Radiation Detectors...Radiation Detectors W. Udo Schröder, 2009 38 Stability and Resolution • Anisotropic diffusion in electric field (D perp >D par). • Electron capture by electro+negative

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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+

∆E <n>≈Linearfor ∆E«E

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Driven Charge Transport in Gases

20 ( )exp

44

:

!

12 2

F ew E drift velocity

mean time between collisions

kT wD mobi

m mv

Mass depe

l

NdN x w tdx D

Charge Diffusion in Electric Fiel

tDt

d

ndence

e

ityE

τ τ

τ λ

µ µ

− ⋅

= ⋅ = ⋅

=

=

= ⋅ − ⋅

⋅ =

x

Pe(x)

x

Pe(x)

t0

t1 >t0

t2 >t1

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

x

Pe(x) Ex

( ); ( )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

Further ionization possible Amplification

Fluctuation-Dissipation Theorem

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Direct-Ionization and Amplification Counters

Single-wire gas counter (PC)

U0

C

-

- +

+

counter gas

gas

signal

R

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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 ∆ε: n= nI =ne= ∆ε /I number of primary ion pairs n at x0, t0

Force: Fe =-e·E= -e·U0/d = -FI

Energy content of detector capacitor C:

Cap

aci

tan

ce C

+

-

U0

∆U(t)

0

x0

xd

R Cs Signal

( ) ( ) ( )

( ) ( ) ( )

( ) ( )

( ) ( ) ( ) ( ) ( )

2 20

0 0

0

0

0

0

1)2

2)

1) 2)

e e e I I I

I e

C U 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 t

W t CU

W tC

U t

U Cd+ −

= − ≈

= − − −

= + +

+

∆ = = + −

⋅

∆

( ) ( )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 + −

+ − −

∆ = + − ∆

t0 te~µs tI~ms t

∆U(t)

0xC dε∆

Cε∆

Drift velocities (w+, w->0)

Total signal: e & I components

Both components measure ∆ε.Both components measure position of primary ion pairs

x0 = w-(te-t0)

For fast counting use only electron component.

Make position independent with Frisch Grid

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Frisch Grid Ion Chambers

0dFG

x0d

x

Anode/FG signals out

cathode

Shielding e- charge-collecting electrode from primary ionization track e- signal no x dependence

Wire mesh (Frisch grid) at position xFG @ UFG=const.

e- produce signal only inside sensitive anode-FG volume, ions are not “seen”.

not x dependent.“Drift chambers” exploit x-dependence

( ) ( ) ( )FGFG

U t w t t tCd

ε − −∆

∆ =

particle

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Electronic Pulse Shape

0

0 0

:,

( ) ln(1 )4

/ , /πε

πε µ µ

ε

−∆ ∝ ⋅ +

= =

=drift

Intrinsic pulse shape for PCtime t PC wire length L

q tU tL t

t CU mobility w Ecounter gas dielectric constant

t

t

∆U

∆U

long decay time of pulse pulse pile up, summary information

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

event 1

event 2

event 4

even

t 1

even

t 2

even

t 4

Use only electronic pulse component (differentiate electronic signal in pre-amp)

R

C∆U

Differentiation

∆U

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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.

∆E1 ∆E2 Eresidual Anodes

∆E

x

FG

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IC Performance

Eresidual (channels)

∆E

(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 ∆

= =

F<1 Fano factor

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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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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 ∆ U(t).

Bias voltage U0 creates charge-depleted zone

20

20

:

2.2

3.7n

p

Capacitance Si

U pF mmC

U pF mm

ρ

ρ

=

U0

+

+

+-n

p

∆U(t)

c

Rcs

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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 1µV ~ 0.5V/µOver-bias reduces dd

ORTEC HI detector

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Charge Collection Efficiency in SSDs

( )

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 EappTypical 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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Position-Sensitive Semiconductor Detectors

Gerber et al., IEEE TNS-24,182(1977)

x

y

Double-sided x/y matrix detector, resistive readout.

