Transcript Slide 1

Primary Ionization Track (Gases)
Det Ionizing Rad
2
incoming particle
ionization track
 ion/e- pairs
e-
I+
Minimum-ionizing particles
Linear
W. Udo Schröder, 2004
Argon
Xenon
CH 4
DME
dE/dx ( keV /cm )
0.32
2.4
6.7
1.5
3.9
n (ion pairs/ cm )
6
25
44
16
55
Statistical ionization process: Poisson statistics
Detection efficiency e depends on average
number <n> of ion pairs
e  1e
DE  n
Helium
GAS (STP)
(Sauli. IEEE+NSS 2002)
 n
GAS (STP)
Helium
Argon
thickness
e
1 mm
45
2 mm
70
1 mm
91.8
2 mm
99.3
Higher e for slower particles
Free Charge Transport in Gases
P(x)
1D Diffusion equation  P(x)=(1/N0)dN/dx
t0
x
x
Det Ionizing Rad
3
P(x)
t1 >t0
x
P(x)
rms
:
x 2   x  2Dt
1
D   v 
3
D diffusion coefficient,
<v> mean speed
 mean free path
Thermal velocities :
t2 >t1
x
W. Udo Schröder, 2004

x 2 
 exp 

4
D

t
4Dt


N0
dN

dx
v 
8kT

m
D(ion)
8
3
D(e )
v2
Maxwell+Boltzmann
velocity distribution
Small ion mobility
Driven Charge Transport in Gases
P(x)
Electric field E = DU/Dx separates +/- charges
dN

dx
t0
x
Det Ionizing Rad
4
P(x)
t1 >t0
x
P(x)
t2 >t1
x
W. Udo Schröder, 2004
E

x
 (x  w  t )2 
 exp 

4
D

t


4Dt
N0
e
E   drift velocity
2m
   v mean collision time
w
kT
D
e
w
 :
mobility
E
Cycle: acceleration – scattering
Drift and diffusion depend on field
strength and gas pressure p (or r).
w  w(E p);
D  D(E p)
Ion Mobility
GAS
ION
Det Ionizing Rad
5
Ar
Ar+
CH4
CH4+
Ar+CH4 80+20 CH4+
W. Udo Schröder, 2004
µ+ (cm2 V-1 s+1) @STP
1.51
2.26
1.61
Ion mobility + = 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/s
slow!
E. McDaniel and E. Mason
The mobility and diffusion of
ions in gases (Wiley 1973)
Electron Transport
Multiple scattering/acceleration produces effective spectrum P(e)
 calculate effective  and :
2 e
  P e  
1

w 
E e 
d
e
D

  e   v  e   P  e  de



3m
e  v  e  
3
Det Ionizing Rad
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Simulations
W. Udo Schröder, 2004
v e   2e m
w- ~ 103 w+
Electron Transport:
Frost et al., PR 127(1962)1621
V. Palladino et al., NIM 128(1975)323
G. Shultz et al., NIM 151(1978)413
S. Biagi, NIM A283(1989)716
http://consult.cern.ch/writeup/garfield/examples/gas/trans2000.html#elec
Det Ionizing Rad
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Stability and Resolution
W. Udo Schröder, 2004
• Anisotropic diffusion in electric field (Dperp >Dpar).
• Electron capture by electro+negative gases,
reduces energy resolution
• T dependence of drift: Dw/w  DT/T ~ 10-3
• p dependence of drift: Dw/w  Dp/p ~ 10-3-10-2
• Increasing E fields
 charge multiplication/secondary+ ionization
 loss of resolution and linearity
 Townsend avalanches
Electronics: Charge Transport in Capacitors
q+
Charges q+ moving
between parallel
conducting plates of a
capacitor influence tdependent negative images
q+ on each plate.
U
8
conducting
plates
q+
Det Ionizing Rad
t
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q+
+
R e
Electronics
If connected to
circuitry, current of
e- would emerge
from plate, in total
proportionally to
charge q+.
Signal Generation in Ionization Counters
Primary ionization: Gases I  20-30 eV/IP, Si: I  3.6 eV/IP
d
+
Det Ionizing Rad
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Capacitance C
+
x
Energy loss De: n= nI =ne= De/I
number of primary ion pairs n at x0, t0
x0
Force: Fe = -eU0/d = -FI
0
DU(t)
U0
Energy content of capacitor C:
C 2
U0  U 2  t    CU0 DU  t 

