Transcript Slide 1

Primary Ionization Track (Gases)
Oct 2001
2
incoming particle
ionization track
 ion/e- pairs
e-
I+
Minimum-ionizing particles
Linear
W. Udo Schröder
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
Oct 2001
3
P(x)
t1 >t0
x
P(x)

x 2 
 exp 

4
D

t
4Dt


N0
:
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
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
Oct 2001
4
P(x)
t1 >t0
x
P(x)
t2 >t1
x
W. Udo Schröder
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
Oct 2001
5
Ar
Ar+
CH4
CH4+
Ar+CH4 80+20 CH4+
W. Udo Schröder
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
v e   2e m
w- ~ 103 w+
Oct 2001
6
Simulations
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
W. Udo Schröder
http://consult.cern.ch/writeup/garfield/examples/gas/trans2000.html#elec
Oct 2001
7
Stability and Resolution
W. Udo Schröder
• 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+
Oct 2001
t
q+
+
R e
Electronics
W. Udo Schröder
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
-
Capacitance C
d
Oct 2001
9
+
R
Cs
U0
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)
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
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 
Oct 2001
10
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
C d
Use electron
component only
for fast counting.
t0
W. Udo Schröder
te~s
tI~ms
t
Frisch Grid Ion Chambers
x
cathode
d
x0
Oct 2001
11
particle
dFG
0
Anode/FG signals out
W. Udo Schröder
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, ions are not “seen”.

De
DU  t  
w  t  t  tFG 
CdFG
not x dependent.
x-dependence used in “drift
chambers”.
Bragg-Curve Sampling Counters
Sampling Ion chamber with
divided anodes
Oct 2001
12
isobutane
50T
DE/Dx
W. Udo Schröder
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)
Oct 2001
13
IC Performance
Energy resolution
 e2  F nip  F
De
I
F<1 Fano factor
Eresidual (channels)
W. Udo Schröder
Solid-State IC
+
+
-
n
Oct 2001
14
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
c
+
Semiconductor n-, p-, i- types
Si, Ge, GaAs,.. (for e-,lcp, g, HI)
DU(t)
Band structure of solids:
R
E
U0
e-
EF
Capacitance Si :
2.2

C 
3.7
W. Udo Schröder
Conduction
h+
2
rnU0 pF mm
2
r pU0 pF mm
-
Valence
+
Bias voltage U0 creates
charge-depleted zone
Ionization lifts eup to conduction
band  free
charge carriers,
produce DU(t).
Particles and Holes in Semi-Conductors
e
eC 0
eF
Fermion statistics:
Conduction Band
eeG
eV
h+
15
e  fe  e 
V  volume
nh  e 
23
2m  V


e  fh  e 
ne  nh !!
2
2
2 3
2 3
e F  e C  e G 2   e G 2 for e C : 0
Valence Band
Oct 2001
ne  e 
23
2m  V



 e  eF
1
f
e

1
+
exp




 e + eG 2  e
 kT
e  : fe  e   1 + exp 



kT




 e + e G 2  
h+ : fh  e   1 + exp 

kT



Small gaps eG (Ge) 
large thermal currents.
Reduce by cooling.
W. Udo Schröder



1
 e + eG 2 


exp
  kT

kT 25meV e G


1
ne2
ne
 2m 2 3 V
 ne nh  
 2 2 3

rms
 e 
exp   G 
 2kT 
2




 e 
e exp   G 
 kT 
 conductivity at T
Oct 2001
e- Potential Si Bloc
16
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
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 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
5
carrier-free space dn,p: d

