Radiation Detectors - University of Rochester€¦ · Radiation Detectors. W. Udo Schröder, 2007....

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W. Udo Schröder, 2007

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Detector Design Principles

• Ionization chambers (gas and solid-state)

• Proportional counters• Avalanche counters• Geiger-Müller counters• Cloud/bubble chambers• Track detectors

Ionization Detectors

• Phosphorescence counters• Fluorescence counters

(inorganic solid scintillators, organic solid and scintillators)

• Čherenkov counters

Scintillation Detectors

Associated Techniques

• Photo sensors and multipliers• Charged-coupled devices• Electronic pulse shape analysis• Processing/acquisition electronics

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Primary Ionization Track (Gases)

incoming particle ionization track ion/e- pairs

Argon DME

<n> (ion pairs/cm) 25 55

dE/dx (keV /cm )

GAS (STP)

2.4 3.9

Xenon

6.7

44

CH4

1.5

16

Helium

0.32

6

Minimum-ionizing particles (Sauli. IEEE+NSS 2002)Different counting gases

Statistical ionization process: Poisson statisticsDetection efficiency ε depends on average number <n> of ion pairs

1 neε −≤ −thickness ε (%)

Argon

GAS (STP)

1 mm 91.82 mm 99.3

Helium 1 mm 452 mm 70

Higher ε for slower particles

e- I+

ΔE } <n>≈Linearfor ΔE«E

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Effective Ionization Energies

Mean energy per ion pair larger than IP because of excitations

Large organic molecules have low-lying excited rotational states excitation without ionization through collisions =“quenching” additives

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Driven Charge Transport in Gases

τ

τ λ

μ μ

=

⎧ ⎫− ⋅⎪ ⎪= ⋅ −⎨ ⎬⋅⎪ ⎪

⋅

=

=

⎭

=

⎩

⋅

20 ( )

exp44

2

:

ew E drift velocity

mv meantime be

NdN

twe

Charge D

en colli

iffusion

sions

kT wD

x w tdx D tDt

in Electric F

mob

ield

ilitye E

x

P(x)

x

P(x)

t0

t1 >t0

t2 >t1

Electric field E = Δ U/Δ x separates +/- charges (q=ne+, e-)

x

P(x)E

x

( ); ( )w w E p D D E p= =

Cycle: acceleration – scattering/ionizationDrift (w) and diffusion (D) depend on field strength E and gas pressure p (or ρ).

λ

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Ion Mobility

GAS ION µ+ (cm2 V-1 s+1) @STPAr Ar+ 1.51CH4 CH4

+ 2.26Ar+CH4 80+20 CH4

+ 1.61

Ion mobility μ+ = w+/E

Independent of field,for given gas at p,T=const.

Typical ion drift velocities(Ar+CH4 counters):

w+ ~ (10-2 – 10-5) cm/μs

slow!

E. McDaniel and E. MasonThe mobility and diffusion of ions in gases (Wiley 1973)

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Signal Generation in Ionization Counters

Primary ionization: Gases I ≈ 20-30 eV/IP, Si: I ≈ 3.6 eV/IP Ge: I ≈ 3.0 eV/IP

Energy loss Δε: n= nI =ne= Δε /I number of primary ion pairs n at x0, t0

Force: Fe = -eU0/d = -FI

Energy content of capacitor C:

Cap

aci

tan

ce C

+

-

U0

ΔU(t)

0

x0

x

d

R CsSignal

( ) ( ) ( )

( ) ( ) ( )

( ) ( )

( ) ( ) ( ) ( ) ( )

e e e I I I

I e

CU U t

W t n F x t x n F x t x

neUx t x t

d

neU t w t w t t

W t CU U t

W t

Ct

CdU+ −

⎡ ⎤= − ≈⎣ ⎦

⎡ ⎤ ⎡ ⎤= − + −⎣ ⎦ ⎣ ⎦

⎡ ⎤= + −⎣ ⎦

+

⎡ ⎤Δ = = −

Δ

−⎣ ⎦

0

0

2 20

0 0

0

0

1)2

2)

1) 2)( ) ( )w t t t+ −

0

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Time-Dependent Signal Shape

( ) ( ) ( ) ( )

( ) ( )0

3

U t w t w t t tCd

w t 10 w t

ε + −

+ − −

⎡ ⎤Δ = − −⎣ ⎦Δ

∼

t0 te~μs tI~ms t

ΔU(t)

0xC dεΔ

CεΔ

Drift velocities (w+>0, w-<0)

Total signal: e & I components

Both components measure Δε and depend on position of primary ion pairs

x0 = w-(te-t0)

For fast counting use only electron component.

