1. A study on stochastic term of calorimetric energy resolution
Ilhan TAPAN and Fatma KOCAK
Uludag University
Physics Department
Bursa-Turkey
Title: Excess Noise Factor of Neutron Irradiated Silicon Avalanche Photodiodes
The XIV International Conference on Calorimetry in High Energy Physics, Beijing, China, May 10-14, 2010.

2. - Simulation and Results
Outline
- Introduction
- PbWO4 Crystals-Avalanche Photodiode Combination
- Calorimetric Energy Resolution and Stochastic Term
- Simulation and Results
- Conclusion
Motivation: CMS & APDs

3. 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.
Motivation: CMS & APDs

4. Introduction CALORIMETERS SUPERCONDUCTING COIL IRON YOKE TRACKER MUON
ECAL
HCAL
Scintillating
PbWO4 crystals
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
MUON
ENDCAPS
MUON BARREL
Drift Tube
Resistive Plate
Cathode Strip Chambers ( )
CSC
Chambers ( ) DT
Chambers ( )
RPC
Resistive Plate Chambers ( )
RPC

5. Introduction An homogenous scintillating crystal detector
Made out of 75,000 crystals
Motivation: CMS & APDs
Subdivided into a barrel and two endcap
Barrel section
contains 61,000 crystals
two APDs per crystal

6. PbWO4 Crystals-Avalanche Photodiode Combination
Disadvantages 
Temperature dependence
Low light yield
Advantages 
Dense and Radiation hard
Short radiation length
Fast
Properties of PbWO4
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
Motivation: CMS & APDs
Scintillation light spectrum of PbWO (CMS ECAL TDR)

7. PbWO4 Crystals-Avalanche Photodiode Combination
Avalanche Photodiode (APD)
Advantages 
compact and robust
very high QE
internal gain
very good time resolution
insensitive to B
Motivation: CMS & APDs
Disadvantages 
small sensitive areas and noisy
gain fluctuations
dependence on high radiation

8. Si-APD Parameters (Hamamatsu S-8148)
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)
Active area
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%
Motivation: CMS & APDs

9. Calorimetric Energy Resolution and Stochastic Term
Energy resolution in the ECAL
E is the energy of the incident particle
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
Introduction: ECAL Energy Resolution

10. Calorimetric Energy Resolution and Stochastic Term
APD contributes to all the terms ECAL energy resolution
a sensitive area, quantum efficiency, excess noise
b gain sensitivity to operating voltage and temperature,
aging and radiation damage
c low capacitance, serial resistance and dark current
By neglecting the intrinsic resolution, the APD photo-electron
statistics contribution to stochastic term is given by
Introduction: ECAL Energy Resolution
Npe is the number of primary photoelectrons
Npe = Nph .QE
Nph ; photons from crystal, QE ; quantum efficiency
F is the avalanche gain fluctuation or excess noise factor

11. Calorimetric Energy Resolution and Stochastic Term
The relative fluctuation of the APD signal in the proportional mode
Npe is the number of primary photoelectrons
: S.D. of the number of primary photoelectrons;
M : Avalanche gain
σM : S.D. of the avalanche gain
APD photo-electron statistics
contribution to stochastic term

12. Calorimetric Energy Resolution and Stochastic Term
The total stochastic term of the energy resolution for crystal- APD 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)

13. 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 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

14. 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

15. Simulation- alateral
Energy deposition in 9 crystal blocs of a 3x3 matrix
central crystal of the 3x3 matrix
Events
deposition in the central crystal to that in all nine crystals is 85%.
Events
Energy (MeV)
Toplam enerji
E (MeV)
Energy deposits in 3x3 PbWO4 crystals for 1 GeV electrons injected into
the center of the central crystal
Energies deposited in the nine crystals

16. Simulation- alateral Comparison of Geant4 and EGS4
200 MeV
400 MeV
600 MeV
800 MeV
1 GeV
Event Numbers
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.
Energy resolution sE/E of the 3x3 crystal matrix
Shimizu, H., et al NIM A: 447,p.467

17. Simulation- alateral Energy deposition in 5x5 matrix
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%.
Deposited energy fraction as a function of incident electron energy

18. Simulation- alateral alateral
Intrinsic energy resolution (alateral) for the 1x1, 3x3 and 5x5
crystals matrices as a function of incident electron energy

19. Simulation- ape PbWO4 – APD Simulation
The light generated by GeV electrons in the PbWO4 crystal has been obtained using with the GEANT4 simulation code.
APDs
electron
The Single Particle Monte Carlo technique has been used to calculate APD output signals and their fluctuations

20. Simulation- ape
Cherenkov and scintillation lights in the electromagnetic shower
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
spectrum.
Cherenkov, scintillation and total photons spectrums at the end of the crystal

21. Simulation- ape PbWO4 Spectrums for 1 GeV electron Number of photons
Cherenkov Spectrum
Spectrum
Scintillation Spectrum
Cherenkov Spectrum
Scintillation Spectrum
Spectrum
Number of photons
Number of generated photons in the crystal
Number of photons at the end of the crystal
Wavelength (nm)

22. Simulation- ape Photon absorption by APD
Wavelength (nm)
Number of photons
Explanations & Work: Simulation Mechanism
Quantum efficiency variation with wavelength for the S8148 APD structure
Total photons spectrums at absorbed in the APD

23. 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
Explanations & Work: Simulation Mechanism

24. 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.
Explanations & Work: Simulation Mechanism
APD Gain and excess noise as a function of wavelength

25. 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.
Explanations & Work: Simulation Mechanism
APD Signal variation versus wavelength
Relative fluctuation in the APD signal versus wavelength

26. Simulation- ape
APD Signal fluctuation or photo-electron statistics contribution on stochastic term has been calculated for Cherenkov, scintillation and total photons from PbWO4 .
Relative fluctuation in the APD signal (ape) as a function of incident electron energy

27. Simulation- stochastic term a
Stochastic term (a) variation as a function of incident electron energy for 3x3 crystal matrice

28. 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
The CMS test beam results : 2.8 % %
CMS Collaboration, JINST 3 S08004, The CMS experiment at the LHC, p.90

29. 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 nm cause an increase of the F for the S8148 APD structure

30. Conclusion
TAPAN, İ., M.A. AFRAILOV, F. KOCAK NIMA, Volume 567 (1):

31. Conclusion ~120 photons/MeV ~66,000 photons/MeV
PbWO4
~120 photons/MeV
~66,000 photons/MeV
The high photon values and the low signal fluctuations make crystal-APD combination an excellent choice for energy measurements.

32. Additional slides Contribution 26% At the end of the crystal
Scintillation – 1 GeV
C+S – 1 GeV
Cherenkov – 1 GeV
Contribution 26%
Frequency
At the end of the crystal
İn the APD
Number of photons

33. Additional slides Npe=number of output photons*0.074*QE
The number of leaving photons as a function of incident electron energy
Npe=number of output photons*0.074*QE

34. Additional slides

35. Additional slides Lateral shower development comparisons
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
with the CMS detector. PhD Thesis. Universita Degli Studi Di Roma “La Sapienza”.