Download Lecture 9

Introduction to Silicon Detectors
E.G.Villani
STFC Rutherford Appleton Laboratory
Particle Physics Department
1
Outlook
• Part I : Introduction to physics of Si and
detection
• Part II: Examples of detectors
• Conclusions
2
Introduction
The Si detection chain
E
Sensing/
Charge creation
Charge transport
and collection
Si physical properties
Conversion
Si device properties
Signal
processing
Data TX
Si device topologies properties
all the boxes of the detection chain process based upon Silicon
1
Silicon Detector physics:
Silicon Physical and Electrical properties
Charge Transport Mechanisms
Detection principles
3
2
Detector system issues:
Conversion - pn junction Detection efficiency
Power
Microstrips
MAPS
Detector examples:
Silicon properties
After Oxygen, Silicon is the 2nd most abundant element
in Earth’s crust (>25% in mass)
Element of IV group in the periodic table
The crystalline structure is diamond cubic (FCC), with lattice spacing of
5.43 A
Each
atom
is
surrounded
by
4
neighbors
Si
•Polysilicon consists of small Si crystals randomly oriented; in α-Si there
is no long range order.
1.48A
4
Apart from its abundance, the key to success of Si is related to its oxide
SiO2, an excellent insulator (BV ~ 107 V/cm).
*Micro crystals but the flexible bond angles make SiO2 effectively an
amorphous: its conductivity varies considerably (charge transport in SiO2
via polaron hopping between non-bonding oxygen 2p orbitals)
Silicon electrical properties
Silicon Band structure
The electronic band structure can be obtained by solving many-body SE in presence of periodic
potential of the crystal lattice: Bloch functions
T  U   E  n,k r   un,k r e jkr  En k 
~ a wave associated with free motion of electrons modulated by the periodic solution un,k. The energy
E is periodic in k so is specified just within the 1 st unit cell of the reciprocal lattice (the Brillouin zone).
5
VB
* The appearance of Energy BAND GAP,
separating CB and VB (semiconductor)
CB
* The 6 CB minima are not located at the center
of 1st Brillouin zone, Indirect BAND GAP
Silicon electrical properties
Ph: DQ~107 m-1
DQ~1010 m-1
p/a
The indirect BG of Si requires higher energy for charge excitation, because energy and
momentum must be conserved (Phonon-assisted pair creation/recombination)
 In Si an average of 3.6 eV is required for pair creation
6
Silicon electrical properties
The detailed band structure is complicated: usually quasi-equilibrium simplifications
are sufficient to study the charge transport.
Assuming that the carriers reside near an extremum, the dispersion relationship
E(k) is almost parabolic:
E k  
2 k
2
2m0*
2m 
 g E  
* 3/ 2
0
2 3
2p 
E  Eo
2
2 k
1
k  p


E k  

v


E
k


k
2m0*

m0* m0*

dk t 
d  p

   rV  F
dt
dt
Under the assumptions of small variation of the electric field, the carrier dynamics
resembles that one of a free particle, with appropriate simplifications.
The effective mass approximation takes into account the periodic potential of the
crystal by introducing an effective carrier mass ( averaged over different longitudinal
and transverse masses) . The lower the mass, the higher mobility (µ  1/m*)
Similar approach used to calculate the E(k)
for phonons.
7
Silicon electrical properties
The carrier density is calculated from:
• The density of states g(E);
• The Fermi distribution function F(E);
CB
At equilibrium the carrier density in CB and VB is obtained
by integrating the product:
VB
nD   g D E F E dE  NC /V e EcEv / kT  ni  pi
3
F E  
2
1
2
1
 E  EF 
1  exp

 kT 
pn  ni  N C NV e
 
 Eg / kT
10
20
@ T  300 K
*Fermi level: energy level @ 50% occupancy
0
In intrinsic Si a creation of e in CB leaves behind a hole in VB,
that can be treated as an e with positive charge and mobility of
the band where it resides
In pure silicon @ room temperature about 1 every 1012 atoms
is ionized
The density of states gD(E) depends on the dimension
8
Silicon electrical properties
Conduction of Si intrinsic @ T = 300K:
σ = q(μn +μp) ni = 3.04x10-6mho-cm ->329 kOhm-cm
By adding atoms of dopants, which require little
energy to ionize( ~10’s mEV, so thermal energies @
ambient temp is enough) we can change by many
orders of magnitude the carrier concentration.
Doping concentration: 1012 to 1020 cm-3
In crystalline Si ~ 5*1022atoms cm-3
In equilibrium the relationship between carrier
concentration and E is the same as in the intrinsic
case:
pn  ni2  N C NV e
 
