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Measuring and Modelling the Light Response ofPixelized Photon Detectors with Significant
Photon-Induced Correlated Noise
Graham W. Wilson
University of Kansas
September 29, 2011
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Introduction
Introduction
Solid-state photon detectors such as those in use by CALICE and T2K are
considered attractive candidates for light detection in a future linearcollider detector when compared with the traditional PMT.
Some advantages
B-field tolerance
Cheap
Apparent photon resolving capability
Low voltage/size/integrability
Some disadvantages
Dark noise rate per mm2 (can be 500 kHz cf 0.5 Hz).
Correlated noise: cross-talk and after-pulsing
Dynamic range
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Introduction
Photo-detector response modelling
Question
Does LED calibration data (points) follow Poisson model (red)?
ch1_ledEntries 108589Mean 523.4RMS 226.5
Integrated Charge (ADC counts)200 400 600 800 1000
Countsperbin
0
1000
2000
3000
ch1_ledEntries 108589Mean 523.4RMS 226.5
ch1_ledEntries 108589Mean 523.4RMS 226.5
ch1_led: MPPC Channel 1
Individual photons often lead to not just 1 fired pixel, but 2, 3, 4 etc. due
to cross-talk and after-pulsing. Technology and device dependent.Graham W. Wilson (University of Kansas) LCWS11 Granada: Calorimetry/Muons September 29, 2011 3 / 36
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Motivation
Noise and Time Structure: Important or Not ?
ILC/CLIC
At ILC with a large inter-bunch spacing (337 ns), a relevant issue is noisewithin a time interval consistent with the BX under consideration. ForCLIC, much tighter specs.Various types of potential detectors: AHCAL, Scint. ECAL,
Muon-detector, scint. fiber tracking have different requirements.
Why this study?
These studies use the 100-pixel Hamamatsu MPPC aimed at highefficiency low light-level detection. I work on the D0 fiber tracker and its
light calibration and have explored instrumenting parts of a LC detectorwith similar instrumentation for time-stamping/TOF. At D0 using VLPCswe have an average threshold per fiber of 1.0 photo-electronscorresponding to 1% dark probability and Poisson distributed LED
distributions....Graham W. Wilson (University of Kansas) LCWS11 Granada: Calorimetry/Muons September 29, 2011 4 / 36
M i i
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Motivation
Literature and this work
Literature
There is a substantial literature from many groups about characterizationmeasurements related to pixelized solid-state photo-multiplier response(see references).
Short-comings
In practice many adopted methods are either approximate, or requirededicated measurements unlikely to be available en masse in situ for LCdetector channel counts, or potentially lose substantial predictive power /precision by using more parameters than warranted by the underlying
effects.
This work
Hopefully helps to put some of the issues better in focus and provides acoherent yet relatively simple integrated experimental method to test the
response modelling and the measurement of associated parameters.Graham W. Wilson (University of Kansas) LCWS11 Granada: Calorimetry/Muons September 29, 2011 5 / 36
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Method
Experimental Goal and Design
GoalMeasure the photo-detector response under essentially identical conditionsusing identical time intervals for both non-illuminated (dark) data andilluminated (LED) data. Currently using MPPC-S10362-11-100C sensorwith 100 pixels.
Design
Use 100-1000 Hz clock to fire LED on every other cycle.Measure total charge integrated within a 240-300 ns time window using
dual-range QDC (FSR 800 pC).Use single-hit TDC in common start mode to check timing characteristics.Bias will be varied from run-to-run, but use 70.65 V corresponding to 0.72V over-voltage as default setting.
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Method
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Method
Experimental Setup
LED Box
Jacketedclear fiber
1mm
Power Supplyand Amplifier
with MPPC-
S10362-11-
100C sensor
Ch1 : Pulses at 2n t (LED trigger)
Ch2 : Pulses at (2n+1) t (Dark count measurement)
HP pulse
generator
(V2)
Lecroy
622
OR
PS744
Linear
FI/FO
V965
QDC
V775
TDC
TDC Start
QDCgate
Ortec
935
CFD
CAEN V993Dual Timer
V1
supply
LabView
interface VM-USB
VM-USB
Linux
DAQ
computer
CAEN
SP5600
Bias andamplification
control
LED intensity control
LED
trigger
pulse
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Method
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Method
LED Circuit
Use Kapustinsky [1] type driver circuit to obtain fast time response.
