A study on stochastic term of calorimetric
energy resolution
Ilhan TAPAN and Fatma KOCAK
Uludag University
Physics Department
Bursa-Turkey
The XIV International Conference on Calorimetry in High Energy Physics, Beijing,
China, May 10-14, 2010.
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China
1
Outline
- Introduction
- PbWO4 Crystals-Avalanche Photodiode Combination
- Calorimetric Energy Resolution and Stochastic Term
- Simulation and Results
- Conclusion
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China
2
Introduction
The energy measurement with scintillation crystal is based
on the energy released of the incident particles in the crystal
material.
An electromagnetic shower is produced by a high-energy
electron, positron or photon enters the crystal.
The light generated in the shower development is detected
by photodetectors.
The ultimate limit for the energy resolution is determined by
fluctuations in the development of showers.
İlhan Tapan
Status of diagnostic system
TAC-IMAC-1, 04-05.12.2009, Ankara University, ANKARA
3
Introduction
SUPERCONDUCTING
COIL
CALORIMETERS
ECAL
Scintillating
PbWO4 crystals
HCAL
Plastic scintillator/brass
sandwich
IRON YOKE
TRACKER
Silicon Microstrips
Pixels
Total weight : 12,500 t
Overall diameter : 15 m
Overall length : 21.6 m
Magnetic field : 4 Tesla
Ilhan Tapan
MUON
ENDCAPS
MUON BARREL
Drift Tube
Resistive Plate
Chambers ( DT) Chambers (RPC )
A study on stochastic term of calorimetric energy resolution
Cathode Strip Chambers ( CSC)
Resistive Plate Chambers ( RPC )
CALOR 2010, 10-14 May, Beijing, China
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Introduction
An homogenous scintillating crystal detector
Made out of 75,000 crystals
Subdivided into a barrel and two endcap
Barrel section
contains 61,000 crystals
two APDs per crystal
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China
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PbWO4 Crystals-Avalanche Photodiode Combination
PbWO4 crystal
Advantages 
• Dense and Radiation hard
• Short radiation length
• Fast
Disadvantages 
• Temperature dependence
• Low light yield
1,2
Properties of PbWO4
Normalised Emission
1
0,8
0,6
Density
8.28 g/cm3
Radiation length
0.89 cm
Interaction length
19.5 cm
Moliére radius
2.2 cm
Emission peak
420 nm
Light yield
120 photons /MeV
Radiation hardness
107 rad
0,4
0,2
0
300
350
400
450
500
Wavelength [nm]
Scintillation light spectrum of PbWO4
Ilhan Tapan
550
600
(CMS ECAL TDR)
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China
6
PbWO4 Crystals-Avalanche Photodiode Combination
Avalanche Photodiode (APD)
Advantages 
• compact and robust
• very high QE
• internal gain
• very good time resolution
• insensitive to B
Disadvantages 
• small sensitive areas and noisy
• gain fluctuations
• dependence on high radiation
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China
7
PbWO4 Crystals-Avalanche Photodiode Combination
Hamamatsu silicon S-8148 APD
Produced by epitaxial growth on
low resistivite n+-type silicon
substrate, followed by ion
implantation.
Si-APD Parameters (Hamamatsu S-8148)
5x5 mm2
Quantum efficiency at 420nm
72%
Operating voltage
380 Volt
Gain [M]
50
Capacitance [C]
80 pF
Excess noise [F]
~2
(1/M) (dM/dV) at M=50
3,3%
(1/M) (dM/dT) at M=50
-2,2%
100
80
QE [%]
Active area
60
40
20
0
300
400
500
600
700
800
900
1000
Wavelength [nm]
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China
8
Calorimetric Energy Resolution and Stochastic Term
Energy resolution in the ECAL
 E 
E
a
c

b
E
E
E is the energy of the incident particle
Ilhan Tapan
Term
Contribution to
Aim for CMS ECAL Barrel
a
Stochastic term
Photoelectron statistic
Shower fluctuations
~ 2.8% GeV1/2
b
Constant term
Calibration
Non-uniformities
~ 0.55%
c
Noise term
Electronic noise
Dark current
155 MeV at low luminosity
210 MeV at high luminosity
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China
9
Calorimetric Energy Resolution and Stochastic Term
APD contributes to all the terms ECAL energy resolution
a
b
c
sensitive area, quantum efficiency, excess noise
gain sensitivity to operating voltage and temperature,
aging and radiation damage
low capacitance, serial resistance and dark current
By neglecting the intrinsic resolution, the APD photo-electron
statistics contribution to stochastic term is given by
F Npe is the number of primary photoelectrons
  (E) 

