new Applying a SiPM response function to 7608 SiPMs of

Applying a SiPM response function to 7608 SiPMs of AHCAL physics prototype

CALICE meeting at Arlington TexasK. Kotera, DESY/Shinshu University

1

CLIC Workshop 2013CLIC Workshop 2013

new

15th September. 2016

2

Contents

1. Brief introduction to the response function using ScECAL case: up date version of Munich,

2. Applying to AHCAL SiPMs,

3

Motivation: Linear response after saturation

incident p.e.0 5000 10000 15000 20000

fired

pix

els

0

500

1000

1500

2000

tquenchPfourtquenchPfour

Often we see like red curve w/ fast recovery SiPMs

?

:the number of fired pixels,:photon detection efficiency (PDE),:the number of incident photons,:the number of pixels.

Equation plot of 1600 pixel SiPM, not data not completely saturating

conventional function

photonWe think this comes from reactivation of pixels in a few nano seconds after fired.

=LON

fire

= Npix

⇣1� e�✏N

in

/Npix

⌘

4


incident p.e.0 5000 10000 15000 20000

fired

pix

els

0

500

1000

1500

2000


Often we see like red curve w/ fast recovery SiPMs

?





=LON

fire

= Npix

⇣1� e�✏N

in

/Npix

⌘

Adjustable parameter

Num

ber o

f fire

d pi

xels

d 0

1000

2000

3000

/NDF = 146 / 122χ

du 11± = 2260 effpixN

PMT response (ADC ch)0 50 100 150 200

dFu

nctio

n-da

ta

200−100−

0100200

5

Example of Npixeff (LO’)


(p.e

./AD

C)

dG

radi

ent

10

210

- Calibration for ScECAL physics prototype.- 1600 pix was measured as 2260 pix (Npixeff).

applicable limit

6

Sample DATA (taken by W. Choi in Shinshu 2010)

72 channels of 30th layer of ScECAL prototype 30 layer-Physics proto. 30th layer (72 ch)

PMT

Laser

a. Scintillator, 3x10x45mm3,b. WLS,c. a hole on reflector,d. MPPC 25μm pitch, in 1x1mm2

e. half mirrorf. PMT,g. lens,h, i. polaroid.

LensPolaroid x 2

ScEcal layer

Half mirror

with 1600 pix MPPC

31ps,FWHM

Num

ber o

f fire

d pi

xels

d 0

1000

2000

3000

/NDF = 146 / 122χ



dFu

nctio

n-da

ta

200−100−

0100200

7



(p.e

./AD

C)

dG

radi

ent

10

210


applicable limit

Num

ber o

f fire

d pi

xels

d 0

1000

2000

3000

/NDF = 146 / 122χ



dFu

nctio

n-da

ta

200−100−

0100200

8



(p.e

./AD

C)

dG

radi

ent

10

210


applicable limit

linear behav

ior

9

= 1)∈Incident photons (

0 1000 2000 3000 4000 5000

Num

ber o

f fire

d pi

xels

0

1000

2000

3000

4000

5000

incide

nt

fired

not fi

red

Not fire photons can make the next contributions

NR = ✏Nin � LO

NNLOfire = LO + ↵NR

Idea: think which photons can hit a reactivated pixels

10


0 1000 2000 3000 4000 5000

Num

ber o

f fire

d pi

xels

0

1000

2000

3000

4000

5000

incide

nt

fired

not fi

red


NR = ✏Nin � LO



waiting photon

waiting photons

11


0 1000 2000 3000 4000 5000

Num

ber o

f fire

d pi

xels

0

1000

2000

3000

4000

5000

incide

nt

fired

not fi

red


Note: Linear of NR @ high light region̶after enough saturation

NR = ✏Nin � LO



waiting photon

waiting photons

Reason, why we see linear like behavior

12

Fitting with NLON

umbe

r of f

ired

pixe

lsd 0

1000

2000

3000

cable: 3, channel: 9

Npix: 2061.9 +- 8.6

’: 56.6 +- 0.2∈

: 0.0907 +- 0.0005α

/NDF = 28.22χ


dFu

nctio

n-da

ta

200−100−

0100200

Fit region increased

However,Fitting is not enough wellboth- highly saturated region- small fired pixel region

Too simple

Limit of LO’

13

Consider Charge contribution by a photon


0 1000 2000 3000 4000 5000

Num

ber o

f fire

d pi

xels

0

1000

2000

3000

4000

5000

incide

nt

fired

not fi

red


Charge contribution by a photon should be a function of #photon/pix.

