will be use
T2K experiment. Their p
insensitivity to magnetic
cross-talk and after-pulsin
after-pulsing are precisely
At an over-voltage of 2V, a
pulsing, whereas it gen
journal homepage: www
Nuclear InstrumenPhysics R08 Published by Elsevier B.V. Alll
photon counters
oad, Vancouver, BC, Canada V6T 1Z1
MPPC) are pixelated Geiger-mode photon manufactured by
Hamamatsu
or reading out all the scintillator elements within the near
detector of the
rmances photo-detection efciency, dark noise and gain, and
their
fulll the ND280 requirements. On the other hand, two known
issues,
ay adversely impact the detector response. In this paper,
cross-talk and
asured by recording waveforms and identifying all the avalanche
pulses.
valanche generates on an average 0.5 additional avalanches due
to after-
tes 0.13 at 1V over-voltage. After-pulses follow two
independent
le at ScienceDirect
lsevier.com/locate/nima
s and Methods insearch Arights reserved.
-
and VBD. The total charge per avalanche is governed by the
diode
ARTICLE IN PRESS
thodcapacitance (C): Q CDV. The output current of the PPD is
thesum of all the diode currents. The number of photons hitting
thedevice is measured by counting the number of pixel
avalanches.The photon detection efciency is the probability that a
photontriggers an avalanche when hitting a PPD. The response is
linear if(i) the number of pixel avalanches detected is small
(o15%)compared to the total number of pixels, and (ii) the light
isuniformly distributed across the surface.
An avalanche in 1 pixel at a given time can trigger
additionalavalanches either in neighboring pixels or in the same
pixel at alater time. The former phenomenon is called cross-talk
whereasthe latter is called after-pulsing. Cross-talk is believed
to becaused by photons produced in an avalanche, which knock
offelectrons in a neighbor pixel and trigger an additional
avalanche[9]. It has been recently shown that the trajectories of
the cross-talk inducing photons may not be straight lines but
instead gothrough reections within the substrate [10]. Either way,
thephoton propagation time is very short, hence the original
andneighbor avalanches occur essentially at the same time.
On the other hand, an after-pulsing avalanche occurs after
theoriginal avalanche. It is believed to be triggered by the
release of acharge carrier that has been produced in the original
avalancheand trapped on an impurity [11,12]. It is also possible
that thephotons produced in the original avalanche generate
after-pulsesif instead of knocking of an electron in the depletion
region of aneighbor pixel, they do so within the silicon substrate.
One of thecharge carriers hence produced may eventually nd its way
backto the pixel and trigger a second avalanche. This
phenomenonwasobserved in Ref. [13] but the carriers were found to
diffuse backinto the depletion region in o1ns, which would be
invisible toPPDs. However, the PPD doping prole may allow for much
longercarrier diffusion time within the substrate.
1.3. Multi-pixel photon counters (MPPCs)
MPPCs are PPDs designed and manufactured by Hamamatsuphotonics
[14,15]. They have been extensively tested in thecontext of the
ND280 detector within the T2K experiment[4,5,16], together with
similar devices [17]. A total number ofabout 50,000 MPPCs will be
used in the T2K experiment. Theirperformances fulll the detector
requirements. A large gain(4500,000), and large (415%)
photo-detection efciency can beachieved while maintaining the dark
noise rate below 1MHz.
The MPPCs that were tested in this paper have 400
pixels(5050mm2) covering a total area of 1 by 1mm2. A 100kOresistor
is used for quenching the avalanche. The total capacitanceof the
device is 35pF, which translates into 87.5 fF per pixel1.2.
Pixelated Geiger-mode avalanche photon detectors
PPD, also called silicon photo-mutipliers (SiPM) are becoming
amature technology, both for particle physics and medical
imaging[57]. A PPD is an array of 100 to several 1000 s
photodiodesarranged into square pixels operating in Geiger-mode
with acurrent limiting resistor. Free charge carriers drifting
through thedepleted region are able to free additional carriers
when thereverse bias voltage across the junction goes above a
criticalbreakdown voltage (VBD). An avalanche develops as described
inRef. [8] until the current owing through the resistor (R) in
serieswith the diode brings the voltage across the junction to VBD.