 
Npe Npe = Nph .QE
 E 
2
Nph ; photons from crystal, QE ; quantum efficiency
F is the avalanche gain fluctuation or excess noise factor
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 10
Calorimetric Energy Resolution and Stochastic Term
The relative fluctuation of the APD signal in the proportional
mode
  N pe
 S 

 
 N pe
 S 

2
2
  1   M  2
 


  N pe  M 

 
Npe is the number of primary photoelectrons
 N pe : S.D. of the number of primary photoelectrons;
M : Avalanche gain
σM : S.D. of the avalanche gain
F
 S 

 
Npe
 S 
 N pe  Npe
F  1
M2
M2
2
Ilhan Tapan
APD photo-electron statistics
contribution to stochastic term
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 11
Calorimetric Energy Resolution and Stochastic Term
The total stochastic term of the energy resolution for crystalAPD combination is composed of a contribution from shower
containment (lateral leakage contribution) and a contribution
from APD signal fluctuation (photo-electron statistics).
1- Event to event fluctuations in the lateral shower containment
......(alateral),
2- Photo-electron statistics contribution from APD (ape)
a pe 
a  alateral  a pe
2
Ilhan Tapan
S
F

N pe
S
2
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 12
Simulation- alateral
The lateral shower shape determines the distribution of the
energy deposition in a cluster of crystals around the impact
point.
The contribution to the stochastic term coming from
fluctuations in the lateral shower containment (lateral
leakage) of PbWO4 crystals has been simulated by GEANT4
for 0.2-100 GeV electrons.
Crystal is same size used in CMS ECAL,
a truncated-pyramidal shape;
a length of 23 cm (25.8X0)
front side 2.2x2.2 cm2
rear side 2.6x2.6 cm2
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 13
Simulation- alateral
Energy deposition in single crystal
Electrons
at
different
energies were injected in
the central of the crystal.
78% of the energy of the incident electron
was deposited
σ E/E (%)
90
80
70
10
Ed (GeV)
60
50
1
40
30
20
10
0
0
Ilhan Tapan
20
40
60
E (GeV)
80
100
120
0,1
0
A study on stochastic term of calorimetric energy resolution
20
40
60
Energy (GeV)
80
100
CALOR 2010, 10-14 May, Beijing, China 14
Simulation- alateral
Energy deposition in 9 crystal blocs of a 3x3 matrix
Events
central
crystal of
the 3x3
matrix
Events
deposition in the central crystal to
that in all nine crystals is 85%.
Toplam enerji
E (MeV)
Energy deposits in 3x3 PbWO4 crystals for 1 GeV electrons injected into
the center of the central crystal
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
Energy (MeV)
Energies deposited in the nine crystals
CALOR 2010, 10-14 May, Beijing, China 15
Simulation- alateral
σ E/E
Event Numbers
Comparison of Geant4 and EGS4
200 MeV
0,1
Geant4
0,08
EGS4
400 MeV
0,06
600 MeV
800 MeV
1 GeV
0,04
0,02
0
Energy (MeV)
Energy spectra obtained by summing up all energy
deposits in the nine crystals for the incident electrons
of 0.2, 0.4, 0.6, 0.8, and 1.0 GeV, respectively.
0
0,2
0,4
0,6
E (GeV)
0,8
1
1,2
Energy resolution E/E of the 3x3 crystal matrix
Shimizu, H., et al. 2000. NIM A: 447,p.467
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 16
Simulation- alateral
Energy deposition in 5x5 matrix
120
100
Ed (GeV)
80
60
1
40
0,95
1x1
3x3
20
0,9
0
0
20
40
60
E (GeV)
80
100
120
Deposited energy as a function of incident electron
energy
78% of the energy of the incident electron
deposited in the central crystal.
The total deposited energy in the 9 crystals 93%
in the 25 crystals 96%.
Ilhan Tapan
Ed/E
5x5
1x1
3x3
0,85
5x5
0,8
0,75
0,7
0
20
40
60
80
100
E (GeV)
Deposited energy fraction as a function of incident