 E g / kT
 1020 @ T  300K
e.g . : N D  1017  pn  pN D  p 
9
ni2
 103
ND
Charge transport
Charge transport:
The charge transport description relies on semi-classical Boltzmann Transport
Equation (BTE, continuity equation in 6D phase space)



f r , k , t 1
F
f r , k , t
  k E k   r f r , k , t     k f r , k , t  
t


t
 
n r, t 
1
V
 f r , k , t 
coll
Q conservation
q
vk  f r , k , t 
V k
P conservation
 
1
E k  f r , k , t 
V k
E conservation
W r, t 
 S r , k , t 
k
 
J r, t  

The distribution function f(r,k) can be approximated near equilibrium:
Near equilibrium
equilibrium
0
10
k

f r , k , t
t


coll
f  f0
f
Charge transport
Under (many) simplifying assumptions the 1st moment of BTE gives the Drift Diffusion model
(DD, in many textbooks ‘The semiconductor equations’):
J n  qn n E r   qDnn
Drift term
Diffusion term
J p  qp p E r   qDp p
n 1
   Jn Un
t q
p
1
    J p U p
t
q
  V   p  n  N D  N A 
Even in low charge injection regime, a small E renders the drift term >> diffusion term
DD expresses momentum conservation: it becomes invalid when sharp variation in energy
of carriers occur (due to steep electric field gradient as in deep submicron devices)
 When feature size is 0.’sμm the DD model becomes invalid: higher moments required to
express
energy conservation (hydrodynamic/Quantum transport/MC…computational electronics)
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Detection principles
When a charged particle penetrates in matter, it will interact with the electrons and nuclei
present in the material through the electromagnetic force: the charged particle feels the EM
fields of nuclei and electrons and undergoes elastic collisions.
If the particle has 1 MeV energy or more, like in nuclear phenomena, the energy is large
compared to the binding energy of the electrons in the atom: to first approximation,
matter can be seen as a mixture of free electrons and nuclei at rest.
Maximum energy transfer in the elastic collision:
•
collisions with nucleus the particle loses little energy, its momentum can be changed
remarkably
• collisions with electrons the particle can transfer large energy to electrons (which can
have enough energy to travel macroscopic distances)
 most of the energy loss due to collisions with electrons, most of change of direction due
to
collisions
with
nuclei
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Detection principles
 Semiconductor detectors are mostly based on Ionization: the detection of
electron–hole pairs created in the semiconductor material by ionising radiation.
Advantage
of
semiconductors
detectors
compared
to
gas
detectors:
•
The amount of energy needed to produce free pair of charge ( around 1/10th in
semiconductors
compared
to
gas)
•
Higher
•
High carrier mobility can improve radiation hardness;
•
Very well developed semiconductor technology implies higher reliability and lower
cost;
•
Can be operated at room temperature;
density
of
semiconductor
means
higher
charge
signal;
Silicon detectors are commonly used in HEP (i.e. E > 1 GeV) used to localise charged
particle trajectories by stacking them onto several layers
13
Detection processes
A: Ionization: by imparting energy to break a bond, electrons are lifted from VB to CB then
made available to conduction. Most exploited concept ( ionization chambers, microstrip, hybrid
pixels, CCD, MAPS…)
B: Excitation: Charge or lattice (acoustic or optical phonons) some IR detectors, bolometer
CB
Quantized levels
VB
14
Detection principles
Ionization energy loss (/ density) : Bethe formula for charged particles through matter
due to interaction with electrons
0.2 <  < 1
15
Detection principles
Ionization energy loss (/ density) : Bethe formula + corrections
Z: charge of particle
: density of material
: relativistic parameter
Ar: relative atomic weight
I: mean excitation potential
Tmax: max energy transfer
: density correction term
c: speed of light
Losses due to relativistic
stretch, bremsstrahlung
emissions
 Bethe formula valid if velocity of particle is larger
than orbital electrons velocity
Nuclear stopping dominates low energy collisions
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Detection principles
In
Silicon
a
Minimum
Ionization
Particle
releases

