MU5PYN03 - DETECTOR PHYSICS

PART 5SOLID STATE DETECTORS (PART I1)

Julien BolmontLPNHE

bolmont@lpnhe.in2p3.fr2019/2020

MU5PYN03 J. Bolmont

EXERCICE 4.7• For 1 MeV, 38 000 photons are produced.• Assuming these photons are produced isotropically, the fraction of

them falling on the pupil is the ratio of solid angles: Ωpup/4π • Then, Ωpup ≈ A/d2, with A = π (1.5 mm)2 and d = 100 mm.• So, Nhits = 38000 x Ωpup/4π ≈ 2.• The observer won't see anything. She/He should use a PMT instead!

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HOW TO DETECT PHOTONS2 - PHOTOMULTIPLIERS

MU5PYN03 J. Bolmont

PHOTOMULTIPLIERS

• Scintillation light is very faint• A photomultiplier

- Converts this light into electrons- Multiply the number of electrons

• A measurable electric signal is obtained• PMTs can have various sizes, shapes

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e-

Signal

Phot

o-ca

thod

e Vacuum tube

Dynode

Ano

de

Scintillationphotons

e-

γScintillator

MU5PYN03 J. Bolmont

VACUUM TUBE - PHOTOCATHODE• A PMT is made of

- A vacuum tube to ensure that electrons can propagate

- A photocathode, where scintillation photons produce photo-electrons (photo-electric effect)‣ 1 photon incident ➔ 1 or 0 photo-electron…‣ The efficiency of the photocathode is the

quantum efficiency (QE), defined by

‣ The QE varies with the energy of incident photons

‣ Its maximum can vary from a few % to ~40%‣ Example of compound used: K2CsSb

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QE =number of emitted electrons

number of incident photons<latexit sha1_base64="gzXg/2nrBcWKUJ4FhLbNF4cVuXk=">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</latexit>

MU5PYN03 J. Bolmont

EXERCICE 5.1• The quantum efficiency of a PMT is 15%. If 8 photons hit the

photocathode, what are the probabilities to produce- No photo-electron ?- Exactly 1 photo-electron ?- At least 1 photo-electron ?

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MU5PYN03 J. Bolmont

EXERCICE 5.1• The quantum efficiency of a PMT is 15%. If 8 photons hit the

photocathode, what are the probabilities to produce- No photo-electron ?- Exactly 1 photo-electron ?- At least 1 photo-electron ?‣ Hint. Binomial coefficients for n= 8 are (1, 8, 28, 56, 70, 56, 28, 8, 1),

and the binomial law for n trials and k successes is given by:

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P (X = k) =

✓nk

◆pk(1� p)n�k

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MU5PYN03 J. Bolmont

FOCUSING- The focusing electrode directs the electrons to the first dynode‣ Some electrons will miss the first dynode. Collection efficiency:

‣ CE should be as high as possible (typically 80-100%)‣ The time of flight of a photoelectron between the photo-cathode to

the first dynode should not depend on the location where it is created

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CE =number of collected photoelectrons

number of emitted photoelectrons<latexit sha1_base64="41oAZQ3ySxdqB7r1qgPc/bZmlFI=">AAADNnicjVFNS8NAEJ1GbbV+VT16WSyCp5JWQS+CWASPClYLRspmu22XJtm42QhS+r/8J8WLN1Fv/gHB2TUFtYpuSDLz5r23Ozt+HIhEu+59zpmanskXZueK8wuLS8ulldXzRKaK8QaTgVRNnyY8EBFvaKED3owVp6Ef8Au/Xzf1ixuuEiGjM30b86uQdiPREYxqhFqlay+kuqfCQf1oSPaJ11GUDcZYlIY+Vx6RHY/gVgFnmrc9EvekltxkSkbJcPgjn4dC/8hulcpuxbWLTAbVLChDtk5kaQQetEECgxRC4BCBxjgACgk+l1AFF2LErmCAmMJI2DqHIRRRmyKLI4Mi2sdvF7PLDI0wN56JVTPcJcBXoZLAJmok8hTGZjdi66l1Nuhv3gPrac52i38/8woR1dBD9C/dmPlfnelFQwf2bA8Ce4otYrpjmUtqb8WcnHzqSqNDjJiJ21hXGDOrHN8zsZrE9m7ultr6s2Ua1OQs46bwYk6JA65+H+dkcF6rVLcrtdOd8sFhNupZWIcN2MJ57sIBHMMJNNB7BG+5fK7g3DkPzqPz9EF1cplmDb4s5/UdHvy+UQ==</latexit>