Themaximum current owing through the diode is Imax DV/R, DVbeing
the over-voltage, i.e. the difference between the reverse bias
Y. Du, F. Retie`re / Nuclear Instruments and Meignoring
parasitic capacitances. With a 1V over-voltage, the gain,i.e. the
number of electrons produced by 1 photo-electron in 1pixel is about
550,000.2. Measuring cross-talk and after-pulsing
2.1. Test setup
The MPPC was housed in a light tight tube. The data weretaken at
a temperature of 25 1C. A Keithley 6485 picoammeter wasused to bias
the MPPC between 69.4 and 70.6V through a 100kOresistor. The MPPC
pulse was readout by decoupling the bias linewith a 1nF capacitor.
A custom amplier was used to achieve again of 10 before feeding the
signal into a CAEN V1729 waveformdigitizer sampling for 2.5ms at
1GHz. The trigger was generatedby further amplifying the signal
using a CAEN N978 amplier anda discriminator, with the threshold
set to 0.10.2 avalancheequivalent signal, depending on the MPPC
bias voltage.
2.2. Waveform analysis: pulse nding
Two events with multiple pulses are shown in Fig. 1 toillustrate
the pulse nders ability. Most events have only onepulse at 270ns,
which is where the trigger happens to be. A pulsender analysis was
performed on the waveforms in order tomeasure the time and
amplitude of the avalanches occurringwithin the acquisition window.
The pulses were found in twosteps. First, all the pulses with a
signal-to-noise ratio over 5 wereidentied unless they were too
close to an earlier pulse, becausethe rst pass algorithm required
the signal to return to thebaseline before accepting a subsequent
pulse. The waveformswere then tted by a superposition of single
avalanche responsefunctions (SARF). The SARFs were extracted
directly from the databy calculating the average waveforms for
events that have only 1avalanche within a 150ns wide integration
window around thetrigger pulse. An analytical function tting the
SARFs perfectlycould not be found and standard spline interpolation
techniqueswould smooth out the SARF too much. A linear
interpolation ofthe SARFs was used instead, which yield to about
1ns resolutionin the reconstruction of the pulse arrival time.
The correlation between the pulse amplitude and trigger
timeintroduced by the leading edge discriminator was corrected
forbefore calculating the average waveform. A w2 was computed
toassess the quality of the t. The number of degrees of
freedom(dof), i.e. the t range, was set to 50 unless two or more
pulsespartially overlapped, in which case the t range was extended
toencompass all the pulses. If the w2 per dof (w2/dof) was found to
bemore than 5, an additional pulse was added and the t was
re-run.Pulses were added until the w2/dof fell below 2 or until
5additional pulses were added. This method was reliable to ndpulses
close to each other, even when they almost fully overlapbecause the
shape of the waveform provides a strong constraint.
2.3. Extracting cross-talk
The time and amplitude of the pulses found in a 500nswindow
following the trigger are shown in Fig. 2. The timeis dened with
respect to the trigger pulse time. The amplitude isthe scale
applied to the SARFs to reproduce the data, so it isautomatically
proportional to the signal given by the avalanche atnominal gain.
The trigger pulses can be seen at time zero as 3narrow bands at 1,
2, and 3 avalanches. Cross-talk can be extracteddirectly from the
frequency distribution of trigger pulse amplitudeobtained by the
projection of these bands onto the y-axis. Cross-talk is calculated
as the probability that 1 pixel triggers at least 1avalanche in a
neighbor pixel: 1N1/Ntotal with N1 being the
s in Physics Research A 596 (2008) 396401 397number of 1
avalanche pulses and Ntotal the total number oftrigger pulses. The
trigger sample is selected by using a 1ns timewindow, which ensures
that the contribution of after-pulsing is
-
ARTICLE IN PRESS
thod25
Y. Du, F. Retie`re / Nuclear Instruments and Me398negligible.
Indeed, within 1ns immediately following an ava-lanche, the pixel
over-voltage is close to zero. Hence, if a chargecarrier happens to
enter or be released within the depleted region1ns or less after
the rst avalanche, it will not generate anavalanche.
Time after trigger (ns)0
Pix
el a
vala
nche
0
1
2
3
100 200 300 400
Fig. 2. Amplitude and time distribution of all the pulses found
by the pulse nderat 70V bias and 25 1C (1.3V over-voltage).
ns0
AD
C
0
5
10
15
20
AD
C
0
5
10
15
20
25
500 1000 1500 2000
ns0 500 1000 1500 2000
Fig. 1. Two events taken at 70V bias and 25 1C (1.3V
overvoltage). The right-hand paneblack curve is the t.25
s in Physics Research A 596 (2008) 3964012.4. Pixel recovery
The over-voltage recovery is clearly visible in Fig. 2 as a
bandbelow 1 avalanche between 0 and 40ns after the trigger. Fig.