Currently using off-the-shelf green LED ( = 565nm).
LED
Agilent E3630A
variable supply
voltage
HP 8131A pulse
generator for
trigger pulse
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Method
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Method
Typical LED Event 1: prompt 1 pixel event ( 40 ns)
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Method
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Method
LED Charge Distribution (gate width = 300 ns)
Measure charge response to LED (black) and dark counts (red). Photon
intensity = 0.22 detected photons/pulse.
ch1_pedEntries 100000Mean 349.4RMS 61.76
IntegratedCharge (ADC counts)300 400 500 600 700 800
Coun
tsperbin
0
500
1000
1500
2000
2500
ch1_pedEntries 100000Mean 349.4RMS 61.76
ch1_ped: MPPC Channel 1 ch1_ledEntries 100000Mean 380.2RMS 94.56
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Method
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LED Charge Distribution - Log
Measure charge response to LED (black) and dark counts (red). Photon
intensity = 0.22 detected photons/pulse.
ch1_pedEntries 100000Mean 349.4RMS 61.76
IntegratedCharge (ADC counts)300 400 500 600 700 800
Coun
tsperbin
1
10
210
310
ch1_pedEntries 100000Mean 349.4RMS 61.76
ch1_ped: MPPC Channel 1 ch1_ledEntries 100000Mean 380.2RMS 94.56
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Method
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LED Time Distribution
Measure time response to LED (black) and dark counts (red). Photon
intensity = 0.22 detected photons/pulse.
ch1_ledEntries 63201Mean 229.8RMS 58.02
Measured TimeAfter Start (TDC counts)150 200 250 300 350 400
Eve
nts
perbin
0
500
1000
1500
2000
ch1_ledEntries 63201Mean 229.8RMS 58.02
ch1_led: MPPC Channel 1 ch1_pedEntries 56495Mean 1905RMS 1158
Find FWHM for this green LED of 5ns. (1 TDC count = 0.3 ns)
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Method
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Typical LED Event 2: prompt 2 pixel event
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Method
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Typical LED Event 3: prompt 3 pixel event + delayed pulse
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Method
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Typical LED Event 4: multiple pixels + likely afterpulses
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Method
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Charge Distribution Studies
Standard conditions mostly:
Room temperature (Kansas summer day ....)
Integration time: 270 nsLED supply voltage: 18.25 V. Leading to 4.5 detected photons at 1 Vover-voltage and nominal intrinsic gain of 2.4e6.
Amplifier gain: 38 dB
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Method
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Fitting Method
Assume that the measured LED distribution, T(Q), arises from the
convolution of N(qdark) and L(qlight), where Q = qdark + qlight.
ch1_pedEntries 100000Mean 109.9RMS 23.3
IntegratedCharge (ADC counts)
0 200 400 600
Countsperbin
0
5000
10000
15000
ch1_pedEntries 100000Mean 109.9RMS 23.3
ch1_ped: MPPC Channel 1 ch1_ledEntries 100000Mean 257.1RMS 102.9
Use measured non-illuminated data (red) for N(qdark) and adjust theparameters of the L(qlight) model to give the best fit to the LED data(black) for the additional charge arising from LED photons.
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Method
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Light Model: Essentially 2 parameters.
Pixel distribution
Use the simple probability distribution model discussed in Vinogradov etal [2] based on a Poisson distributed random variable for the number ofphotons, , which result in a detected primary avalanche. Each primaryavalanche may then create a secondary avalanche with a duplicationprobability, pD, and likewise a secondary avalanche may create a tertiaryavalanche with the same probability etc, etc ... pD includes both cross-talkand after-pulsing assuming for simplicity equal charge response to bothsources.