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Amplification Counters

Single-wire gas counter

U0

C

-

- +

+

counter gas

gassignal

R

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Proportional Counter

Anode wire: small radius RA ¡ 50 μm or less

Voltage U0 ¡ (300-500) V

counter gas

0 1( )ln( )

= ⋅C A

Field at r from wire

UE rR R r

e- q+

RA RI

UI RI

Ano

de W

ire

Avalanche RI RA, several mean free paths needed

Pulse height mainly due to positive ions (q+)

U0

C-

- +

+

gas

signal

R

Rc

E(RI)=

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Pulse Shape

0

0 0

: ,

( ) ln(1 )4

/ , /πε

πε μ μ

ε

−Δ ∝ ⋅ +

= =

=drift

Pulse shape time t wirelength Lq tU tL t

t CU mobility w E

dielectric constant

t

t

ΔU

ΔU

long decay time of pulse pulse pile up, summary information

differentiate electronically, RC-circuitry in shaping amplifier, individual information for each event (= incoming particle)

R

C

event 1

event 2

event 4

even

t 1

even

t 2

even

t 4

ΔU

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isobutane 50T

Bragg-Curve Sampling Counters

Sampling Ion Chamber with divided anode

Sample Bragg energy-loss curve at different points along the particle trajectory improves particle identification.

ΔE1 ΔE2 Eresidual Anodes

ΔE

x

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IC Performance

Eresidual (channels)

ΔE

(ch

an

nels

)

ICs have excellent resolution in E, Z, A of charged particles but are “slow” detectors.Gas IC need very stable HV and gas handling systems.

Energy resolution

2ipF n F

Iεεσ Δ

= =

F<1 Fano factor

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Solid-State IC

Solids have larger density higher stopping power dE/dx more ion pairs, better resolution, smaller detectors (also more damage and little regeneration max accumulated dose ~ 1023 particles

iSemiconductor n-, p-, i- types

Si, Ge, GaAs,.. (for e-, lcp, γ , HI)

Band structure of solids:

Valence

ConductionE

EF

+-

e-

h+

Ionization lifts e- up to conduction band

free charge carriers, produce Δ U(t).

Bias voltage U0 creates charge-depleted zone

20

20

:

2.2

3.7

n

p

Capacitance Si

U pF mmC

U pF mm

ρ

ρ

⎧⎪= ⎨⎪⎩

U0

+

+

+-n

p

ΔU(t)

c

R

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Particles and Holes in Semi-Conductors

Fermion statistics:

( ) ( ) ( )

( ) ( ) ( )

( )

( )

e e

h h e h

F C G G C

Fe

GkT meV G

Ge e h

m Vn f V volume

m Vn f n n

for

fkT

kT

m Vn n

n

nkT

ε

ε ε επ

ε ε επ

ε ε ε ε ε

ε εε

ε ε

εε

π

−

≈

⎡ ⎤⎢ ⎥= ⋅ =⎢ ⎥⎣ ⎦⎡ ⎤⎢ ⎥= ⋅ =⎢ ⎥⎣ ⎦

= − = − =

⎡ ⎤−⎛ ⎞= +⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦

+⎛ ⎞⎯⎯⎯⎯⎯⎯⎯→ −⎜ ⎟

⎝ ⎠

⎛ ⎞ ⎛ ⎞⎜ ⎟= = −⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠

2 3

2 3

2 3

2 3

1

25

22 32

2 3

2

2

2!!

2

2 2 : 0

1 exp

2exp

2exp

2

Ge rms

conductivitykT

at Tε⎛ ⎞

∝ −⎜ ⎟⎝ ⎠

∝exp2

0

ε

εF

Valence Band

Conduction Band

e-

h+

εG

εV

εC

( )

( )

e

Gh

G

h fkT

Occupation

e fkT

numbers f

ε ε

ε εε

ε−

−−

+

⎡ ⎤+⎛ ⎞= +⎢ ⎥⎜ ⎟

⎡ ⎤− +⎛ ⎞= +⎢

⎝ ⎠⎣ ⎦

⎥⎜ ⎟⎝ ⎠⎣ ⎦

1

12

: 1 exp

2: 1 exp

Small gaps εG (Ge) large thermal currents.Reduce by cooling.

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Semiconductor Junctions and Barriers

Need detector with no free carriers.Si: i-type (intrinsic), n-type, p-type by diffusing Li, e- donor (P, Sb, As), or acceptor ions into Si.