MU5PYN03 J. Bolmont

EXERCICE 5.2• The quantum efficiency of a PMT is 15% and its collection efficiency is

assumed to be 100%. This PMT is used together with an organic scintillator with a density ρ = 1.1 g cm-3 where 104 photons are created per MeV of deposited energy. Because the scintillator absorbs photons, scintillation photons have a 5% probability to reach the PMT. What should be the thickness L of the scintillator so that a particle at MIP is detected with an efficiency of at least 99% ?‣ Assumptions/Hints:

• At MIP, dE/dx ~ 1.5 MeV cm2 g-1

• The Poisson law for n observed events and X expected is :

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P (n,X) =Xn

n!e�X

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MU5PYN03 J. Bolmont

EXERCICE 5.3• We use a NaI(Tl) detector with a scintillation efficiency R = 12%. The

average energy of the N scintillation photons emitted is Eph = 3 eV and QExCE = 10%. Compute the required energy that must be absorbed in the scintillator (noted Ea) to create one primary photoelectron. We’ll note Etot the total energy of scintillation photons.

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MU5PYN03 J. Bolmont

DYNODES - ANODE- A set of dynodes act as an electron multiplier

(secondary emission) ‣ The kinetic energy of photoelectrons is

converted into excitation energy of theelectrons in dynodes ➔ some of them can escape

‣ The higher the kinetic energy, the higher thenumber of electrons produced

‣ It's a random process !‣ Gain for a dynode :‣ For N dynodes, the overall gain is

‣ G is usually around ~105-108

- One (or more) anode(s) allow(s) to collect the electrons

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G = �N

�E

E=

1p� � 1

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� =number of secondary electrons emitted

number of primary electrons<latexit sha1_base64="bi/Ogdk7O9NbAsTc0QMu0OGD2lE=">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</latexit>

MU5PYN03 J. Bolmont

PHOTOMULTIPLIERS• Remarks:

- One photo-electron, if collected by the firstdynode, gives on average G (~105) électronssur l’anode‣ Random processes occurring at dynode level‣ The obtained signal can be measured !

- The gain δ (and so G) depends on the kineticenergy of the electrons, and so on the high voltage supplied to the PMT

- The gain δ hardly depends on the number of photoelectrons‣ The number of charges collected on the anode is proportional to the number of

photoelectrons, and so to the quantity of light !‣ Warning : charge saturation is possible when the gain and/or the amount of light is

too high. In extreme cases, the tube can even be destroyed.

115

G / V n (n 2 {6, ..., 9})

MU5PYN03 J. Bolmont

PMT POWER SUPPLY• PMT require a HV power supply (O(1 kV))• This voltage is divided over the dynodes so that each one has a correct biais

with respect to the next one. This is to allow the acceleration and multiplication of electrons towards the anode

• Voltages should be kept as stable as possible, especially for the last dynodes

116

MU5PYN03 J. Bolmont

IMAGING ATMOSPHERIC TCHERENKOV TELESCOPES

• Production of a shower of particles when a HE gamma hits the atmosphere

• Faint and short flash of Cherenkov light• Image of the shower on a fast camera in the

focal plane• Analysis of the image:

- Shape ➔ Type of the particle- Intensity ➔ Energy- Orientation ➔ Direction

• Stereoscopy: direct measurement of the origin of the γ, multiplicity of the images

117

Hadron Gamma

MU5PYN03 J. Bolmont

H.E.S.S.-1• High Energy Stereoscopic System• 4 telescopes located in Namibia• 12 m diameter, 15 m focal length• Field of view ~5°• Angular resolution < 0.1°• Energy resolution ~15%• Energy range from ~100 GeV to ~100 TeV• More than 80 sources discovered

118

120 m

MU5PYN03 J. Bolmont

H.E.S.S.-II

• Started in 2012• A new telescope• Total mirror area: 600 m2• Focal Length: 36 m• 2048 pixels• FOV: 3.2 deg• Weight: 2.8 tons• Energy threshold: ~30 GeV

119

MU5PYN03 J. Bolmont

H.E.S.S.-II• 128 « drawers »• 16 PM per drawer

• « Analog memory board » : Store analog signals until the trigger decision is taken

• « Slow-control board» : controls temperatures, HV, HVI

120

Photomultiplier tubePhotonis XP-29600

ISEG High Voltagegeneration board

Length = 58 cm

Analog memory boards

Slow Control Board(hidden)

Resistive divider board

MU5PYN03 J. Bolmont

PMT GAIN CALIBRATION• Gain calibration

‣ Find the correct HV of each PMT to get a nominal gain of 2x105

• The camera is lit with a faint flash of light‣ 1 p.e. produced on average at

photocathode‣ (1) — « Pedestal »‣ (2) — 1 p.e.