<390>
eV/m
the average energy required to produce electrons /holes pairs in Silicon is 3.62 eV
 Approximately an average of 108 electrons / hole pairs generated in Silicon / m
A typical wafer Silicon is  300 m thick ->  32,000 electrons / hole pairs on average
generated in a standard thickness size Silicon detector by a MIP
17
Detection principles
Whilst the Bethe formula describes the average energy loss of charged particles through
matter, one has to consider also the fluctuations of such energy loss by ionization to
estimate the most probable value of energy loss.
 These fluctuations in energy loss in thin (i.e. thin compared to the particle range)
detectors, due to delta electrons, are described by a Landau probability density function
In a typical 300 μm thick sensor:
* 32000 electrons / holes pair generated on average
* 21700 electrons / hole generated most probable
18
MPV of energy loss normalized to the mean loss of a
MIP
Detection principles
As the particle penetrates in the medium, its
energy loss per unit length will change. The energy
loss increases towards the end of the range. Close
to the end it reaches a maximum and then abruptly
drops to zero.
This maximum of the energy loss of charged
particles close to the end of their range is referred
to in the literature as the ‘Bragg peak’.
 For example, this is of particular importance for
hadron therapy applications, where the aim is to
maximise the energy deposited at a specific point
within the human body and spare the neighbouring
ones.
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Detection principles
Electromagnetic interactions of Charged Particles:
Electrons: excitation and ionisation of atoms along the very irregular trajectory. At higher
energies, bremsstrahlung loss mechanism becomes important. For energies > 100 keV,
electrons will lose about 2 MeV/cm multiplied by the density;
Muons: very high energy muons can travel kilometres in matter before losing all
energy
Positrons: same behaviour of electrons, but after coming to rest, a positron will annihilate
with electrons that are always present. This annihilation gives rise to a pair of back-to-back
gamma rays of 511 keV. Exploited in PET.
Protons: higher ionisation compared to electrons but less than alpha particles.
Straight trajectory. The range in solids is of the order of 1 mm.
Alpha particles: The energy loss of alpha particles is of the order of 1000 MeV/cm times
the density of the medium. Range of only tens of microns in solids and a few centimeters
in gases. Straight trajectory.
20
Detection principles
Interactions of photons
X-rays: photons in the energy range of 1 – 100 keV
Gamma rays: photons of energy > 100 keV
Photoelectric process: a photon undergoes an interaction with an atom and completely
disappears. The energy of the photon is used to increase the energy of one of the electrons in
the atom. The electron becomes free or there is Auger emission.
Compton scattering: elastic collision between a photon and an electron.
Pair production: If the energy of the photon is at least two times larger than the
mass of an electron, the energy of the photon can be used to create an electron
and positron pair in the nucleus electric field.
21
Detection principles
Interactions of photons
10 eV
22
1 keV
1 MeV
1 GeV
.1 TeV
Detection
MIP charge density
n
Photoelectric charge density
dE 1 1

 3 1015 cm 3
2
dx  i p  R
R
 v
I
 110nm
A MIP forms an ionization trail of radius R
when traversing Si, creating ~ 100 e-/μm
I z   I o e   E z
z  

n
Pin
   z
  e
 5.6 106 e  / m
h
An optical power of -60dBm (= 1nW) of 1keV
photons generates ~ 6*106e-/μm
h
 1015 cm
2m E
L  0.5  1107 cm

Low injection regime:
The associated wavelength is much smaller than mean free path:
Each charge is independent from each other;
The dynamics of generated carriers does not require QM
The generated charge is too small to affect the internal electric field
23
High injection regime:
Plasma effects
The internal electric field can be affected by
the generated charge
Half summary
E
Sensing/
Charge creation
Charge transport
and collection
Si physical properties
Physical
characteristics:
Quasi equilibrium;
Homogeneity;
‘Room’ temperature;
Non degenerate Si;
Under conditions of
• quasi stationary conditions
• non degenerate semiconductor
• not small feature size
• low injection
•…
24
Conversion
Si device properties
Charge transport:
Charge generation:
Big devices, DD
adequate;
Ionization: Small
injection, QM not
needed;
Small injection, electric
field as static;
Stopping power,
average ionization
energy, fluctuations
Outlook
• Part I : Introduction to physics of Si and
detection
• Part II: Examples of detectors
• Conclusions
Detectors examples
 The working principle of almost all present-day electronic devices is based on
the pn semiconductor junctions.
The same principle is the basis of the use of semiconductors as detectors for
ionising radiation.
Strip / pixel detectors
HEP, Scientific applications
PN junction
Monolithic Active Pixel Sensors (MAPS)
Consumer and scientific applications
Charge Coupled Devices (CCD)
Imaging, scientific and consumer applications
26
Detectors examples
Almost all HEP experiments use Si detectors:
The high density track region usually covered by pixel detectors; by strip
at larger radius (cost reason)
27
Signal conversion: The pn junction
Homojunction: two pieces of same semiconductor materials
with different doping levels:
• In thermal equilibrium, the Fermi level equalizes throughout the
structure
F
• thermal diffusion of charge across the junction leaves a depleted
region, with the ionized dopants : an electric potential Φ, and a field
F, develops
• the charge concentration depends exponentially on Φ:
 0
In equilibrium J = 0
0  qnn E r   qDnn  n  n0e
D
Vt
0  qp p E r   qDpp  p  p0e