2
2) W  t   ne Fe  xe  t   x0  + nI FI  x I t   x0 
1) W  t  
neU0
 x I  t   xe  t  
+
d
1) + 2)
DU  t  
W. Udo Schröder, 2004
Ge: I  3.0 eV/IP
w
W t 
CU0

+
t  t
 t0 
ne  +
w  t   w   t    t  t0 

Cd 
Time+Dependent Signal Shape
De  +
DU  t  
w  t   w   t    t  t0 

Cd 
Det Ionizing Rad
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w + t 
De
C
103 w   t 
Total signal:
e & I components
Drift velocities (w+>0, w+<0)
Both components
measure De and
depend on position
of primary ion pairs
DU(t)
x0 = w-(te-t0)
De
x0
Cd
Use electron
component only
for fast counting.
t0
W. Udo Schröder, 2004
te~s
tI~ms
t
Frisch Grid In Ion Chambers
Suppress position dependence
of signal amplitude by
shielding charge+collecting
electrode from primary
ionization track.
Insert wire mesh (Frisch grid)
at position xFG held constant
potential UFG.
e+ produce signal only when
inside sensitive anode+FG
volume.
Signal
De
DU  t  
w   t   t  tFG 
CdFG
x
11
d
x0
Det Ionizing Rad
dFG
0
Anode/FG signals out
W. Udo Schröder, 2004
not x dependent.
x+dependence used in “drift
chambers”.
Bragg+Curve Sampling Counters
Sampling Ion chamber with
divided anodes
Det Ionizing Rad
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isobutane
50T
DE/Dx
W. Udo Schröder, 2004
Sample Bragg
energy+loss curve
at different points
along the particle
trajectory
improves particle
x identification.
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.
DE (channels)
Det Ionizing Rad
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IC Performance
Eresidual (channels)
W. Udo Schröder, 2004
Solid+State IC
n
i
p
+
+
+
Solids have larger density  higher
stopping power dE/dx  more ion pairs,
better resolution, smaller detectors (also
more damage, max dose ~ 107 particles
+
Semiconductors ideal types: n, p, I
Si, Ge, GaAs,..
DU(t)
Det Ionizing Rad
14
Band structure of solids:
E
U0
e+
EF
h+
+
W. Udo Schröder, 2004
Conduction
Valence
+
Bias voltage U0 creates
charge+depleted zone
Ionization lifts e+
up to conduction
band  free
charge carriers,
produce DU(t).
Det Ionizing Rad
e- Potential Si Bloc
15
Semiconductor Junctions and Barriers
eo-+ o+ +o
Donor Acceptor
ions
n
p
h+
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
space charge
o o o o o o
o o o o o o
d
Pure “intrinsic” Si can be made to
n-type or p-type Si by diffusing edonor (P, Sb, As) and acceptor ions
into Si. Junctions occur when both
are diffused into Si bloc from
different sides.
Diffusion at interface  e-/h+
annihilation  space charge
Contact Potential and zone
depleted of free charge carriers
Depletion zone can be increased
by applying “reverse bias” potential
Similar: Homogeneous
n(p)-type Si with reverse
bias U0 also creates
carrier-free space dn,p: dn, p  3.3  105 rn, pU0  m
rn, p
W. Udo Schröder, 2004
20 k  cm, U0  500V
 d  70  m
Surface Barrier Detectors
Insulation
Metal contact
Silicon wafer
Metal case
Det Ionizing Rad
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Connector
W. Udo Schröder, 2004