• Requires the camera is triggered externally.

121

Charge (ADC Counts)-11700 -11600 -11500 -11400

Cou

nts

per b

in

0

200

400

600

800

1000

1200

14000.1 ADC Counts± = 10.51σ = PEDσ

2PEDσ - 2

2σ = SPEσ

0.6 ADC Counts± = 19.10.5 ADC Counts± = 48.8SPE-PEDΔ

1 2

MU5PYN03 J. Bolmont

TRIGGERING• Two triggering levels

- At pixel level (L0)- At camera level (L1)

• L0 : charge above 4 p.e.- Compromise between (Night Sky

Background) and PM after pulses• L1 : more than 3.5 pixels above the

L0 threshold in a sector

• Dead time : 20 µs• Trigger rate < 5000 Hz

122

Drawer (16 pixels)Trigger sector (64 pixels)

L0 threshold (p.e.)0 2 4 6 8 10 12 14 16

L0 tr

igge

r rat

e (H

z)

1

10

210

310

410

510

610

710

810

910

MU5PYN03 J. Bolmont

PHOTOMULTIPLIERS• Advantages

- Linearity- Fast- Sensitive- Internal amplification- Low noise- Cost- Simple to use- …

123

• Drawbacks- Spatial resolution- Energy resolution- Limited quantum efficiency- Sensitive to magnetic fields- Size- Fragile- …

MU5PYN03 J. Bolmont 124

MU5PYN03 J. Bolmont 125

HOW TO DETECT PHOTONS3 - SILICON / GERMANIUM

DETECTORS

MU5PYN03 J. Bolmont

SEMICONDUCTORS• Periodic lattice of atoms → Crystal• Energy levels very close to each-other → Bands• Gap (or bandgap) → no energy level• For a semiconductor, with no electric field, the thermal energy can elevate

electrons from the VB to the CB

• Probability that an electron-hole pair is thermally generated per unit time:

127

Bande de valence

Bande de conduction

IsolantGap ~ 6 eV

GapEg

Eth << Eg

ConducteurPas de gap

Semi-conducteurGap ~ 1 eV

p(T ) = CT 3/2 exp

✓� Eg

2kBT

◆

<latexit sha1_base64="jWn60mmy5xgy0J6Klvau3BpKkK0=">AAAC/HicjVHLattAFD1WmtR183DTZTdDTcGBPGS3kG4KJqHQpQt+BKLESJOxPViWxGhUGoTzJ9l1F7LND2Tbrkv/oP2L3pnIkAelGSHpzLn3nJl7b5CEMtWu+6vkLDxZXHpaflZ5vryyulZ9sd5L40xx0eVxGKuDwE9FKCPR1VKH4iBRwp8GoegHk30T738RKpVx1NGniTia+qNIDiX3NVGD6m5S72ywD2y/c5y/3WnOvE1PfE2YF4qhrrMtb6h8nn8cjGZ5czLY68yYp+RorDcG1Zq77drFHoJGAWooVjuu/oSHE8TgyDCFQARNOISPlJ5DNOAiIe4IOXGKkLRxgRkqpM0oS1CGT+yEviPaHRZsRHvjmVo1p1NCehUpGd6QJqY8Rdicxmw8s86G/Zd3bj3N3U7pHxReU2I1xsT+TzfPfKzO1KIxxHtbg6SaEsuY6njhktmumJuzW1VpckiIM/iE4oowt8p5n5nVpLZ201vfxn/bTMOaPS9yM/wxt6QBN+6P8yHoNbcbhD+/q7X2ilGX8QqvUad57qKFT2ijS97nuMZ3/HDOnG/OhXN5k+qUCs1L3FnO1V/VcqN6</latexit><latexit sha1_base64="jWn60mmy5xgy0J6Klvau3BpKkK0=">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</latexit><latexit sha1_base64="jWn60mmy5xgy0J6Klvau3BpKkK0=">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</latexit><latexit sha1_base64="jWn60mmy5xgy0J6Klvau3BpKkK0=">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</latexit>