electron energy
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 17
alateral
σ E/E (%)
Simulation- alateral
10
1x1
3x3
5x5
1
0,1
0
20
60
40
Energy (GeV)
80
100
Intrinsic energy resolution (alateral) for the 1x1, 3x3 and 5x5
crystals matrices as a function of incident electron energy
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 18
Simulation- ape
PbWO4 – APD Simulation
The light generated by 0.2-100 GeV electrons in the PbWO4 crystal
has been obtained using with the GEANT4 simulation code.
electron
APDs
The Single Particle Monte Carlo technique has been used to
calculate APD output signals and their fluctuations
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 19
Simulation- ape
Cherenkov and scintillation lights in the electromagnetic shower
1,2
Normalized Emission
1
Cherenkov (C)
Scintillation (S)
C+S
As the scintillation light is
emitted in the wavelength
region of 320 nm to 600 nm
peaking at around 420 nm,
the Cherenkov light is
emitted with a characteristic
1
2 spectrum.
0,8
0,6
0,4
0,2
0
300
400
500
Wavelength (nm)
600
Cherenkov, scintillation and total photons spectrums at the end of the crystal
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 20
Number of
generated
photons in
the crystal
Number of photons
Simulation- ape
PbWO4 Spectrums for 1 GeV electron
Cherenkov Spectrum
Cherenkov Spectrum
Scintillation Spectrum
Scintillation Spectrum
Number of
photons
at the end
of the
crystal
Spectrum
Spectrum
Wavelength (nm)
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 21
Simulation- ape
Photon absorption by APD
100
Number of photons
QE [%]
80
60
40
20
Experiment [1]
Simulation
0
300
400
500
600
700
800
Wavelength [nm]
900
1000
Quantum efficiency variation with wavelength
for the S8148 APD structure
Wavelength (nm)
Total photons spectrums at absorbed in the APD
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 22
Simulation- ape
• A Single Particle Monte Carlo code
• by tracking the generated charge carriers through the APD
• motion of particles is spatially restricted in the device model
• each charge carrier is assumed to be independent of the
others
• diffusion, drift and impact ionisation processes
• the charge released by an incident photon or by an impact
ionisation can modify externally applied field
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 23
Simulation- ape
Avalache gain, number of electrons left from the avalanche
region per number of primary photoelectrons entered.
As the photon absorbtion depth is a function of wavelength,
the charge generation in the avalanche region decreases the
avalanche gain and increases the excess noise factor.
60
20
Gain
Excess noise
50
16
Gain
12
30
8
20
10
4
0
0
360
440
520
600 680 760 840
Wavelength [nm]
Excess Noise
40
920 1000
APD Gain and excess noise as a function of wavelength
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 24
Simulation- ape
The behaviour of the mean signal and its fluctuation results
from the combined effect of the wavelength dependent
absorption coefficient of the incident photons and of the
depth dependent avalanche gain in the depletion.
3
2,5
40
Relative Fluctuation .
Mean Signal [arbitrary units] .
50
30
20
10
0
300
1,5
1
0,5
400
500
600
Wavelength [nm]
700
APD Signal variation versus wavelength
Ilhan Tapan
2
800
0
300
400
500
600
Wavelength [nm]
700
800
Relative fluctuation in the APD signal versus wavelength
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 25
Simulation- ape
APD Signal fluctuation or photo-electron statistics
contribution on stochastic term has been calculated for
Cherenkov, scintillation and total photons from PbWO4 .
10
a pe 
S
F