Charge Measurement Model Parameters
1 pixel gain, g (ADC counts per pixel)
1 pixel intrinsic fractional gain resolution, 1 = g/g
N-pixel non-linearity, , where qlight = Ng(1 + N)/(1 + )
N-pixel variance non-linearity, , where
2
N = N(1 + N)
2
g)/(1 + )Graham W. Wilson (University of Kansas) LCWS11 Granada: Calorimetry/Muons September 29, 2011 18 / 36
Method
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Light Model Continued
Examplep(nA = 0) = exp{}
p(nA = 1) = exp{}(1 pD)
p(nA = 2) = exp{}{pD(1 pD) +12
2(1 pD)2}
p(nA = 3) =exp{}{p
2D(1 pD) +
2pD(1 pD)2 + 16
3(1 pD)3}
etc ..
Needless to say - currently neglect finite pixel number
Characteristics
Mean pixel count: /(1 pD)
Variance of pixel count: (/(1 pD))(1 + pD)/(1 pD)
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Results
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Example Fit (Run6 70.35V 38dB L)
ch1_led
Entries 100000Mean 257.1RMS 103
Integrated Charge (ADC counts)0 200 400 600
Countsperbin
0
1000
2000
3000
ch1_led
Entries 100000Mean 257.1RMS 103
ch1_led
Entries 100000Mean 257.1RMS 103
ch1_led: MPPC Channel 1
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Results
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Example Fit (Run6 70.35V 38dB L)
ch1_led
Entries 100000Mean 257.1RMS 103
Integrated Charge (ADC counts)0 200 400 600
Countsperbin
1
10
210
310
ch1_led
Entries 100000Mean 257.1RMS 103
ch1_led
Entries 100000Mean 257.1RMS 103
ch1_led: MPPC Channel 1
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Results
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Example Fit (Run6 70.35V 38dB L)
ch1_ledEntries100000Mean 257.1RMS 103
Integrated Charge (ADC counts)0 200 400 600
Countsperbin
0
1000
2000
3000
ch1_ledEntries100000Mean 257.1RMS 103
ch1_ledEntries100000Mean 257.1RMS 103
ch1_led: MPPC Channel 1
2.150(7)pD(%) 5.00(25)
g 66.35(6)1 0.113(1) -0.0022(4) 0.007(10)2/dof 936 / 794
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Results
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Example Fit (Run1 70.65V 38dB L)
ch1_led
Entries 108589Mean 523.7RMS 226.9
IntegratedCharge (ADC counts)200 400 600 800 1000 1200
Countsperbin
0
1000
2000
3000
ch1_led
Entries 108589Mean 523.7RMS 226.9
ch1_led
Entries 108589Mean 523.7RMS 226.9
ch1_led: MPPC Channel 1
Fit: = 3.36 0.01, pD = 14.0 0.2%,
2
/dof=1921/1594.Graham W. Wilson (University of Kansas) LCWS11 Granada: Calorimetry/Muons September 29, 2011 23 / 36
Results
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Example Fit (Run10 70.65V 30dB L)
ch1_ledEntries 100000Mean 269.4RMS 93.42
Integrated Charge (ADC counts)100 200 300 400 500 600
Countsperbin
0
500
1000
1500
2000
2500
ch1_ledEntries 100000Mean 269.4RMS 93.42
ch1_led: MPPC Channel 1h_fittedEntries 1600
Mean 275.3RMS 90.95
ch1_ledEntries 100000Mean 269.4RMS 93.42
Fit: = 3.36 0.01, pD = 13.0 0.3%, 2/dof=774/794.
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Results
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Example Fit (Run8 70.20V 38dB L)
ch1_led
Entries 100000Mean 158.6RMS 47.55
IntegratedCharge (ADC counts)100 200 300
Countsperbin
0
500
1000
1500
2000
ch1_led
Entries 100000Mean 158.6RMS 47.55
ch1_led
Entries 100000Mean 158.6RMS 47.55
ch1_led: MPPC Channel 1
Fit: = 1.268 0.006, pD = 0, 2/dof=510/394.
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Results
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Example Fit (Run11 70.65V 38dB 0.3L)
ch1_ledEntries 100000Mean 222.7RMS 133.7
Integrated Charge (ADC counts)200 400 600
Countsperbin
0
1000
2000
3000
4000
ch1_ledEntries 100000Mean 222.7RMS 133.7
ch1_ledEntries 100000Mean 222.7RMS 133.7
ch1_led: MPPC Channel 1
Fit: = 0.961 0.004, pD = 15.0 0.3%, 2/dof=1424/1194.