C : constant characteristic of the materialkB : Boltzmann constantEg : bandgap energy

MU5PYN03 J. Bolmont

SEMICONDUCTORS• Si atoms are tetravalent (4 neighbors)• Fermi level (Ef): by definition, it has 50% probability to be occupied• At low temperature, all the electrons participate in bonds between the atoms

128

Basse températureEth << Eg

E

Ef

P

0 1

Si

SiSi Si

Si

MU5PYN03 J. Bolmont

SEMICONDUCTORS• At higher temperature, some bonds are broken by thermal energy → (free)

electron - hole pairs creation• For an intrinsic semiconductor, electron density = hole density

‣ This is true only for completely pure semiconductors‣ Extremely difficult to realize in practice

129

Température ambiante

E

Ef

P

0 1

Si

SiSi Si

Si

ni = pi<latexit sha1_base64="3oFFrMguVt5ToWjSxdmASPzSgwM=">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</latexit><latexit sha1_base64="3oFFrMguVt5ToWjSxdmASPzSgwM=">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</latexit><latexit sha1_base64="3oFFrMguVt5ToWjSxdmASPzSgwM=">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</latexit><latexit sha1_base64="3oFFrMguVt5ToWjSxdmASPzSgwM=">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</latexit>

ni : concentration of e- in the conduction bandpi : concentration of holes in the valence band

MU5PYN03 J. Bolmont

INTRINSIC SEMICONDUCTORS• Silicium (Si), Germanium (Ge)• Si: 1,5x1010 cm-3 à 300 K

- Example of a detector: 1 cm x 1 cm x 300 µm = 0,03 cm3

- Thermal energy alone: 4,5x108 e-/hole free pairs at 300 K- A particle at MIP generates ~3x104 e-/hole pairs‣ The signal is lost in thermal noise !‣ It is necessary to reduce the number of free e-/hole pairs

130

Température ambiante

E

Ef

P

0 1

Si

SiSi Si

Si

MU5PYN03 J. Bolmont

P-TYPE DOPING• Very low concentration !

‣ ~1013 atoms/cm3 to be compared to ~1020 atoms/cm3 of Si or Ge• P-type doping: addition of impurities with 3 valence electrons

‣ B, Ga, etc.‣ electrons are missing → acceptor level added in the bandgap‣ This level is filled with e- from the BV because of thermal energy

131

E

0.04

5 eV

Ef

P

0 1

SiTrou en excès

BSi Si

Si

Ion accépteur

MU5PYN03 J. Bolmont

N-TYPE DOPING

132

• N-type doping: addition of impurities with 5 valence e-‣ As, P, etc.‣ Excess of electrons → donor level added in the bandgap‣ All the e- in excess in the donor level are transferred to the CB

because of thermal energy

E

0.05

4 eV

Ef

P

0 1

Sie- en excès

AsSi Si

Si

Ion donneur

MU5PYN03 J. Bolmont

PN JUNCTION• Obtained by diffusing P-type impurities on

one side of a N-type Silicon rod• Diffusion of (free) holes towards the N side

which capture e- • Diffusion of (free) e- towards the P side,

which fill the holes‣ Creation of a depletion region where

there is no free charge carrier• The N side is now charged +• The P side is now charged -

‣ Creation of an electric field gradient which stops the diffusion

‣ Equilibrium

133

N P

N

N

P

P

Migration des e- en excès

Migration des trous en excès

e-

Trous

Champ Electrique

MU5PYN03 J. Bolmont

DEPLETION REGION• It is possible to compute the width of the

depletion region starting from simple hypotheses on the geometry of the charge distribution:

• The net charge must be zero:• 1D Poisson equation to be solved:

• Using boundary conditions (the electric field should vanish at both edges of the distribution), we get the potential at contact (in Volts):

• And the width of the depletion region:

134

p(x)

V{x)

Vo ----~

-Xp Xn

⇢(x) =

⇢+eND 0 < x < xn

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NA xp = ND xn<latexit sha1_base64="4I0JWJB+OtiQaI5OMR/DdHjX57A=">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</latexit><latexit sha1_base64="4I0JWJB+OtiQaI5OMR/DdHjX57A=">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</latexit><latexit sha1_base64="4I0JWJB+OtiQaI5OMR/DdHjX57A=">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</latexit><latexit sha1_base64="4I0JWJB+OtiQaI5OMR/DdHjX57A=">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</latexit>

d2V

dx2= �⇢(x)

