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Semiconductor Detectors
 It may be that when this class is taught 10
years on, we may only study semiconductor
detectors
 In general, silicon provides
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Excellent energy resolution
Excellent charge carrier collection properties
Excellent position resolution (EPP)
High density (versus gas e.g.)
On the negative side, they are subject to radiation
damage
 Semiconductor detectors are found in many
fields of physical research and industry
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Semiconductor Detectors
 Let’s look at the energy required to produce a
signal
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Scintillation detectors – 1 photon / 100 eV
Ionization detectors – 1 ion pair / 16 eV
Silicon detectors – 1 electron-hole pair / 3.6 eV
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Semiconductor Detectors
 In EPP, the main use of silicon detectors is for
precision tracking

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Finn showed an expression for the momentum
resolution of a “tracker” in a magnetic field
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 x 8 p
  pT   s 

 2
pT
s
0.3BL2
Additionally, silicon detectors are used for b-quark
tagging
 b quarks are an indication of interesting physics
 t b-quarks ~ 1.5 ps
 Distance traveled in lab = gct ~ 4500 mm
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B-quark Tagging
SVT (secondary vertex tagging)
L
Secondary vertex
Primary vertex
IP (impact parameter) b = distance of closest
b
beam
approach of a
reconstructed track
to the true interaction point
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B-quark Tagging
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Silicon
 Intrinsic silicon
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Egap (valence – conduction) = 1.12 eV
Intrinsic electron density n = hole density p = 1.45
x 1010/cm3 (300K)
300K=1/40 eV
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Silicon
 Other properties of pure (intrinsic) silicon
 There are alternatives to silicon

Germanium (Ge), diamond, gallium arsenide (GaAs),
silicon carbide (SiC), …
 But the silicon’s wide technology base makes it
the usual choice for a detector
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Silicon
Recall the drift velo city v  mE
The mobilities determine the current in a semiconduc tor
C m
 A
J   ch v  2  3  
m s
m
J  eni me  mh E
We also have
J  σE
1 E
1
cm 
  
 J eni me  mh 
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Silicon
Consider an Si detector 1 cm x 1 cm x
300 mm
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In this volume there will be 4.5 x 108 free
charge carriers
A mip will produce 3.2 x 104 electron-hole
pairs
Not a great particle detector!
In order to make a useful detector we
need to reduce the number of free
charge carriers
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Doping
 n-type
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Replace Si with P, As, Sb (donor)
Electrons (holes) are majority (minority) carriers
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Doping
 p-type
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Replace Si with B, Al, Ga, In (acceptor)
Holes (electrons) are majority (minority) carriers
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Doping
 The result of doping is to increase the number
of charge carriers by adding impurity levels to
the band gap

n-type
p-type
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Doping
 Typical impurity concentrations are 1012-1018 /
cm3
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Detector grade silicon (1012 / cm3)
Electronics grade silicon (1017 / cm3)
To be compared with silicon density of 1022 / cm3
More heavily doped concentrations (1018-1020 / cm3)
are called p+ or n+
 In nearly all cases, the impurity concentrations
are large compared with the intrinsic carrier
concentration (1010/cm3)
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n ~ ND for n-type
p ~ NA for p-type
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Doping
Regardless of the concentrat ion we have from the law of mass action
np  n  AT exp
3
2
i
 Eg
kT
Also, since the semiconduc tor is neutral
ND  p  N A  n
In n - type material
n ~ N D and
1

   eN D m e
In p - type material
1
p ~ N A and    eN A m h

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p-n Junction
 Majority carriers diffuse into the boundary
 Resulting exposed donor (+) and acceptor (-) atoms
build up an E field that halts further diffusion
 A thin (< 100 mm) depletion region (no free charge
carriers) is created at the boundary
 No current flows (at equilibrium)
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p-n Junction
NA > ND
(a)Current flow
(b)Charge density
(c)Electric field
o
(d)Electrostatic potential
o : built in potential under zero bias
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Forward Bias p-n Junction
 Positive on p side, negative on n side
 The electrons can easily overcome the (~1V) contact
potential
 Current easily flows across the junction even for small
values of forward bias voltage
 The depletion region becomes smaller
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Reverse Bias p-n Junction
 Negative on p side, positive on n side
 Majority carriers are swept away from the boundary
region and the depletion region becomes larger
 Little current flows across the boundary
 Unless the reverse bias voltage becomes large enough
to overcome the space charge in the depletion region
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Reverse Bias p-n Junction
 Most silicon detectors are reversed biased p-n
junctions
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The charged carrier concentration in the depletion
region is now very low (~<100 / cm3)
Electron-hole pairs created by ionizing particles
will be quickly swept out of the depletion region
by the electric field
The motion of these electron-hole pairs
constitutes the basic signal for particle detection
As in gas detectors, the electrical pulse on the
electrodes arises from induction caused by
movement of the electrons and holes rather than
the actual collection of the charge itself
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Diode
 p-n junction is what makes a diode
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Note there is a diode “drop” of ~0.7V to get current
flowing in the forward bias region
With one exception, the breakdown (Peak Inverse
Voltage) region usually destroys a diode
PIV
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Diode
anode
p-type
n-type
cathode
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Depletion Depth
Consider an n - p junction
eN D for 0  x  xn
 x  
 eN A for  x p  x  0
 x 
d 2V
(Poisson' s equation)

2

dx
We also have N A x p  N D xn
Integratin g and using boundary conditions (dV/dx  0
at x  xn and x  -x p gives the electric field
dV    x  xn  for 0  x  xn

dx eN A x  x  for  x  x  0
p
p
eN D

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Depletion Depth
Another integratio n gives the potential

eN D  x 2
  xn x   C for 0  x  xn

 2

V x  

eN A  x 2
  x p x   C  for  x p  x  0
 2

The two solutions are equal at x  0 so C  C 
eN D 2
V  V0 at x  xn so V0 
xn  C
2
eN A 2
V  0 at x   x p so 0  
xp  C
2
e

then V0 
N D xn2  N A x 2p 
2
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Depletion Depth
Eliminatin g xn or x p using N A x p  N D xn
1/ 2


2V0

xn  
 eN D 1  N D / N A  
1/ 2


2V0

x p  
 eN A 1  N A / N D  
Usually one side or the other is more heavily doped
e.g. if N A  N D then xn  x p
1/ 2
 2V0 N A  N D 

d  xn  x p  
N AND 
 e
1/ 2
 2V0 

forN A  N D we find d  
 eN D 
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Depletion Depth
The main results are
 2V 
d 

 eN 
1/ 2
d  2Vm d 
1/ 2
1
since  
emN
d  2  11.7  55.4  1  480  104  104  1.6  1019   31mm
 e

cm 2
d  
V 
 cm 
Vs
 Vmm

Depletion depth at V  1V  31mm
V to fully deplete 300mm  100V
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Depletion Depth
 The depletion region acts like a capacitor
A
 eN 
C
 A

d
 2V 
1/ 2
 It is often the case that electronic noise is the
dominant noise source hence it is desirable to
have the detector capacitance as small as
possible

Large V and large d
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Semiconductor Detectors
Many varieties
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Si strip detector
Si pixel detector
Si drift chamber
CCD (Charged Coupled Device)
Surface barrier
PIN photodiode
Avalanche photodiode
a-Se + TFT (Thin Film Transistor) arrays
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