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Results
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Example Fit (Run12 70.65V 38dB 1.6L)
ch1_ledEntries 100000Mean 746RMS 293.9
Integrated Charge (ADC counts)500 1000 1500
Countsperbin
0
500
1000
1500
ch1_ledEntries 100000Mean 746RMS 293.9
ch1_ledEntries 100000Mean 746RMS 293.9
ch1_led: MPPC Channel 1
Fit: = 5.22 0.02, pD = 13.4 0.2%, 2/dof=2327/1994.
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Results
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Bias Scan
Bias Voltage (V)70 70.2 70.4 70.6 70.8 71
G
ain(ADCc
ountsperfiredpixel)
0
50
100
150
2002.5 (ADC counts/V)Slope = 153.6
0.01 (V)= 69.93BDV
2/ndf = 8.6 / 4
Bias Scan
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Results
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Measured Photon Number
Measure the Poisson parameter of the detected primary LED photons, .
(gives relative photon detection efficiency vs V).
Over-Voltage (V)0.2 0.4 0.6 0.8 1
LED
phot
onnumber
0
1
2
3
4
0.11 (photons/V)Linear term = 5.41
0.13 (photons/V^2)NL term = -0.97
2/ndf = 10.3 / 4
Bias Scan
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Results
D li P b bili
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Duplicate Probability
Over-Voltage (V)0.2 0.4 0.6 0.8 1
Pulseduplication
probability(%
)
0
10
20
30 0.80 (V^-2)Quadratic term = 27.54
2/ndf = 4.5 / 5
Bias Scan
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Results
Ph R l i Q li
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Photon Resolving Quality
Over-Voltage (V)
0 0.2 0.4 0.6 0.8 1 1.2 1.4
GainDispe
rsionParamet
er
0
0.05
0.1
0.15
0.2
0.25
Pixel Number Resolution
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Results
D k C t P b bilit
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Dark Count Probability
Can measure charge exceeding arbitrary threshold in charge integration
window (has not been the focus of this work so far) using measurednon-illuminated ADC spectrum.
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Results
F t R fi t
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Future Refinements
Adjust LED intensity at each bias voltage to keep number of detectedphotons approximately constant. Should be a better method formeasuring the photon-induced noise dependence on over-voltage.
Incorporate after-pulsing time structure together with pulse shapetime constant and resolve cross-talk and after-pulsing importance.
Improve/better characterize charge measurement systematics -amplifier/ADC linearity.
Improvements in the fitting, statistical method and convolution.
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Conclusions
C l si s
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Conclusions
Summary
Find that measured pixel number distributions can be well modelledusing a simple light-detection model including duplicate avalanches.Important for understanding particle detection efficiency close tothreshold.
Experimental technique allows simultaneous determination of gain,duplicate probability, relative PDE, dark rate and pixel resolvingcapability for this particular sensor.
Conclusions
New PPDs have significant noise which is sometimes correlated andneeds to be taken into account when evaluating detector/sensoroptions, predicting performance and measuring performance.
Correlated noise makes the standard procedure of setting a thresholdat 1.5 photo-electrons not as useful as might be expected.
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References
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J.S. Kapustinsky et al.A Fast Timing Light Pulser for Scintillation Detectors
NIM A, 241 (1985) 612.S. Vinogradov et al.Probability Distribution and Noise Factor of Solid StatePhotomultiplier Signals with Cross-Talk and Afterpulsing2009 IEEE Nuclear Science Symposium, N25-111.
Y. Du and F. Retiere,After-pulsing and cross-talk in multi-pixel photon countersNIM A, 596 (2008) 396.
A. Vacheret et al.,Characterization and simulation of the response of MPPCs to lowlight levelsNIM A, 656 (2011) 69.
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References
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H. Oide et al.,Studies on multiplication effect of noises on PPD, and a proposal of anew structure to improve performanceNIM A, 613 (2010) 23.
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Backup Slides
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Backup Slides
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