✏<latexit sha1_base64="GryrGrr3eyc1sFK6VZCezfNnW2Y=">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</latexit><latexit sha1_base64="GryrGrr3eyc1sFK6VZCezfNnW2Y=">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</latexit><latexit sha1_base64="GryrGrr3eyc1sFK6VZCezfNnW2Y=">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</latexit><latexit sha1_base64="GryrGrr3eyc1sFK6VZCezfNnW2Y=">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</latexit>

V0 =e

2 ✏(NDx2

n +NAx2p)

<latexit sha1_base64="bNafzRCGDTD0VNwjNq8veJFoL54=">AAAC9HicjVHLSsNAFD3G97vq0k2wCIqiaRF0I9THwpUo2CpYDck41cE0CZOJWEo/w507cesPuNVvEP9A/8I7YwpqEZ2Q5My595yZe68fByJRjvPaZXX39Pb1DwwODY+Mjo3nJiYrSZRKxsssCiJ55HsJD0TIy0qogB/Fknt1P+CH/uWWjh9ecZmIKDxQjZif1L3zUNQE8xRRbm654jr2ul2tSY81eatZrC5WeZyIIApbc7vu9rUbnhYXdt0N+9qNT4vzbi7vLDlm2Z2gkIE8srUX5V5QxRkiMKSogyOEIhzAQ0LPMQpwEBN3giZxkpAwcY4WhkibUhanDI/YS/qe0+44Y0Paa8/EqBmdEtArSWljljQR5UnC+jTbxFPjrNnfvJvGU9+tQX8/86oTq3BB7F+6duZ/dboWhRrWTA2CaooNo6tjmUtquqJvbn+pSpFDTJzGZxSXhJlRtvtsG01iate99Uz8zWRqVu9ZlpviXd+SBlz4Oc5OUCkuFQjvr+RLm9moBzCNGczRPFdRwg72UCbvGzziCc/WlXVr3Vn3n6lWV6aZwrdlPXwA65qg6A==</latexit><latexit sha1_base64="bNafzRCGDTD0VNwjNq8veJFoL54=">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</latexit><latexit sha1_base64="bNafzRCGDTD0VNwjNq8veJFoL54=">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</latexit><latexit sha1_base64="bNafzRCGDTD0VNwjNq8veJFoL54=">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</latexit>

d = xn + xp =

✓2✏V0

E

NA +ND

NA ND

◆1/2

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Dielectric constant

NA : acceptor concentration (= 0 for N type)ND : donor concentration (= 0 for P type)

MU5PYN03 J. Bolmont

DEPLETION REGION• Very often, the doping level is not the same on N and P side• If e.g. NA >> ND, then xn >> xp, the depletion region is

shifted towards the N side. Then,

• The conductivity is given by where µ is the mobility.

• For a N type doping, NA = 0, sowhere ρ is the resistivity (in Ω cm).

• We obtain:‣ The width d is given by charge carrier

mobility‣ For typical values V0 = 1 V, ρn = 20 kΩ cm, µe = 1350 cm2 V-1 s-1, ϵr = 12, d ≈ 75 µm → Small ! → High noise

135

p(x)

V{x)

Vo ----~

-Xp Xn

d ' xn '✓2✏V0

eND

◆1/2

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� = e(NDµe +NAµh)<latexit sha1_base64="EZ3TWnRI/r/lbg5YiloIsMwDppc=">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</latexit><latexit sha1_base64="EZ3TWnRI/r/lbg5YiloIsMwDppc=">AAAC53icjVHLSsNAFD2Nr1pfVZduhhahIkgqgm4EXwtXpYKtBVtCko51MC+SiVCKe3fuxK0/4Fb/RPwD/QvvjCn4QHRCkjPn3nNm7r1O5IlEmuZLzhgZHRufyE8WpqZnZueK8wvNJExjlzfc0AvjlmMn3BMBb0ghPd6KYm77jsdPnIt9FT+55HEiwuBY9iPe8e1eIM6Ea0uirGKpnYieb7NtxlmlZh2wtp9anK2ymrWr8fmKVSyba6Ze7CeoZqCMbNXD4jPa6CKEixQ+OAJIwh5sJPScogoTEXEdDIiLCQkd57hCgbQpZXHKsIm9oG+PdqcZG9BeeSZa7dIpHr0xKRmWSRNSXkxYncZ0PNXOiv3Ne6A91d369HcyL59YiXNi/9INM/+rU7VInGFL1yCopkgzqjo3c0l1V9TN2aeqJDlExCncpXhM2NXKYZ+Z1iS6dtVbW8dfdaZi1d7NclO8qVvSgKvfx/kTNNfXqoSPNso7e9mo81hCCRWa5yZ2cIg6GuR9jQc84skQxo1xa9x9pBq5TLOIL8u4fwfzPprR</latexit><latexit sha1_base64="EZ3TWnRI/r/lbg5YiloIsMwDppc=">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</latexit><latexit sha1_base64="EZ3TWnRI/r/lbg5YiloIsMwDppc=">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</latexit>

