Semiconductor detectors •properties of semiconductors •p-i-n diode •interface metal-semiconductor •measurements of energy •space sensitive detectors •radiation damage in detectors
Literatura: W.R.Leo: Techniques for Nucear and Particle Physics Experiments H. Spieler: Semiconductor Detector Systems G. Lutz: Semiconductor Radiation Detectors S.M. Sze: Physics of Semiconductor Devices Glenn F. Knoll: Radiation Detection and Measurement V. Cindro and P. Križan, IJS and FMF
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Why semiconductors? •
Energy resolution of a detector depends on statistical fluctuation in the number of free charge carriers that are generated during particle interaction with the detector material
•
Low energy needed for generation of free charge carriers → good resolution
•
Gas based detectors: a few 10eV, scintillators: from a few 100 do to 1000 eV Semiconductors: a few eV!
•
V. Cindro and P. Križan, IJS and FMF
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Comparison: radiation spectrum as measured with a Ge (semiconductor) in NaI (scintillation) detector
V. Cindro and P. Križan, IJS and FMF
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good energy resolution → easier signal/background sepairstion
V. Cindro and P. Križan, IJS and FMF
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Principle of operation: Semiconductor detector operates just like an ionisation chamber: a particle, which we want to detect, produces a free electron – hole pair by exciting an electron from the valence band: electron
conduction band forbidden band, width Eg
Eg hole
V. Cindro and P. Križan, IJS and FMF
valence band
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Drift velocity in electric field: vd = µ ⋅ E µ mobility different for electrons and for holes!
vd = µ × E
V. Cindro and P. Križan, IJS and FMF
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properties of semiconductors ρ [kg dm-3]
ε
Eg [eV]
µe [cm2V-1s-1]
µh [cm2V-1s-1]
Si
2.33
11.9
1.12
1500
450
Ge
5.32
16
0.66
3900
1900
C
3.51
5.7
5.47
4500
3800
GaAs
5.32
13.1
1.42
8500
400
SiC
3.1
9.7
3.26
700
GaN
6.1
9.0
3.49
2000
CdTe
6.06
1.7
1200
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Intrinsic (pure) semiconductor (no impurities)
n - concentration of conduction electrons N(E) density of states p - concentration of holes 1 F (E) = Et E − EF 1 exp( ) + n = N ( E ) F ( E )dE kT Ec EF Fermi energy level
∫
Pure semiconductor Neutrality: n=p
EF =
Ec + Ev 3kT mh ln( ) + 2 4 me
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Fermi-Dirac distribution
ratio of effective masses of holes and electrons Semiconductor detectors
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Ec energy of the bottom of conduction band Ev energy of the top of the valence band Eg =Ec-Ev width of the forbidden band
( Ec − EF ) ) n = Nc × exp( − kT ( EF − Ev ) ) p = Nv × exp( − kT n × p = n = N c N v exp( − 2 i
ni = N e N v exp(−
Eg 2kT
Nc, Nv: effective density of states in the conduction and valence bands
Eg kT
)
)
ni number density of free charge carriers in an intrinsic semiconductor (only for electrons and holes) At room themperature:
ni = 1.4 ×1010 cm −3 [Si ]
ni = 2.4 ×1013 cm −3 [Ge] 22
out of 10 atoms cm
−3
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Properties of semiconductors are modified if we add impurities Donor levels → neutral, if occupied charged +, if not occupied • Acceptor levels → neutral, if not occupied chargedi -, if occupied shallow acceptors – close to the valence band (e.g. three-valent atoms in Si – examples B, Al) shallow donors – close to the conduction band (e.g. five-valent atoms in Si – examples P, As)
•
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n-tip semiconductor, with added donors p-tip semiconductor, with added acceptors Binding energy of a shallow donor state is smaller because of a smaller effective mass and because of the diectric constant
for Si
13.6eV ⋅
meff m0
≈ 0.025eV
ε In most cases it can be assumed that all shallow donors (acceptors) are ionized since they are far from the Fermi level. Neutrality:
n + N A = p + ND As a result, the Fermi level gets shifted: EF − Ei = kT ln(
ND ) ni
if ND » NA , n type semiconductor
Ei − EF = kT ln(
NA ) ni
if NA » ND , p type semiconductor
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Properties of semiconductors with imputies (doped semiconductors)
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Resistivity of semiconductors vd = µ × E j =σ ×E =
ρ=
E
ρ
Charge drift in electric fieldu E, µ mobility
= e0 ⋅ vd e ⋅ n + e0 ⋅ vd h ⋅ p
1 e0 ( µ e n + µ h p )
specific resistivity
at room temperature, intrinsic semiconductor : ρSi = 230kΩcm
ρ Ge = 47Ωcm
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p-n structure At the p-n interface we have an inhomogenous concentration of electrons and holes difussion of electrons in the p direction, and of holes into the n direction At the interface we get electric field (Gauss law)
Potential difference
kT N a N d ln 2 Vbi = q ni
Vbi = built-in voltage difference, order of magnitude 0.6V
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To the signal only those charges can contribute that were produced in the depleted region with a non-zero electric field Thedetectors depleted region should cover most14 Semiconductor of the detector volume!