NR = ✏Nin � LO


firednot fired

waiting photons

waiting photon

14

2 4 6 8 10

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

2 4 6 8 10

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

pulse shape ~ recovery of a pixel.

�t

V2nd

max

delayed photon

delayed photon comes before complete recharge

V 2nd

max

= 1� e��t/⌧R

Vmax

e�t/⌧R

⌧R = Rquench

Cpixel

charge by the second photon　　 is 　 :as is full charge case,

Q1Q0

Q1 = Q0(1� e��t/⌧R)

Consider Charge contribution by a photon (case multi-photons come)

15

0 2 4 6 8 10

2

4

6

8

10

12photons come from WLS fiber

dn

dt/ e�t/⌧s

2 4 6 8 10

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

Suppose: we have k photons waiting for...First: we have k candidate ➡ ⌧s/ksecond we have k-1;　　　　　 , then⌧s/(k � 1) ⌧s/(k � 2) · · · ⌧s

j th rate ; ⌧j = ⌧s/(k � j + 1)

Time distribution of photons ̶Charge by jth photon

note: we have photons coming later than .⌧s

D. Jeans arXiv:1511.06528

inverse proportion

16

Number of photons / pixel0 5 10 15

Cha

rge

cont

ribut

ion

/ pho

ton

0

0.2

0.4

0.6

0.8

1 = 0.5sτ/Rτ:

= 1.0sτ/Rτ:

= 2.0sτ/Rτ: Q0

h1 +

kX

j=2

�1� ⇣

⇣ + (k + 1� j)�1

i/k

Q(k)/k =

curve

h#photon/pixelfiredi = hki = ✏Nin

LO

h#photon/pixelfiredi = hki

Plot of Q(k)/k

=� + 1

� + k

NNLO0

fire = NNLOfire

� + 1

� + ✏Nin/LO

Num

ber o

f fire

d pi

xels

d 0

1000

2000

3000

4000

cable: 3, channel: 9 Npix: 1600.0 +- 0.0’: 61.5 +- 0.2∈ : 0.224 +- 0.003α : 17.7 +- 0.4β /NDF = 4.72χ

Fitting limit of LO’


dFu

nctio

n-da

ta

100−

0100

17

Fitting with NLO’

Npix was fixed @ 1600only one additional free parameters to LO’

If Npix was free:= 1583±29

(72 sample)

high saturated region

small light region- modified

- good agreement

NNLO0

fire = NNLOfire

� + 1

� + ✏Nin/LO

hNpix

i

Num

ber o

f fire

d pi

xels

d 0

1000

2000

3000

4000

cable: 3, channel: 9 Npix: 1600.0 +- 0.0’: 56.8 +- 6.1∈ : 0.288 +- 0.015α : 12.8 +- 1.0β

cross talk ratio: 0.19 +- 0.08 after pulse ratio: -0.032 +- 0.04

/NDF = 2.52χ



dFu

nctio

n-da

ta

100−

0100

18

Considering Xtalk and After pulse

Npix was fixed @ 1600

NLO0C.A = NLO0 ⇥ (1 + PCe

�✏Nin

/Npix)(1 + PA)

<PC> = 0.22±0.02<PC>direct = 0.11±0.02

<PA> = 0.08±0.02<PA>direct = 0.1

High crosstalk ratio requires additional knowledge.

19

χ2/NDF

most channel < 10for both NLO’ NLO’C.A


�✏Nin

/Npix)(1 + PA)

/NDF2χ0 10 20 30 40 50

Entries

0

10

20

30

: w/ after pulse, crosstalk

: w/o after pulse, crosstalk

: w/ after pulse, crosstalk

: w/o after pulse, crosstalk

NLO0C.A

NLO0

NLO’ NLO’C.A

<χ2/q> 9.4±9.0(RMS) 6.9±7.9(RMS)

Uncertainty of each data point is statistical one.