� =1

⇢n' eND µe

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d ' (2 ✏ ⇢n µe V0)1/2

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Table 10.1. Sorne physical properties of silicon and germanium

Atomic number Z Atomic weight A Density [g/cm2] Dielectric constant (relative) Intrinsic resistivity (300 K) (Qcm] Energy gap (300 K) (eV] Energy gap (0 K) [eV] Electron mobility (300 K) (cm2/Vs] Hole mobility (300 K) [cm2/Vs]

Si

14 28.1

2.33 12

230000 1.1 1.21

1350 480

Ge

32 12.6 5.32

16 45

0.7 0.785

3900 1900

MU5PYN03 J. Bolmont

DIRECT AND REVERSE BIAIS• Depletion region: no free

charge carriers• For a direct polarization (biais),

the depletion region is reduced‣ The electric field is too weak

to stop charges‣ The electrons can cross

• For a reverse biais, the depletion area is wider‣ The electric field is more

intense‣ The electrons cannot cross

136

N PZone de déplétion et

champ électrique réduits

Polarisation directe

Polarisation inverse

e- repoussés Trous repoussés

N PZone de déplétion et

champ électrique augmentés

e- repoussés Trous repoussés

MU5PYN03 J. Bolmont

FROM THE JONCTION TO THE DETECTOR• Depletion region = useful volume

- Every ionizing particle crossing it willproduce e-/hole pairs

- The e- (holes) are immediately diffused towards the N (P) side → current pulse at the electrodes proportional to the energy deposit‣ Very similar to what we have with gas detectors

• Depletion region thickness from ~100 µm to ~5 mm:• A biais of ~300 V gives d ≈ 1,3 mm

and a field E ≈ 2,3x105 V m-1 with values of slide 131 • Electrode voltage linearity:

137

Polarisation inverse

N Pe- repoussés Trous repoussés

Particule incidente

d ' (2 ✏ ⇢n µe Vbias)1/2

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V =Q

C= n

E

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E : energyw : energy needed to create a pairn : collection efficiencyC : capacitance

MU5PYN03 J. Bolmont

Si / Ge

138

• Si: Z = 14, bandgap at 300K: 1,1 eV- Average energy required to create a e-/hole pair : 3,76 eV at 77 K- Low Z: good for e-/alpha

• Ge: Z = 32, bandgap at 300K: 0,7 eV- Average energy required to create a e-/hole pair : 2,96 eV à 77 K- High Z: good for photons (cross section for photoelectric effect x60 as compared to Si)- Small bandgap: need to be

cooled down (liquid nitrogen, 77 K)

MU5PYN03 J. Bolmont

MORE ON RESOLUTION• It is reasonable to assume the formation of each charge carrier is a Poisson

process• If a total of N charge carriers are generated, the statistical fluctuations on

that number are simply √N• Since N is usually large, detector response will follow a Gaussian distribution• For a linear detector, H0 = K N, where K is a constant, and σ = K √N, and

since FWHM = 2.35 σ,

‣ This is the limiting resolution, due only to statistical fluctuations of charge carriers!