3presents a clearer view of recovery in a 100ns window
following
Time after trigger (ns)0
Pix
el a
vala
nche
0
1
2
3
20 40 60 80 100
Fig. 3. Amplitude and time distribution of the rst pulse
following the triggerpulse at 70V and 25 1C (1.3V over-voltage).
The solid red curve shows the expectedsingle pixel recovery.
ns250
AD
C
0
5
10
15
20
AD
C
0
5
10
15
20
25
300 350 400 450 500
ns250 300 350 400 450 500
ls are zooms around the trigger pulse. The lled grey histogram
is the data and the
-
the trigger. The recovery behavior is well reproduced by
theexpected function 1et/t, with t 100kO8.75 fF 8.75ns.
2.5. Measuring after-pulsing
Each avalanche may result in trapped charge carriers. However,as
discussed earlier, it is possible that some of the after-pulseshave
nothing to do with trapped carriers but originate insteadfrom
charge carriers created by photons in the substrate, in thesame
fashion as cross-talk. In order to avoid making
unnecessaryassumptions, we will quantify after-pulsing as the
averagenumber of delayed carriers triggering an additional
avalancheper original avalanche. This nomenclature has the
advantage ofaccounting for the fact that a carrier released while
the voltage isnot fully recovered will have a smaller probability
of triggering anavalanche than at the nominal operating
voltage.
We build the timing distribution of the rst pulse following
thetrigger pulse, because the probability distribution of the rst
pulsearrival time is fairly simple to express mathematically, which
isnot the case when multiple after-pulses created by
avalanchesfollowing the trigger pulse have to be considered. We
selecttrigger pulses with only one simultaneous avalanche,
hencediscarding the ones with cross-talk. We also ensure that
noavalanche happened within the 270ns before the trigger pulse
in
0 0
ARTICLE IN PRESS
Y. Du, F. Retie`re / Nuclear Instruments and Methodorder to
avoid selecting avalanches that may themselves be after-pulses. The
amplitude and time distribution of the rst pulsefollowing the
trigger pulse is shown in Fig. 3. This gure is verysimilar to the
one shown in Ref. [18]. Three bands for 1, 2, and 3pixel avalanches
are clearly visible when the pulses occur laterthan 40ns after the
trigger. Cross-talk is responsible for the2 and 3 pixel avalanche
bands. The bands split into two for thepulses within 40ns after the
trigger: one constant and the otherfollowing the pixel recovery
time constant as discussed earlier.The constant band is unaffected
by the pixel recovery, hence mustoriginate from a different pixel
than the trigger pulse. It ispresumably due to thermally generated
dark pulses. On the otherhand, after-pulses occurring earlier than
40ns after the trigger
Time after trigger (ns)10 102 103
Pro
babi
lity
of th
e ne
xt a
vala
nche
(ns-
1 )
10-4
10-3
10-2
69.4 V
70.0 V
70.6 V
Fig. 4. Timing distribution of the rst pulse following the
trigger. The dotted lines
are ts with a single after-pulsing time constant, while the
solid lines included two
time constants. The dashed lines show the two exponential
function behaviors
beyond the t range.The dotted curve in Fig. 4 shows a t using
this function. Thequality of the t is poor, so a second after-pulse
time constant hasto be introduced to obtain a good t. The t is
limited to time laterthan 10ns because the pulse nder is not very
accurate for ndingpulses with signicantly reduced gains, which
typically occurwithin 10ns after the trigger. While the pulse nding
efciencyremains fair (except for low bias voltage), the t
parameters (timeand amplitude) become less accurate, especially the
pulse time,which tends to be shifted later due to an artifact in
the pulsender algorithm.