Num

ber o

f fire

d pi

xels

d 0

500

1000

1500

2000

cable: 1, channel: 1 Npix: 1600.0 +- 0.0’: 71.6 +- 3.8∈ : 0.240 +- 0.021α : 6.9 +- 0.6β


/NDF = 13.82χ


dFu

nctio

n-da

ta

100−

0100

20

Fast pulse inputNLO0

C.A = NLO0 ⇥ (1 + PCe�✏N

in

/Npix)(1 + PA): applied to scinti-MPPC w/o WLS fiber

WLS fiberWLS fiberw/ w/o

α 0.30 0.24

β 12 6.9

α: large small

smallβ: large

recovery

pulse width/recov.time

21

Applying to 7608 SiPM data of AHCAL physics prototype

ITEP SiPM 1156 pixels/(1.1×1.1mm2) Recovery time: 20ns (from CALICE JINST 5 P05004),LED UV light via Y11 WLS, at dV = 2V,Xtalk : < 35%, MPV~22%,

LED

SiPMs

WLS fibers

naked SiPM w/o scintillator

from CALICEJINST 5 P05004

22

Motivation

23

MotivationFelix’s (Eva Sicking’s) talked at LCWS Whistler: W-AHCAL

Rather artificial linear extrapolation

Num

ber o

f fire

d pi

xels

d 0200400600800

10001200

nch: 7301, SiPM: 23204 Npix: 1156.0 +- 0.0’: 2.8 +- 0.1∈ : 1.101 +- 0.006α : 5.4 +- 0.1β

cross talk ratio: 0.21 +- 0.00 after pulse ratio: 0.000 +- 0.00

/NDF = 6.32χ


PMT response (ADC ch)0 500 1000 1500 2000 2500

dD

iff./f

unc.

0.02−0.01−

00.010.02

# photons in

1156N

umbe

r of f

ired

pixe

lsd 0

200400600800

10001200

nch: 7200, SiPM: 30756 Npix: 1156.0 +- 0.0’: 1.3 +- 0.0∈ : 0.685 +- 0.024α : 2.9 +- 0.1β


/NDF = 0.12χ



dD

iff./f

unc.

0.02−0.01−

00.010.02

24

ITEP SiPM in AHCAL physics prototypefitting example/7608, various fired/in

(# photons in: normalized at small number of fired pixels)

1156

Npix: fixed at 1156

Fitting: 7608 samples takes ~22min(0.17sec/ch)➡ light function

# photons in

Num

ber o

f fire

d pi

xels

d 0

200

400

600

800

nch: 7600, SiPM: 21222 Npix: 1156.0 +- 0.0’: 1.3 +- 0.0∈ : 0.456 +- 0.009α : 2.5 +- 0.1β


/NDF = 2.42χ



dD

iff./f

unc.

0.02−0.01−

00.010.02

# photons in

25

ITEP SiPM in AHCAL physics prototype some parameters

0 5 10 15 200

500

1000

1500

2000

redchiredchi

0

200

400

600

800

1000scale:aftP

0.5− 0 0.5 10

1

2

3

4

scale:aftP

0.12 0.14 0.16 0.18 0.2 0.22 0.240

500

1000

1500

2000

crosstalk ratiocrosstalk ratio

χ2/NDF < 20 7425ch/7608ch

χ2/NDF crosstalk ratio

mean 0.17 ± 0.01

after pulse ratio

ε

✏ =0.88

1.02 + afterPulse


�✏Nin

/Npix)(1 + PA)

in our simple model, P_afterpulse is a scale factor in N_fired (no effect on shape).

negative peak (-0.28) indicates some systematics.

:

26

ITEP SiPM in AHCAL physics prototype some parameters

0 5 10 15 200

500

1000

1500

2000

redchiredchi

0

200

400

600

800

1000scale:aftP

0.5− 0 0.5 10

1

2

3

4

scale:aftP

0.12 0.14 0.16 0.18 0.2 0.22 0.240

500

1000

1500

2000

crosstalk ratiocrosstalk ratio

χ2/NDF < 20 7425ch/7608ch

χ2/NDF crosstalk ratio

mean 0.17 ± 0.01

after pulse ratio

ε

✏ =0.88

1.02 + afterPulse


�✏Nin

/Npix)(1 + PA)

in our simple model, P_afterpulse is a scale factor in N_fired (no effect on shape).

negative peak (-0.28) indicates some systematics.

:Our function works well for also ITEP SiPMs in AHCAL

27

α vs. β

020406080100120140160180200220

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15alpha:beta {alpha<15}alpha:beta {alpha<15}

β

α

α and β have a relation with each other.However, a clear peak indicates that those both 　　　　　　　　　　　　　have meanings of　　　　　　　　　　　　　 existences respectively.