1 2

3 4

1 2 3 4

( )

( )

n x n

x x

y mm

y y

x L xQ Q Q Q

L LL yy

Q Q Q QL L

Q Q Q Q Q E

−= ⋅ = ⋅

−= ⋅ = ⋅

+ = + = ∝ ∆

R

R

R

R

Q

~2000 Ωcm, 300µ U0160V

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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 (SS-IC)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 10% solution: bundle in 4π-arrays GammaSphere,Greta EuroGam, Tessa,…

Superior energy resolution, compared to NaI

∆Eγ ~ 0.5keV @ Eγ =100keV

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Townsend (Gas) Avalanche Amplification

U0

M

IC Region

Non-linear

Region

( )

1 ( ) ;

: 1.ip ip

ipn primary InM i t dtn n

nM d Townsend coef

P

ficientα

= ∝

=

=∫

Amplification M

Radiation

U0

I

d

+U0~kV/cm

_Avalanche

Region

Gas or SS avalanche counters

Avalanche Formation

Townsend CoefficientElectron-ion pairs through gas ionization

0

0 0( ) exp

)

(

(

)

α

α

α

α

⋅

= ⋅ ⋅

⋅

′= ⋅

= =

′∫x

x

dn n dxfor const

n x n x d

e

x

n x n

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

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Avalanche Quenching

in Argon

A. Sharma and F. Sauli, Nucl. Instr. and Meth. A334(1993)420

Reduce λ and energy of ions by collisions with complex organic molecules (CH4, …).

Excitation of rotations and vibrations already at low ion energies

CH4

Organic vapors = “self quenching”

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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(∆E)

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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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Electronics: Charge Transport in Capacitors

Charges q+ moving between parallel conducting plates of a capacitor induce t-dependent negative images q- on each plate.

t

U

Connected to circuitry, current of e- from negative electrode is proportional to charge q+.

q+

q-

q-

conducting electrodes

Electronics

R e-

Simple charge motion, no secondary ionization/amplification

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Electron Transport

( )( ) ( ) ( ) ( )1

323

Pdew E D

mv P d

vε

ε ε λ ε ε ε εε ε

− ∂⋅ ⋅ ⋅ ∂

= =

∫ ∫

Multiple scattering/acceleration produces effective spectrum P(ε) calculate effective λ and τ:

Simulations

http://consult.cern.ch/writeup/garfield/examples/gas/trans2000.html#elec

( ) 2v mε ε=

Electron Transport:Frost et al., PR 127(1962)1621

V. Palladino et al., NIM 128(1975)323G. Shultz et al., NIM 151(1978)413

S. Biagi, NIM A283(1989)716

w- ~ 103 w+

http://consult.cern.ch/writeup/garfield/examples/gas/trans2000.html

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Stability and Resolution

• Anisotropic diffusion in electric field (Dperp >Dpar).• Electron capture by electro+negative gases,

reduces energy resolution• T dependence of drift: ∆w/w ∆T/T ~ 10-3

• p dependence of drift: ∆w/w ∆p/p ~ 10-3-10-2

• Increasing E fields charge multiplication/secondary+ ionization loss of resolution and linearity Townsend avalanches

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Free Charge Transport in Matter

xrms

NdN x Gaussiandx D tDt

x x Dtσ

= ⋅ − ⋅

= = =

20

2

exp44

: 2x

P(x)

t0

x

P(x)

t1 >t0

x

P(x)

t2 >t1

1D Diffusion equation P(x)=(1/N0)dN/dx

13

D v λ= ⋅ ⋅D diffusion coefficient,

<v> mean speed λ mean free path

Thermal velocities :

28 83

kTv vmπ π

= =

( ) ( )D ion D e−

Maxwell+Boltzmann velocity distribution

Small ion mobility

Documents

Radiation Detectors...Radiation Detectors W. Udo Schröder, 2009 38 Stability and Resolution • Anisotropic diffusion in electric field (D perp >D par). • Electron capture by electro+negative