3. Parameterization of cross-talk and after-pulsing as a
functionof over-voltage
The parameters extracted from the t using the 2 timeconstant
after-pulsing models are summarized in Fig. 5, asfunctions of
over-voltage. The VBD was found to be 68.7V byextrapolating the
gain down to zero. The after-pulsing parametershown in this gure is
1el, the probability that an avalanche isfollowed by at least one
after-pulsing avalanche. The errors areboth statistical and
systematic. The statistical errors dominate atlow over-voltage
whereas systematic ones dominate at above 1V.The main source of
systematic error comes from the lack ofefciency for nding the
pulses in the 010ns time interval.Indeed the probability
distribution used in the t assumes thatthe rst pulse is always
found. However, if it occurs too early to bedetected, the second
pulse will be substituted as the rst pulseand distort the
experimental time distribution. We performedsimulations to estimate
this effect. Assuming that all the pulsesoccurring 10ns or less
after the trigger pulse are missed, we foundthat the dark noise
rate, the number of after-pulses per avalanche,and the long
after-pulse time constant were overestimated by asmuch as 40%, 15%,
and 15%, respectively, when those parametersare large, i.e.
corresponding to an over-voltage of 1.9V. On theother hand, the
short time constant appears to be underestimatedby as much as 15%.
This effect was found to be small for thehave reduced gains because
the over-voltage is not recovered toits original level.
Fig. 4 shows the time distribution of the rst pulse followingthe
trigger for three different bias voltages. The rst pulsefollowing
the trigger pulse comes either from after-pulsing orfrom dark
noise. The probability of the rst pulse occurring in thetime
interval t and t+dt, is an after-pulse is
PAPt X1i1
li
i!el
i
t eti=t
with l being the average number of delayed carriers triggering
anavalanche per original avalanche, t, the carrier release or
diffusiontime constant. The probability for a thermally generated
darkpulse is
PDNt ReRt
with R being the dark noise rate. The sum over the
Poissonprobability accounts for the possibility of having more than
onedelayed carrier created per avalanche, which was not taken
intoaccount in Ref. [4]. When combining after-pulses and
thermallygenerated dark pulses, the probability must be mutually
exclusive,i.e. a dark (after) pulse occurring at t with no after
(dark) pulseoccurring between 0 and t, which leads to the
probability
Pt Z t
1 PAPxdxPDNt Z t
1 PDNx dxPAPt.
s in Physics Research A 596 (2008) 396401 399parameters
corresponding to over-voltages o1.3V. The error onthe over-voltage
is primarily due to day-to-day temperaturevariation.
-
ARTICLE IN PRESS
thodOver-voltage (V)0.5
Dar
k no
ise
rate
(kH
z)
0
100
200
300
400
afte
r-pu
lsin
g tim
e co
nsta
nt (n
s)
5
10
15
20
1 1.5 2
Y. Du, F. Retie`re / Nuclear Instruments and Me400The data shown
in Fig. 5 were tted to extract trends as afunction of over-voltage.
The dark noise rate rises linearly withover-voltage at a rate of
21279kHz/V. The dark noise remainsbelow 500kHz even at 2V
over-voltage. The after-pulsing andcross-talk probabilities vary
quadratically with over-voltage in thefollowing fashion:
Prob(APshort) 0.07370.003V2, Prob(APlong) 0.05470.003V2, and
Prob(cross-talk) 0.04470.002V2.Cross-talk is smaller than the sum
of both short and long after-pulsing probabilities by roughly a
factor of 3. At 1.9V over-voltage(70.6V at 25 1C), the average
number of late carriers per avalancheis 0.5. At that level
after-pulsing may become problematic. It isindeed not uncommon to
see trains of avalanches produced by asingle dark noise pulse. The
average after-pulsing time constantsare 15.070.6 and 83.573.9 ns.
There appears to be a slightdecrease of the time constants with
over-voltage, which runscontrary to the expectation that the trap
release time constant isindependent of the bias voltage. As
mentioned earlier, therobustness of the method has been veried by
simulations andthe necessary systematic errors have been included
in thereported results. Nevertheless, the systematic errors on the
longtime constant are likely underestimated. Indeed calculating
thelong time constant with only the three lowest over-voltage
pointsyields 92.775.8 ns. The time constants measured for the
MPPCsare consistent with the ones reported for single photon
avalanchediode in Ref. [10], which suggests that after-pulsing can
beinterpreted solely as being due to trapping. In Ref. [10], a
thirdtime constant of about 1ms has been found as well. However,
ourmeasurement method is not sensitive to it because
thermallygenerated dark pulses dominate the timing distribution
beyond500ns after the trigger.
