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Semiconductor detectors
Main principalSemiconductor works like
´ionisation chamber´
- detection volume with
electric field
- energy deposition creates
pos. and neg charge carrier
- charges move along
the field lines
- current in external circuit
AdvantagesSolid state device -> ionisation density dq/dx high,
Si: dE/dx~39 keV/100µm
Semiconductor -> small band gap, very high energy resolution
High E-field -> fast charge collection (timing, efficiency)
High position sensitivity
Semiconductor detectors
Semiconductor crystals (Si, Ge)
Lattice constante a Si: 5.43 A, Ge: 5.65 A
Semiconductor detectors
Band gap between
valence and conduction
band:
Ge: 0.7 eV
Si: 1.1 eV
GaAs: 1.4 eV
Diamond: 5.5 eV
Ionisation energy to
create electron-hole pairs
is proportional to band
gap, but 2-3 higher.
Energy, momentum
conservation
=> phonon excitation
(chapter Fano factor)
Semiconductor detectors
extended wave function of
donator atoms e.g. P in Si
weak binding of elektrons
reduced Coulomb potential
2
)()(
atomElatticeE i
i
valence band
conduction band Donator
level
- bound level ~ 0.1 eV
below conduction band
- at room temp. (E=0.026 eV)
electrons are also in cond. band
Semiconductor detectors
valence band
conduction band
acceptor
level
equivalent situation with acceptor doping
Bound state ~ 0.01 eV above
band level.
Bor doping in Si Ev+0.045 eV
Semiconductor detectors
Properties of silicon and germanium
Band gap between valence and conduction band:
Ge: 0.7 eV
Si: 1.1 eV
Ionisation energy to create electron hole pairs
is proportional to band gap, but 2-3 higher.
Detector Properties Resolution
N
FR
Limitlstatistica 35.2
- Relative energy resolution increases with energy!
- In gas- and semiconductor detectors energy resolution is 3 – 4
higher!
Fano factor
- Assumption for Poisson statistics and energy absorbtion of
radiation is not properly right. Variation of energy losses is due to
energy conservation restricted.
(Statistics: events are not independent.)
NkN
Nk
H
FWHMR
LimitPoiss
35.235.2
0
Fano Factor
Extreme assumption: full energy must be detected due to
energy conservation -> no fluctuation
realistic scenario:
band gap (@ 80 K): 1.115 eV for Si,
0.73 eV for Ge
energy for electron hole pair : 3.62 eV for Si,
2.95 eV for Ge
Energy is not solely used to break bonds and to ionise.
Other excitations are e.g. phonons (lattice vibrations).
Division of energy deposition in electron hole pair creation
and phonon excitation.
Fano Faktor
- lattice vibrations
Nx excitatons -> Np phonons
- ionisation
Ni ionisations -> Nq charge pairs
- energy conservation
E0 = Ei Ni + Ex Nx
- variance of lattice excitations
sx= Nx1/2
variance of ionisations
si= Ni1/2
- fluctuations equilibrate between
themselve
Ex DNx + Ei DNi = 0
Ei si = Ex sx
si = Ex /Ei Nx1/2
eV 3.6
eV 1.1EE
eV 0.037E :silicon example
: charge of variance
1
:onconservatienergy
:pair charge creates ionisationevery
i
gi
x
000
00
k
FN
E
k
E
E
k
E
k
E
E
E
E
E
E
E
E
NEEN
k
ENN
i
i
i
x
iix
i
xi
xi
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iix
i
Qi
s
s
Fano Factor
Fano factor : F = 0.08
F = 0.1 measured
A detector device depends on a volume with high electrical
field, very low current and high signal charge.
Semiconductor: Si charge carrier density ~1011 cm-3 at 300 K
Intrinsic specific resistance: ~5.0 x 10 4 Wcm
(example: Si 1 mm thick, Ubias=500V, Idc=0.1 A is too high!
typical signal: 104-6 electrons or Is~10-8..-6 A
=> requires low leakage current of ~ 10-8-10-9 A)
Solution: semiconductor pn-junction allows for high field strength
at very low leakage current.
-> Doping of semiconductor is used to controle conductivity
needed concentration: ~1012 - 1018 cm-3
additional valence electrons from atoms of fifth main group
e.g.: P, As, Sb -> donators, n-type
missing valence electrons from atoms of third main group
e.g.: B, Al, Ga, In -> acceptors, p-type
Semiconductor detectors
Semiconductor detectors
pn junction without
external potential
diffusion of e and h
E- field and potential
at contact potential ~1V
charge carrier free zone
´depletion zone´
Electric field
Potential
conduction band
valence band
Semiconductor detectors
pn-junction with
external voltage:
- forward direction
pos. voltage at p-side
neg. voltage at n-side
=> large electron current
- reverse bias
neg. voltage at p-side
pos. voltage at n-side
=> higher potential barrier
larger depletion zone
0for C` )2
(
)(
0for C )2
(
)(
0for )(
0for )(
and for 0 with :nintegratio
:onconservati charge
0for )( :acceptors
0for )( :donators
)(
equationPoisson
2
2
2
2
xxxxxeN
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xxxxxeN
xV
xxxxeN
dx
dV
xxxxeN
dx
dV
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dV
xNxN
xxeNx
xxeNx
x
dx
Vd
ppA
nnD
ppA
nnD
pn
nDpA
pA
nD
Semiconductor detectors
-xp xn
Vb
V(x)
D
bn
DA
DA
DAbpn
DAA
bp
ADD
bn
nDpA
pAnDb
ppA
nnD
b
eN
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doping asymmetric with for
)(
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:zonedepletion ofwidth
)/1(
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)/1(
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:onconservati charge
) (2
for C
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for C 2
´ 0at x V(x) of continuity
22
2
2
Semiconductor detectors
-xp xn
Vb
V(x)
w
VVV
w
x
w
VVxE
VV
VweN
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dwd
VV
w
x
w
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eN
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bidbbid
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bib
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)(1
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: voltagebias
increased, isstrength field tageshigher volat
2 : is voltageingcorrespond
for depletedcomplety is essith thickndetector w
potential externalthout account wi into voltage takes
1)(2
)( :strength field
2with
2
Semiconductor detectors
Si semiconductor detectors
basic design
surface barrier detector with high density of electrons/holes at surface
- (n-typ Si and Au contact) or (p-typ Si and Al contact)
- structure e.g. n-Si – thin Si oxide layer – Au contact (40µg/cm2)
- charge carrier free zone => dE/dx measurement
- sensitive to light (Elight: 2 - 4 ev), sensitive to vapors…
Semiconductor detectors
Semiconductor detectors
Production silicon
micro-strip detector
Semiconductor detectors
losses:
- trapping
- recombination
Energy resolution
X-ray spectroscopy
DE/E=4% at 5 KeV
Semiconductor detectors
Light ions
a-spectroscopy
DE/E=0.8%
heavy ions
Puls heigth defect
- large E loss in dead zone
- nuclear vs. electronic loss
- recombination in plasma
He, C, SUran