How to excrease the size of the depleted region: apply external voltage Vbias •
•
+ Vbias
if the potencial barrier is increased, the depleted region increases larger active volume of the detector – voltage in the reverse direction if the potencial barrier decreases, the active volume is reduced, we get a larger current, voltage is in the conduction direction. The height of the potential barrier: VB= Vbias+ Vbi
How large is the depleted region (xp+xn)? Neutrality: Na xp = Nd xn For the electric field we have the Poisson equation:
dV e0 N d ( x − xn ) 0 ≤ x ≤ xn = − dx εε 0 e0 N a (x + xp ) − xp ≤ x ≤ 0 εε 0 V. Cindro and P. Križan, IJS and FMF
ρ e e0 N a ,d d 2V = − = 2 εε 0 εε 0 dx
The electric field varies linearly, potential quadratically on the coordinate
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xn = (
2εε 0Vbias )1/ 2 e0 N d (1 + N d / N a ) 1/ 2
2εε 0Vbias xp = e0 N a (1 + N a / N d )
1/ 2
2εε 0Vbias ( N a + N d ) d = xn + x p = Na Nd e0
1/ 2
2εε 0Vbias example : N a >> N d ⇒ d ≈ xn ≈ e0 N d in terms of the spec. resistivity ρ :
increases as Vbias1/2
d ≈ (2εε 0 ρ n µ eVbias )
1/ 2
0.53( ρ nVbias )1/ 2 µ m n - type example: silicon d = 0.32( ρ V )1/ 2 µ m p - type p bias
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Semiconductor detectors
if ρ=20000kΩcm and Vbias=1 V → d~75µm
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Leakage current = current in the reverse direction difussion current: • difussion of minority carriers into the region with electric field • current of majority carriers with large enough thermic energy, such that they overcome the potencial barrier generation current: generation of free carriers with the thermal excitation in the depleted layer
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The probability of excitation is dramatically increased in the presence of intermediate levels. V. Cindro and P. Križan, IJS and FMF
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generation current:
j gen ∝ N tT exp(− 2
Eg 2kT
)
N t concentration of traps
→ high T – high generation current → wider forbidden band Eg , lower generation current Consequence: some detectors have to be cooled (Ge based, radiation damaged silicon detectors)
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metal-semiconductor interface (Schottky barrier) Χ electron affinity Φ work function Assumption Φm >Φs Vbi = Φm- Φs
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No external voltage
voltage in the conduction direction
voltage in the reverse direction
Ohmic contact: high concentration of impurities → thin barrier → tuneling
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Manufacturing of semiconductor detectorjev 1. manufacturing of monocrystals in form of a cylinder: • Czochralski (Cz) method
Liquid silicon is in contact with the vessel – higher concentration of impurities
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Float zone method:
No contact of the liquid semiconductor with the walls – higher purity of the material.