Sho
rt
0
Over-voltage (V)0.5 1 1.5 2
Fig. 5. Parameters extracted from the ts to the
distributionOver-voltage (V)0.5
Pro
babi
lity
per p
ixel
ava
lanc
he
0
0.05
0.1
0.15
0.2
0.25 1 after-pulse, short 1 after-pulse, long 1 cross-talk
fter-
puls
ing
time
cons
tant
(ns)
40
60
80
100
1 1.5 2
s in Physics Research A 596 (2008) 3964014. Impact of
after-pulsing and cross-talk on the T2K ND280detector
performance
In order to estimate the impact of cross-talk and
after-pulsing,we have developed a Monte Carlo simulation code that
allowsturning each effect on and off. The simulations include
analgorithm that tracks the operating voltage of every
pixeldropping down the voltage to VBD as avalanches occur
andrecovering according to the 8.75ns time constant. This
algorithmis important because it introduces avalanches with reduced
gains,which are clearly visible in the dark noise spectrum or for
lowlight level (o20 avalanches). The simulations use a model for
thephoto-detection efciency, consistent with preliminary
datashowing a linear increase up to 1.5V over-voltage followed byan
onset of saturation. Light is injected onto the MPPC followingan
exponential with a 9ns decay constant emulating the emissionof the
WLS ber. The time zero of the light pulse is chosenrandomly within
540ns, which corresponds to the beam bunchwidth. Signal amplitude
and time are calculated by mocking upthe electronics response. The
signal amplitude is given by theintegral of the avalanche charge
within the 540ns gate. Timing isobtained by generating a
discriminator output when the inte-grated charge goes above a
programmable threshold. The T2K negrain detector uses different set
of electronics, based on waveformdigitization at 50MHz. However,
the conclusions drawn below forthe gate and discriminator
electronics remain qualitatively thesame.
The number of pixels red is chosen to be about 20 at 1V
over-voltage, according to beam test measurements for a
minimumionizing particle [4]. Cross-talk and after-pulsing increase
the
Long
a
0
20
Over-voltage (V)0.5 1 1.5 2
of the arrival time of the rst hit following the trigger.
-
average number of pixels avalanching from 20 to 23.2 and 29.3
to49.3 at 1 and 2V over-voltage, respectively. However,
suchincrease does not help the photo-detection efciency becausethe
number of avalanches generated by dark noise also increasesin the
same fashion. At 1V over-voltage, the energy resolutiondegrades
from 21.3% without cross-talk and after-pulsing to 22.1%when they
are turned on. At 2V over-voltage, the energyresolution goes from
17.8% to 21.2%. Cross-talk and after-pulsinghence have a marginal
impact on the energy resolution up to 2Vover-voltage. However, the
energy resolution does not improveand eventually worsens beyond
1.5V over-voltage as the photo-detection efciency saturates, while
cross-talk and after-pulsingkeep on increasing rapidly.
Nevertheless, in the T2K detectors, theMPPCs will be operated
between 0.5 and 1.5V over-voltage, whichmeans that cross-talk and
after-pulsing will not affect the energyresolution signicantly.
The simulations also show that cross-talk and after-pulsing
5. Conclusions
operating voltage that is expected to be used by the
ND280detectors.
In the future, it would be benecial to redesign the MPPCs
byincreasing the quenching resistor from 100 to 500kO or
moreeffectively by changing the quenching circuit from a passive
oneto an active circuit. If avalanches were followed by a 50ns
voltagedrop to the VBD, then after-pulsing would be reduced by
morethan a factor of 2.
The authors wish to thank the ND280 photosensor group
forfruitful discussions, Thomas Lindner and Antonin Vacheret
forproviding many useful suggestions regarding the experiment
andthe manuscript, Thomas Lindner and Scott Oser for providing
thesimulation code, Roman Tacik for pioneering the use of
singleavalanche response functions, the TRIUMF DAQ group for
settingup the waveform digitizer and Leonid Kurchaninov for
providingthe low noise amplier and the TRIUMF pienu experiment
forsupporting Yubo Dus work.
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ARTICLE IN PRESS
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temperature with goodaccuracy. At 2V over-voltage, the average
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over-voltage.While such large after-pulsing and to a lesser extent
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After-pulsing and cross-talk in multi-pixel photon
countersIntroductionThe T2K near detector experimentPixelated
Geiger-mode avalanche photon detectorsMulti-pixel photon counters
(MPPCs)
Measuring cross-talk and after-pulsingTest setupWaveform
analysis: pulse findingExtracting cross-talkPixel recoveryMeasuring
after-pulsing
Parameterization of cross-talk and after-pulsing as a function
of over-voltageImpact of after-pulsing and cross-talk on the T2K
ND280 detector performanceConclusionsReferences