NNLO0

fire = NNLOfire

� + 1

� + ✏Nin/LO

LO = Npix

⇣1� e�✏N

in

/Npix

⌘

28

crosstalk ratio vs. β

020406080100120140160180200220

0 0.2 0.4 0.6 0.8 1 1.20

5

10

15alpha:beta {alpha<15}alpha:beta {alpha<15}

β

α

020406080100120140

0 0.5 10.14

0.16

0.18

0.2xtalk:beta {0.14<xtalk&&xtalk<0.2}xtalk:beta {0.14<xtalk&&xtalk<0.2}

β

cros

stalk ratio

- Correlation between cross-talk ratio and β has a clear peak and no clear correlation (only small amount of large β has correlation.

- without crosstalk correction, fitting results are very much degrading

β and crosstalk individually affect on the shape of function

Three parameters α，β，and crasstalk ratio are individually required.

29

Summary- We developed functions having high performance to represent SiPM behavior in wide ranges.

- Light function (0.17sec/fit).- The function models reactivating pixels in a event more carefully than taking the number of effective pixels;•the number of photons fire reactivated pixels,•charge contribution par one photon is implemented by an approximation of the first principle method.

- Crosstalk and after pulse models improves fitting performance, whereas it did not work with LO’(Npixeff).

- The function successfully worked on 7608 SiPM for AHCAL physics prototype.

Next- Understand detail effects of individual parameters.- Usage in calibration procedure.

30

Backup

31

0 2 4 6 8 10

2

4

6

8

10

12photons come from WLS fiber

dn

dt/ e�t/⌧s

2 4 6 8 10

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

Suppose: we have k photons waiting for...First: we have k candidate ➡ ⌧s/ksecond we have k-1;　　　　　 , then⌧s/(k � 1) ⌧s/(k � 2) · · · ⌧s

j th rate ; ⌧j = ⌧s/(k � j + 1)

Time distribution of photons ̶Charge by jth photon

note: we have photons coming later than .⌧s

Incorrect: no effect in .⌧s < ⌧R

by D. Jeans

32

charge by the jth photon

Qj = Q0

Z 1

0dt

1

⌧je�t/⌧j (1� e�t/⌧R)

⌧j = ⌧s/(k � j + 1)

= Q0

⇣1� ⌧R

⌧R + ⌧j

⌘

= Q0

⇣1� ⇣

⇣ + (k � j + 1)�1

⌘

⇣ = ⌧R/⌧scharge by ks photons

Q(k) = Q0

n

1 +k

X

j=2

⇣

1� ⇣

⇣ + (k � j � 1)�1

⌘o

Charge by ks photons on a cell

D. Jeans arXiv:1511.06528

33

Hamamatsu MPPC (2008)Hamamatsu MPPC: corresponding to S10362-11-25P1600pixels/(1×1mm2) Recovery time: 4ns,at dV = 3V,crosstalk : 11% measured in lab,after pulse : 10% from some references.

408nm 31ps (FWHM) Laser via Scintillator + Y11 WLS, Y11 decay time: 11ns

34

Purpose of developing functions

Practical usage in experiments using SiPMs in wide range of number of photons,

based on much reasonable̶detail̶model of SiPM phenomena than current others.

- detector calibration,- simulation of detector responses

35

DataCALICE DATA base we can access it using CaliceSoft.

each data (7608) has:one SiPM ID20 data of # photons injected,20 data of fired pixels corresponding,no uncertainty information.

- Wrote a processor to read and create a TTree.

Applying our function to # of fired pix. as a function of # of photons injected.

Num

ber o

f fire

d pi

xels

d 0

200

400

600

800

nch: 7600, SiPM: 21222 Npix: 1156.0 +- 0.0’: 1.8 +- 0.1∈ : 0.616 +- 0.179α : 2.4 +- 0.8β


/NDF = 0.02χ



dD

iff./f

unc.

0.05−

00.05

36

Some example of fittingN

umbe

r of f

ired

pixe

lsd 0

200400600800

10001200

nch: 7200, SiPM: 30756 Npix: 1156.0 +- 0.0’: 1.3 +- 0.1∈ : 0.504 +- 0.139α : 4.7 +- 1.7β


/NDF = 0.02χ



dD

iff./f

unc.

0.05−

00.05

Num

ber o

f fire

d pi

xels

d 0200400600800

100012001400

nch: 7300, SiPM: 21156 Npix: 1156.0 +- 0.0’: 2.0 +- 0.2∈ : 1.025 +- 0.038α : 4.2 +- 0.7β


/NDF = 0.02χ



dD

iff./f

unc.

