radiation detectors...radiation detectors w. udo schröder, 2009 38 stability and resolution •...
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Rad
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W. Udo Schröder, 2009
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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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Rad
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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+
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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