Semi-Conductor Detectors
Niels van Bakel
Intro - History
1200 strips, 50 x 50 mm2,
4.5 μm resolution
2
Intro - Future
http://benasque.org/2012imfp/talks_contr/307_Sergio.pdf
3
Intro - What I would like to achieve
Particle tracking vs. Imaging detectors
Mature technology
Complex and large field
Semi-Conductor Physics
Silicon Detector principle
Calculations - back of envelope
Simulations (GEANT) -details
State of the Art - Future
4
Silicon as detector material
Abundant
Conductance
Expensive: purity & low-noise
readout
Proven technology
Alternatives: Ge, Diamond,
GaAs, CdTe
Conductance:102 to 10−9 Ω−1cm−1
5
Silicon
Si: 1s (2e-), 2s (2e-), 2p (6e-), 3s (2e-) filled
3p (2e-) ⟹ 2 out of 6 filled
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Silicon - Energy band structure
Germanium
Silicon
GaAs
Conduction
band
Bandgap
Valence
band
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Intrinsic Semi-conductor Properties
8
•
Dispersion relation
•
Density of states
•
Fermi-Dirac distribution
•
Electron density
Intrinsic Semi-conductor Properties
Confusing:
compared to
previous fig
•
•
•
Carrier concentration in conduction and valence band:
No impurities:
m*e/m*h
Si
Ge
GaAs
0.8
2.1
0.13
Yields the Fermi-level:
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Silicon - Energy gap
SiO2
Si
10
Al
Intrinsic Semi-conductor Properties
Atomic number
Density [g/cm3]
Radiation length [mm]
Lattice constant [Å]
Gap energy @ 300/0K [eV]
ni @ 300K [cm-3]
Electron mobility [cm2/(Vs)]
Hole mobility [cm2/(Vs)]
NC @ 300K [cm-3]
NV @ 300K [cm-3]
Max. electric field [Vμm-1]
Intrinsic resistivity [Ω cm]
Energy e/h pair [eV]
Fano factor
Energy loss MIP [MeV/cm]
All numbers at 300K?
Si
14
2.33
93.6
5.4307
1.124/1.170
1.45 x 1010
1350
450
3.22 x 1019
1.83 x 1019
30
230000
3.62
0.12
3.87
Ge
32
5.32
23
GaAs
31/33
5.32
23.5
0.66 (77K)
2.4 1013
36000 (77K)
42000 (77K)
1.424
5 107
>8000
400
50
2.9 (77K)
0.13
3.3 108
4.2
0.10
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Recap - Silicon
•
Material: semi-conductor, used in industry, different materials for different
applications
•
Silicon crystal: the energy levels are N-fold degenerate, in a crystal this
leads to a forbidden gap (bandgap), for T=0 all electrons bound (in
valence band) ⟹ insulator, for T>0 some electrons jump to conduction
band ⟹ semiconductor. = weak conductivity
•
Band structure: ionization depends also on momentum transfer for Si &
Ge, hence ionization energy larger than bandgap
•
Intrinsic semi-conductor: from solving wave equation for electrons in
solids to the density of states of electrons (and holes), to Fermi level
•
•
Difference insulator, semi-conductor, metal - energy gap
Use/understand the properties for different materials
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Doped Semi-conductors
(ne ≠ nh)
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Doped Semi-conductors
D
A
Extrinsic region:
n-type: n ≈ ND
p-type: p ≈ NA
[NA = 0; n » p]
[ND = 0; p » n]
Typical concentrations:
Dopants: ≥ 1013 atoms/cm3
[Strong doping: 1020 atoms/cm3; n+ or p+]
Compare to Si-density: 5⋅1023/cm3
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Band model: n-doping in Si
T=0
T>0
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Resistivity
•
Resistivity
•
Mobility
[Ω cm]
[cm2/Vs]
~10 ns readout time in 100 μm thick Si
•
!intrinsic = 230 103 Ωcm
E.g. ND ≫ ni
Doping 0.2 ppb or 2 donor atoms
per 1010 Si atoms!
!doped = 463 Ωcm
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The pn-junction
e- ⇠
⇢ h+
Intrinsic Si:
free charge carriers
but only ∼2 × 104 signal electrons
∼109
Built-in voltage
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The pn-junction - Electric Characteristics
⇢ h+ / e- ⇠
y-axis is junction
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The pn-junction: forward and reverse bias
e- ⇠
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The pn-junction: I-V curve
Characteristic I(V) curve of a diode
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Basic Semiconductor Detector
Depletion width
Full depletion voltage for w = D
Capacitance of depleted detector
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Recap - Semiconductor detector
•
Doped semi-conductor: donors & acceptors, additional states in
the forbidden region NA and ND (Fermi level changes), effect of
impurities, changes in energy needed to excite electron
•
•
•
Band model
•
Basic semi-conductor detector
Resistivity
pn-junction: built-in voltage, electric characteristics, biasing,
leakage current
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LHCb Vertex detector
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The pn-junction - Si diode
Leakage current with ni(T)
defined by the life time of the
impurities Nt
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End first half
25
Strip & pixel sensors
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Signal generation
MIP
27
Noise contributions
• Shot noise - leakage current
• Thermal noise - bias resistor
• Thermal noise - strip resistance
• Load capacitance
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Ionisation yield - energy resolution
Energy resolution:
Intrinsic resolution of sensor
At T = 300 K
Since both fluctuations in lattice
excitations and in ionization are related
and this reduces the fluctuations in the
charge signal.
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Position resolution - S/N
•
•
Segmentation into strips, pads, pixels …
•
Improve resolution: calculate center of gravity
•
Delta electrons limit position resolution due to shift of
center of gravity
Geometric resolution
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Electric field
31
Charge collection
• Diffusion
• Drift
Use depletion width to get collection time
Assume constant mobility
(Partial) depleted
•Electrons:
•Holes:
32
Over depleted