N pe
S
ape (%)
ape (S+C)
ape (S)
ape (C)
1
0,1
0
20
40
60
80
100
E (GeV)
Relative fluctuation in the APD signal (ape) as a function of
incident electron energy
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 26
Simulation- stochastic term a
10
a
a toplam
stochastic term
pe
ape
alateral
enine
1
0,1
0
20
40
60
80
100
E (GeV)
Stochastic term (a) variation as a function of incident electron
energy for 3x3 crystal matrice
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 27
Simulation results- stochastic term a
For 1 GeV incident electrons
ape (photo-electron contribution) : 2.07 %
alateral
For 3x3 crystal matrice: 1.90 %
For 5x5 crystal matrice: 1.42 %
The total the stochastic term contribution to the energy resolution
for 3x3 matrice
a  a pe  alateral  2.07 2  1.90 2  2.81 %
2
2
The CMS test beam results : 2.8 %
CMS Collaboration, 2008. JINST 3 S08004, The CMS experiment at the LHC, p.90
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 28
Conclusion
Simulation shows that;
PbWO4 crystal- Hamamatsu S8148 APD are good combination
for energy measurements.
The Hamamatsu S8148 APD had been optimised for the
photons with around the peak wavelength of the PbWO4
emission spectrum.
• PbWO4 crystal has low light yield,
• In the case of the entire emission spectrum of PbWO4
crystal; one part of the photons, between in the wavelength
region of 320-450 nm cause an increase of the F for the S8148
APD structure
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 29
Conclusion
TAPAN, İ., M.A. AFRAILOV, F. KOCAK. 2006. NIMA, Volume 567 (1): 268-271.
100
QE [%]
80
60
40
20
S8148 Structure [1]
ZnS-Si Structure
0
3
40
Relative Fluctuation .
Mean Signal [arbitrary units] .
50
30
20
10
400
500
2,5
600 700 800
Wavelength [nm]
900
1000
2
1,5
1
0,5
S8148 Structure
ZnS-Si Structure
0
300
S8148 Structure
ZnS-Si Structure
0
300
Ilhan Tapan
400
500
600
Wavelength [nm]
700
800
300
A study on stochastic term of calorimetric energy resolution
400
500
600
Wavelength [nm]
700
800
CALOR 2010, 10-14 May, Beijing, China 30
Conclusion
CsI(Tl)
PbWO4
1,2
1,2
1
Normalised Emmision
Normalised Emission
1
0,8
0,6
0,4
0,2
0,8
0,6
0,4
0,2
0
300
350
400
450
500
Wavelength [nm]
550
600
0
300
~120 photons/MeV
400
500
600
Wavelength (nm)
700
800
~66,000 photons/MeV
The high photon values and the low signal fluctuations make crystalAPD combination an excellent choice for energy measurements.
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 31
Additional slides
Cherenkov – 1 GeV
Contribution 26%
At the
end of
the
crystal
Frequency
Scintillation – 1 GeV
İn the APD
C+S – 1 GeV
Number of photons
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 32
Additional slides
Number of output photons
1,E+08
1,E+07
1,E+06
1,E+05
1,E+04
1,E+03
Cherenkov (C)
Scintillation (S)
C+S
1,E+02
1,E+01
0,001
0,01
0,1
1
10
100
Energy (GeV)
The number of leaving photons as a function of incident electron energy
a pe 
Npe=number of output photons*0.074*QE
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
F
N pe
CALOR 2010, 10-14 May, Beijing, China 33
Additional slides
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 34
Additional slides
Lateral shower development comparisons
1
0,95
E1 /E9 data
E1 / E9 Geant4
E1 / E25 data
E1 / E25 Geant4
E9 / E25 data
E9 / E25 Geant4
0,9
0,85
0,8
0
20
40
60
80
100
E (GeV)
The ratio of the energy contained into a single crystal (E1) over
the energy contained into a 3×3 and a 5×5 crystal matrix center
around the hit crystal (respectively E9 and E25).
MERIDIANI, P. Optimization of the discovery potantial of the Higgs Boson in the decay channel
H  ZZ (*)  2e  2e  with the CMS detector. PhD Thesis. Universita Degli Studi Di Roma “La Sapienza”.
Ilhan Tapan
A study on stochastic term of calorimetric energy resolution
CALOR 2010, 10-14 May, Beijing, China 35