Trick: Increase effective gap Junctions diffuse donors and acceptors into Si bloc from different ends.Diffusion at interface e-/h+

annihilation space chargeContact Potential and zone depleted

of free charge carriersDepletion zone can be increased by

applying “reverse bias” potentialSimilar: Homogeneous n(p)-type Si with reverse bias U0 also creates carrier-free space dn,p:up to 1mm possible.

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

- - - - - - - -

- - - - - - - -

- - - - - - - -

o o o o o o

o o o o o o

o o o o o o

o o o o o o

o o o o o o

o o o o o o

n p

o o o o o o o o o o o o

e- h+

Donor Acceptorions

space charge

Si B

loc

e-P

ote

nti

al

d

5, , 0

, 0

3.3 10

20 , 500 70

n p n p

n p

d U m

k cm U V d m

ρ μ

ρ μ

−≈ ⋅

Ω = → ≈∼

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Surface Barrier Detectors

Metal film

Silicon wafer

Metal case

Insulation

Connector

EF

JunctionM

etal

CB Semi conductor

VB

Different Fermi energies adjust to on contact. Thin metal film on Si surface produces space charge, an effective barrier (contact potential) and depleted zone free of carriers. Apply reverse bias to increase depletion depth.

Ground +BiasFront: Au Back: Alevaporated electrodes

Insulating Mount

depleted

dead layer

Possible: depletion depth ~ 300μdead layer dd é 1μV ~ 0.5V/μOver-bias reduces dd

ORTEC HI detector

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Charge Collection Efficiency

( )

PhD deposit app

b Z A a Z APhD deposit deposit

Pulse height defectE E E

Fit

E E E

= −

= ⋅( , ) ( , )

:

:

10

High ionization density at low electric fields: Edeposit > EappLower apparent energy due to charge recombination, trapping. Low ionization density (or high electric fields): Edeposit ≈ Eapp

Typical charge collection times: t ~ (10-30)ns

Moulton et al.

5 2( ) 2.230 10 0.5682

( ) 14.25 / 0.0825

6 2( ) 3.486 10 0.5728

( ) 28.40 / 0.0381

a Z Z

b Z Z

a A A

b A A

−= ⋅ +

= − +

−= ⋅ +

= − +

Affects charge collection time signal rise time.Exploit for A, Z identification

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Si-Strip Detectors

Typically (300-500)μ thick. Fully depleted, thin dead layer.Annular: 16 bins (“strips”) in polar (θ) , 4 in azimuth (φ) (Micron Ltd.)

Rectangular with 7 strips

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Ge γ−ray Detectors

Ge detectors for γ-rays use p-i-n Ge junctions. Because of small gap EG, cool to -77oC (LN2)

Ge Cryostate (Canberra)

Ge cryostate geometries (Canberra)

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Properties of Ge Detectors: Energy Resolution

Size=dependent mall detection efficiencies of Ge detectors é10% solution: bundle in 4π-arrays GammaSphere,Greta EuroGam, Tessa,…

Superior energy resolution, compared to NaI

ΔEγ ~ 0.5keV @ Eγ =100keV

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Townsend Gas Avalanche Amplification

U0

M

IC Region

Non-linear

Region

( )

1( ) ;

: 1.

ip ipipn primary I

nM i t dt

n n

nM d Townsend coef

P

ficientα

= ∝

=

=∫Amplification M

Radiation

U0

I

d

+U0~kV/cm

_

Avalanche Formation

Townsend CoefficientElectron-ion pairs through gas ionization

{ }0

0 0

( )

( ) exp ( )

x

x

dn n dxn x n e for const

n x n x dx

α

α

α

α

⋅

= ⋅ ⋅

= ⋅ =

′ ′= ⋅ ∫Electrons in outer shells are more readily removed, ionization energies are smaller for heavier elements.

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Parallel Plate Counters: t-Resolution

sensitive layerd~1/α

e-

cathode -

anode +

R

+

PP

AC

PP

AC

U

p

ffffPPACs for good time resolution, U(p,f)f

Charges produced at different positions along the particle track are differently amplified.

non-linearity nip(ΔE)

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Sparking and Spark Counters

α/pγ

Impact ionization Probability γ

Prevent spark by reducing λ for ions: collisions with large organic molecules quenching additives, self-quenching gases

d

0

1 3

1 1

: 1(10 10 )

α

α

α

γ

γ

⋅

⋅

⋅

− −

= =⎡ ⎤− ⋅ −⎣ ⎦

⋅ ≈

−∼

d

d

d

Amplification byimpact ionization

n eMn e

Sparking ep Torr

Different cathode materials

-

+

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