• Careful measurements show the resolution of some types of detectors is better than this…

139

R ⌘ FWHM

H0=

2.35KpN

N=

2.35pN

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MU5PYN03 J. Bolmont

MORE ON RESOLUTION• Processes which lead to the formation of charge carriers are

probably not completely independent → departure from Poisson statistics

• The Fano factor F is used to quantify the departure from pure Poisson statistics

• In that case, the resolution is now expressed as

• For Si/Ge detectors, F ~ 0.1• Scintillation detectors have a resolution compatible with Poisson

statistics, F = 1 140

w : energy required to create a pair

F ⌘ observed variance in N

Poisson predicted variance (= N)<latexit sha1_base64="FJ956h8jVPIe79sfH/lb7FJ92rE=">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</latexit>

R =2.35K

pNpF

KN= 2.35

rF

N= 2.35

rFw

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MU5PYN03 J. Bolmont

RESOLUTION• For a 1 MeV photon• NaI(Tl):

- 40000 photons/MeV- Light collection efficiency ~ 0,2- QE ~ 0,25- Np.e. ~ 2000- σ(E)/E = 1/sqrt(2000) ~ 2%

• Si:- 300000 e-/holes pairs per MeV- Essentially all carriers collected- For F = 0.1,σ(E)/E = sqrt(0,1/300000) ~ 0,06%

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MU5PYN03 J. Bolmont

SURFACE BARRIER DETECTORS• Junction semiconductor - metal

- N-type + Au- P-type + Al

• Similar situation than for PN junction• The depleted area is entirely in the

semiconductor‣ Easy to produce‣ Different thicknesses are possible‣ Good for alpha, beta spectroscopy‣ Drawbacks: fragile, sensitive to light

(photons of 2-4 eV for a bandgap of 1,1 eV)

142

Metal Semiconductor [~=--=conduction

band EFm~~~ •----E~

Metal EFm

:~~ alence band . - -

Junction _, . . ,_.... . ...,_ .. ... .. ...... ____. ___ . ·-·· -___.... __

__ ,__, -.. ... ...... ___ .........,._ _ ----·- ----·- . .,_. - -~---...-----·--------·-· .. , __ --- ·-- ···-·· --- ·--·- -· ......... -·,· - . ·- --· -··--·· . . ·-- -- ·-·- -- . . ·- ... ... --- . _.,_ -· . . . . . .. -· . . . . .. . . . . . ........ -- .. ·--

MU5PYN03 J. Bolmont

SILICON MATRIX• Example of AMS-02 Si-Tracker

- Substrate of high purity Si, thickness 300 µm, N-type

- Perpendicular n+ and p+ strips- Aluminium electrodes- Passage of a particle located

with a ~10 µm resolution

‣ Sensitive area: 6,2 m2

‣ 2264 elements‣ 200000 readout channels

143

a,

Electrode str i ps

High purity germanium

Charge -splitting resistor network

Electrode stri ps

Fig. detec trod< vider NS-:

MU5PYN03 J. Bolmont

SOME OTHER Si DETECTORS

• To conclude this part, we will focus on SiPM and APD

144

MU5PYN03 J. Bolmont

PHOTODETECTORS: APD• « Avalanche Photodiode »• High biais voltage

- Charge carriers are accelerated enough to create new e-/hole pairs (see the course on gas detectors)

- Formation of an avalanche, very fast process (< ns)

• High amplitude (gain ~ 100)• Poor energy resolution (fluctuations in the

avalanche), extremely sensitive to voltage changes

145

p+ n+ p

- /

i... 1 r1 + ' -r,.._

7t Light

..,_

--1-- -1 1 1 1 1 1 1 1

1 1 1

.------Drift region-------.i1 : :

y Multiplying region

MU5PYN03 J. Bolmont

PHOTODETECTORS: APD• QE ~ 80% at 500-800 nm → the

scintillator must be chosen accordingly• Log(gain) linear with the biais voltage

between 150 et 350 V‣ Exponential increase

• Above, Geiger region

146

MU5PYN03 J. Bolmont

PHOTODETECTORS: SI-PM• Si-PM = array of APDs in Geiger

mode- An individual cell cannot measure

an energy: on/off- Lot of cells: possibility to count

those which are hit → measure the photon flux

• Gain similar to the one of a PMT• Good charge resolution• No need for HV• Problems with « crosstalk »,

« afterpulses »…

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MU5PYN03 J. Bolmont

COMPARISON

148

MU5PYN03 J. Bolmont

SUMMARY• Semiconductor detectors

- Widely used in HE physics for tracking, energy measurements…- Fast (~ns)- Possible use as pixels or strips → good spatial resolution- Almost always doped- The biais voltage is used to create a depleted area where no current

pass, except when e-/hole pairs are created when a particle pass through the detector

- Signals on the electrodes are produced by the movement of charges near the electrodes

- A lot of different designs are possible (strips, pixels, APDs, SiPM, etc.)