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Photolitography for pattern fabrication V. Cindro and P. Križan, IJS and FMF
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Typical tracking device in particle physics: silicon strip detector
pitch
20 cm 50 cm
Two coordinates measured at the same time Typical strip pitch ~50µm, resolution about ~15 µm
June 5-8, 2006
Course at University of Tokyo
Signal development in a semiconductor detector 1. interaction of particles with matter (generation of electron – hole pairs)
Z dE ∝ ρ for M.I.P. (minimum ionizing particle, Z = 1) A dx ion 1 dE MeV v ≈ 1.6 = ≈ 0.96 β −2 ρ dx gcm c 2. drift of charges in electric field causes an induced current on the electrodes (signal) – similar as in the ionisation detector
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dQd = qdx 1 E=− eN A x εε 0 E=−
Signal development For an electron-hole pair created at x0 in p-n detector, p-doped and higly n doped (n+)
1 x , with τ = ρεε 0 and = eN A µ h µ hτ ρ
electrons :
µ x dx = v = −µe E = e dt µh τ
µe t x(t ) = x0 exp µh τ e e µ e t - 1 Qe (t ) = − ( x(t ) − x0 ) = − x0 exp d d µ h τ dx x holes : = v = µh E = − dt τ t x(t ) = x0 exp − τ e e t Qh (t ) = ( x(t ) − x0 ) = − x0 1 − exp − d d τ
µh d for t < τ ln µe x0
Signal development 2 Relation between charge carrier propagation and induced current: detector volume V=S*d n = concentration of carriers I=j*S current through surface S I=e0*v*n*S For a single drifting electron: n*V=n*S*d=1 n*S=1/d and therefore for a single drifting electron we get: I=e0*v/d and dQ*d = e0*dx
Signal development 3 electrons : e e µ e t - 1 Qe (t ) = − ( x(t ) − x0 ) = − x0 exp d d µ h τ holes : e e t Qe (t ) = ( x(t ) − x0 ) = − x0 1 − exp − d d τ
For an electron-hole pair created at x0 for t < τ
µh d ln µe x0
dE / dx [MeV / cm ]
Number of pairs/cm
ε (eV)
Si
3.87
1.07 106
3.61
Ge
7.26
2.44 106
2.98
C
3.95
0.246 106
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gas
~keV/cm
a few 100
~30 ~3001000/ph.e.
Scint.
Si on average ~100 electron-hole pairs /µm
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Radiation damage Damage caused by: • Bulk effect: lattice damage, vacancies and interstitials • Surface effects: Oxide trap charges, interface traps.
C. Joram, Academic training, CERN, 2002
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Main radiation induced macroscopic changes
How to mitigate these effects? • Geometry: build sensors such that they stand high depletion voltage (500V) • Environment: keep sensors at low temperature (< -10ºC) Slower reverse annealing. Lower leakage current. Semiconductor detectorsC. Joram, Academic training, CERN,32 2002
Absorption of gamma rays •
Photoeffect
σ ph ∝ Z 5
1 E γ7 / 2
σ ph ∝ Z 5
1 ( Eγ >> me c 2 ) Eγ
( EK < Eγ < me c 2 )
gamma ray
photo-electron
• Compton scattering
σ ∝Z • Pair production
σ ∝Z
2
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V. Cindro and P. Križan, IJS and FMF
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V. Cindro and P. Križan, IJS and FMF
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V. Cindro and P. Križan, IJS and FMF
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Germanium detectors
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Energy resolution of gamma detectors Depends on the statistical fluctuation in the number of generated electron-hole pairs. If all energy of the particle gets absorbed in the detector – E0 (e.g. gamma ray gets absorbed via photoeffect, and the photoelectron is stopped): on average we get gamma ray _
Ni =
photo-electron
E0
εi
generated pairs
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εi ~ 3.6eV for Si ~ 2.98 eV for Ge Average energy needed to create an e-h pair
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If we have a large number of independent events with a small probability (generation of electron-hole pairs) → binominal distribution → Poisson Standard deviation – r.m.s. (root mean square): __
σ=
Ni
The measured resolution is actually better than predicted by Poisson statistics
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•
Reason: the generated pairs e-h are not really independent since there is only a fixed amount of energy available (photoelectron looses all energy). • Photoelectron looses energy in two ways: - pair generation (Ei ~ 1.2 eV per pair in Si) - excitation of the crystal (phonons) Ex ~0.04 eV for Si _
Nx
Average number of crystal excitations
_
Average number of generated pairs
Ni _
σ x = Nx
standard deviation
_
σ i = Ni Since the available energy is fixed (monoenergetic photoelectrons): Ei = energy needed to excite an Ei ∆N i = − E x ∆N x ⇒ Eiσ i = E xσ x electron to the valence band (=Eg)
E ⇒ σi = x Ei
_
Nx
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Width of the energy loss distribution Semiconductor detectors
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_
_
_
_
Ei N i + E x N x = E0 ⇒ N x =
E0 − Ei N i Ex
_
E σi = x Ei
E0 − Ei N i Ex _
⇒ σ i = Ni
F
_
make use of N i =
E0 εi
_ Ex ε i ( − 1) = F N i Ei Ei
Fano factor – improvement in resolution
F ~ 0.1 for silicon
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