3.3

10
rn, pU0  m
n, p
up to 1mm possible.
rn, p 20 k  cm, U0  500V
W. Udo Schröder
 d  70  m
Surface Barrier Detectors
EF
Metal
Junction
CB Semi
conductor
Oct 2001
17
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.
Insulation
Metal film
Insulating
Mount
Silicon wafer
depleted
dead layer
Ground
+Bias
Front: Au Back: Al
evaporated electrodes
W. Udo Schröder
Possible:
depletion depth ~ 100
dead layer dd 1
V ~ 0.5V/
Over-bias reduces dd
Metal case
Connector
ORTEC
HI detector
Charge Collection Efficiency
Heavy ions: Edeposit > Eapp = apparent energy due to charge
recombination, trapping. Light ions EdepositEapp
Typical charge collection times: t~(10-30)ns
EPhD : Edeposit  Eapp
18
Moulton et al.


a( Z , A)
Fit : EPhD Edeposit  10b(Z , A) Edeposit
a( Z )  2.230  10
5 2
Z + 0.5682
Oct 2001
b( Z )  14.25 / Z + 0.0825
a( A)  3.486  10
6 2
A + 0.5728
b( A)  28.40 / A + 0.0381
Affect also collection time
 lower signal rise time.
W. Udo Schröder
Ge gray Detectors
Ge detectors for g-rays use p-i-n Ge junctions.
Because of small gap EG, cool to -77oC (LN2)
Oct 2001
19
Ge Cryostate (Canberra)
Ge cryostate geometries (Canberra)
W. Udo Schröder
Properties of Ge Detectors: Energy Resolution
Superior energy resolution,
compared to NaI
Oct 2001
20
DEg ~ 0.5keV @ Eg =100keV
W. Udo Schröder
Size=dependent mall
detection efficiencies of Ge
detectors  10%
solution: bundle in 4arrays GammaSphere,
EuroBall, Tessa,…
Townsend Gas Amplification
Radiation
Nonlinear
Region
M
Oct 2001
21
IC Region
U0
d
I
U0
Amplification M
W. Udo Schröder
M
n
1

i(t )dt

nip
nip
 :  nM  d 1.Townsend coefficient
Avalanche Formation
Townsend Coefficient
Electron-ion pairs through
gas ionization
dn    n  dx
n( x)  n0  e  x for   const
Electrons in outer shells are more readily
removed from atom. Ionization energies
are smaller for heavier elements.
n( x)  n0  exp
  ( x)dx
x
0
Sparking and Spark Counters
/p
g
Impact ionization
Probability g
+
d
Oct 2001
23
Amplification by
impact ionization
e d
 e d  1
Sparking :g  e d  1
n
M

n0 1  g
Prevent spark by reducing for ions:
collisions with large organic molecules
 quenching
W. Udo Schröder
p (101  103 ) Torr
Avalanche Quenching
A. Sharma and F. Sauli, Nucl. Instr. and Meth. A334(1993)420
Oct 2001
24
in Argon
W. Udo Schröder
Reduce and
energy of ions by
collisions with
complex organic
molecules (CH4, …).
Excitation of
rotations and
vibrations already
at low ion energies
Effective Ionization Energies
Oct 2001
25
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
W. Udo Schröder
Amplification Counters
Single-wire gas
counter
signal
gas
Oct 2001
26
C
W. Udo Schröder
+
counter
gas
-
U0
+
Proportional Counter
gas
Rc
Anode Wire
W. Udo Schröder
C
Voltage U0  (300-500) V
R
-
U0
+
RA
27
Oct 2001
+
-
counter
gas
signal
RI
eUI
RI
e- q+
Anode wire: small radius
RA  50 m or less
Field at r from wire
U0
1
E (r ) 

ln( RC RA ) r
Avalanche RI RA, several
mean free paths needed
Pulse height mainly due to
positive ions (q+)
Pulse Shape
t
event 1
q
t
DU (t ) 
 ln(1 + )
4e L
t0
event 2
t0  e /  CU 0 , mobility   wdrift / E
e  dielectric constant
event 4
DU
event 4
event 2
event 1
28
DU
Oct 2001
Pulse shape : time t , wire length L
C
R
W. Udo Schröder
t
long decay time of pulse 
pulse pile up, summary
information
differentiate electronically, RCcircuitry in shaping amplifier,
individual information for each
event (= incoming particle)