149

MU5PYN03 J. Bolmont

EXERCICE 5.4• We’d like to design an instrument onboard a satellite allowing to

detect and find the track and energy for MeV photons. What should be the main characteristics of the detector(s) ?

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MU5PYN03 J. Bolmont

EXERCICE 5.5• Scintillators, gaseous and silicon detectors can be used to measure the

energy lost by a particle. The key parameter is the energy necessary to create a scintillation photon (or a e/ion pair, or a e/hole pair). Three cases are considered:• (1) Scintillator. 1 photon emitted for 100 eV deposited, 6% of

photons reach the PMT, QE = 30%• (2) Si detector. 3.6 eV are necessary to create a pair e/hole.• (3) Gaseous detector. 20 eV necessary to create a pair e/ion.

• What is the relative precision with which energy losses of (a) 100 keV, (b) 5 MeV, (c) 20 MeV can be measured in the three detectors? NB. We assume a Gauss statistics, the error on a count N is sqrt(N).

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MU5PYN03 J. Bolmont

EXERCICE 5.1• The quantum efficiency of the PMT is 15%, so the probability to emit

one p.e. when 1 photon hits the photo-cathode is p = 0.15. This is the probability of success. If 8 photons hit the photocathode (so 8 trials are made), and using the binomial law with n = 8, coefficients being (1, 8, 28, 56, 70, 56, 28, 8, 1),- P(X = 0) = 1 x 0.150 x (1-0.15)8-0 = 0.27- P(X = 1) = 8 x 0.151 x (1-0.15)8-1 = 0.38- P(X ≥ 1) = 1 - P(X = 0) = 0.73

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MU5PYN03 J. Bolmont

EXERCICE 5.2• From the value of dE/dx and ρ, we get the energy deposited for 1 cm:

1.65 MeV/cm.• For a length L (in cm !), the energy loss is then ∆E = 1.65 L MeV.• The number of scintillation photons is then nph = ∆E x 104 = 1.65x104 L.• Probability to get a photoelectron on the first dynode (= with a signal):

Pdet = 0.05 x 1 x 0.15 = 0.0075.• Number of detected photons: Pdet x nph = 123.75 L.• We are looking for X so that P(0,X) = 1 - 0.99 = 0.01. X is the expected

number of detected photons, that is Pdet x nph = 123.75 L.• Since P(0,X) = e-X = 0.01, then X = 4.605 = 123.75 L, so L = 0.37 mm.

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MU5PYN03 J. Bolmont

EXERCICE 5.3• By definition, R = Etot/Ea, so Etot = R Ea

• If N photons have an average energy of Eph, then we must have Etot = N Eph, and so N = Etot/Eph = R Ea/Eph

• To get 1 primary p.e., we must have N QE = 1, so Ea = Eph/(QE R) ≈ 250 eV.

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MU5PYN03 J. Bolmont

EXERCICE 5.4• Important points to consider :

• We want to detect photons from astrophysical sources ➔ no beam !

• We want to maximize the number of detections➔ large collection area

• At MeV, Compton scattering will dominate. We need to be able to track and measure the energy of both the scattered photon and the electron.➔ tracker + calorimeter

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MU5PYN03 J. Bolmont

EXERCICE 5.4

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MU5PYN03 J. Bolmont

EXERCICE 5.5• For (1), produce one photon per 100 eV... but in practice it's 0.06x0.3=0.018 useful

photons per 100 eV, i.e. 0.018x104 = 180 useful photons per MeV.• For (2), produce one e-h pair per 3.6 eV → (106 / 3.6)=280k e-h pairs per MeV• For (3), produce one e-i pair per 20 eV → (106 / 20) = 50k e-i pairs per MeV• Assume one useful charge carrier per pair for (2) and (3)• So for (1) : 0.1/5/20 MeV → 18 / 900 / 3600 photons → rel error : 24% / 3.3% /

1.7%• So for (2) : 0.1/5/20 MeV → 28k / 1.4M / 5.6M charge carriers → rel error : 0.6% /

0.08% / 0.04%• So for (3) : 0.1/5/20 MeV → 5k / 250k / 1M charge carriers → rel error : 1.4% /

0.2% / 0.1%• Relative error = sqrt(N)/N. Note that we've neglected other sources of uncertainty,

such as noise, or (for PMT) fluctuations in gain of dynode chain.

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