0.05−

00.05

Fine fitting result.Too large error estimation :(

net # of pix. 1156net # of pix. 1156

# photon arrived?

# photon arrived?

# photon arrived?

Each error #photons × 0.01

Evaluation of fitting (good)

37

0 0.5 1 1.5 2 2.5 30

200

400

600

800

1000’∈’∈

#photon arrived was already normalized at small p.e. response. (linear pixels? )

~1

PMT, PDE scale factor: ✏example

38

Error estimation trial (sqrt)N

umbe

r of f

ired

pixe

lsd 0

200400600800

10001200

nch: 7200, SiPM: 30756 Npix: 1156.0 +- 0.0’: 1.1 +- 0.0∈ : 0.461 +- 0.006α : 4.7 +- 0.1β


/NDF = 4.12χ



dD

iff./f

unc.

0.02−0.01−

00.010.02

net # of pix. 1156net # of pix. 1156

Error = √(N_fired) × 0.01

- a bit reasonable error- S structure .... 0 5 10 15 20

0

500

1000

1500

2000

redchiredchi

0 0.01 0.02 0.03 0.040

1000

2000

3000

redchiredchiχ2/ndf

χ2/ndf

rea

sona

ble

適当

Parameters with error∝√(#photon)

39

0 0.5 1 1.5 2 2.5 30

500

1000

1500

’∈’∈

0 0.5 1 1.5 2 2.5 30

200

400

600

800

1000’∈’∈

0 0.5 1 1.5 20

200

400

600

αα

0 5 10 15 200

200

400

600

800

1000

1200ββ

0 0.5 1 1.5 20

200

400

600

800

1000

αα

0 5 10 15 200

200

400

600

800

ββ

Error = sqrt(N_fired) × 0.01 makes parameter distributions to be narrower ➡ better estimation

εPMT, PDE scale factor αRecovery parameter β# photons/cell effect

　√(#photon)× 0.01 or 0.005?

40

0 5 10 15 20

200

400

600

800

1000

1200

1400redchiredchi

0 5 10 15 200

500

1000

1500

2000

redchiredchiχ2/NDF with × 0.01 χ2/NDF with × 0.005

Too small error estimation makes fits.

χ2/NDF < 20: 7178channels χ2/NDF < 20: 4918ch

Num

ber o

f fire

d pi

xels

d 0200400600800

10001200

nch: 7200, SiPM: 30756 Npix: 798.0 +- 15.1’: 0.8 +- 0.0∈ : 0.727 +- 0.017α : 2.6 +- 0.0β


/NDF = 0.22χ



dD

iff./f

unc.

0.02−0.01−

00.010.02

Example of fitting results

41

Num

ber o

f fire

d pi

xels

d 0200400600800

10001200

nch: 7200, SiPM: 30756 Npix: 1156.0 +- 0.0’: 1.1 +- 0.0∈ : 0.461 +- 0.006α : 4.7 +- 0.1β


/NDF = 4.12χ



dD

iff./f

unc.

0.02−0.01−

00.010.02

net # of pix. net # of pix. net # of pix.

Current best fitting

apply to calibration?Next step

Fixed Npix at 1156

Free Npix

42


incident p.e.0 5000 10000 15000 20000

fired

pix

els

0

500

1000

1500

2000

tquenchPfourtquenchPfour ?

:the number of fired pixels,:scale factor of horizontal direction,:the number of incident photons,:the number of pixels.




To date, we take

for such a case.

Often we see like red courve especially w/ MPPC

43


incident p.e.0 5000 10000 15000 20000

fired

pix

els

0

500

1000

1500

2000


Often we see like red courve especially w/ MPPC

?





=LO

44

Sample DATA (taken by W. Choi in Shinshu 2010)

72 channels of 30th layer of ScECAL prototype 30 layer-Physics proto. 30th layer (72 ch)

PMT

Laser

a. Scintillator, 3x10x45mm3,b. WLS,c. a hole on reflector,d. MPPC 25μm pitch, in 1x1mm2

e. half mirrorf. PMT,g. lens,h, i. polaroid.

LensPolaroid x 2

ScEcal layer

Half mirror

with 1600 pix MPPC

31ps,FWHM

45

Some remind of ScECAL response curve

Hamamatsu MPPC1600pixels/(1×1mm2) Recovery time: 4ns,408nm 31ps Laser via Scintillator + Y11 WLS, at dV = 3V,crosstalk : 11% measured in lab,after pulse : 10% from some references.

46

Contents

1. Brief introduction to the response function using ScECAL case,

2. Applying to AHCAL data,

3. Discussion on parameters and fitting conditions.

Documents

new Applying a SiPM response function to 7608 SiPMs of