D
Vt
• by applying a small voltage to decrease the barrier, the charge
increases exponentially
• by applying a voltage to increase the barrier, the depleted region
Increases
Unidirectionality of current characteristics
28
Signal conversion: The pn junction
• when charge is generated in the depleted region is swept
across by the electric field sustained by the ionized dopants
and the biasing.
 PN junction as signal converter: capacitor with a F across
W
• A device with a large depleted region can be used to
efficiently collect radiation generated charge (Solid state
ionization chamber)
• the capacitance is a source of noise: lower capacitance (large
depleted region) increases the S/N
Depletion width W 
Capacitance
29
C=
2Vb N a  N d
q Na  Nd
qe N a × N d
×A
2Vb N a + N d
The full depletion voltage is the minimum voltage at which the bulk of the sensor
is fully depleted. Signal
The operating
voltage is usually
chosen
tojunction
be slightly higher
conversion:
The
pn
(over depletion).
 To achieve large W high field region:
• Low doping (high resistivity)
• Large voltages
• typical values:
Na= 1015 cm-3,Nd= 1012
W (0V) ≈ 23 μm
W(100V) ≈ 360 μm
reverse bias voltage V [V]
High-resistivity material (i.e. low doping) requires low depletion voltage.
Depletion voltage as a function of the
material resistivity for two different
detector thicknesses (300 µm, 500 µm).
resistivity r [kOhm cm]
Depletion voltage vs. resistivity
ay 2011
30
Thomas Bergauer (HEPHY Vienna)
40
Detectors examples
Strip detectors
(high res)
F
≈ 300μm
80μm
Q transversal diffusion
Vbias ~100’sV
Array of long silicon diodes on a high resistivity silicon substrate
A strong F in the high resistivity Si region helps collect charge efficiently.
 The high resistivity Si is not usually used in mainstream semiconductor industry:
Hybrid solution: detector (high resistivity) connected (wire/bump-bonded) to the readout
electronic (low resistivity)
31
Detectors examples
ATLAS SCT RO ASIC (ABCD3TA)
12 RO ASIC
768 Strip Sensors
128 channels/ASIC
RAD-HARD DMILL technology
ASICS glued to hybrid
40 MHz Ck
ATLAS SCT
4 single-sided p-on-n sensors
2x2 sensors daisy chained
Stereo angle 40 mrad
Strip pitch 80 um
768 channels/side
Binary RO
Bias Voltage up to 500 V
Operating temperature -2 C
Space point resolution: rPhi 17um / z 50 um
Power consumption: 5.6 W (initially ) to 10 W ( after 10y)
Rad hard upto 2x10^14 1-MeV n eqv/cm2
32
Detectors examples
ATLAS SCT
61 m2 of Si
6.3 * 106 channels
50 kW total power consumption
1 barrel
-
4 layers
-
2100 modules
2 endcaps
-
9 disks/each
-
988 modules
2 T solenoidal field
33
Detectors examples
ATLAS Tracker overview
Pixel: (n+ on n) 1.8m2, 80M channels
SCT: 6.3M 61 m2 channels
TRT: 0.4M channels
34
Detectors examples
Barrel insertion in the ATLAS Cavern
35
Detectors examples
36
Detectors in operation
37
Detectors in operation
38
Detectors examples
MAPS detectors
≈1’s m
RO electronic
RO electronic
3T ( 3MOS) MAPS structure
2 D array of pixels
 Monolithic solution: detector and readout
integrated onto the same substrate
39
Detectors examples
MAPS detectors
Vbias ~V’s
N++ (low res)
Electronics
0.’s μm
Active region
P+ (low-med res)
‘s μm
P++ (low res)
Mechanical substrate
100’s μm
 The charge generated in the thin active region moves by diffusion mainly:
‘Long’ collection time
Small signal
Low radiation hardness
Complex circuit topologies allow DSP on pixels for low noise
40
Detectors examples
Example of MAPS detectors:
10-7
n
l2
 Dn 2 n  U n  tcoll 
t
Dn
Charge collection time (s) in MAPS vs. perpendicular MIP hit
41
TPAC 1 pixel size 50x50 μm2
Chip size ~1cm2
Total pixels 28k
>8Meg Transistors
approximately 2000 m2 of Silicon
 1012 pixels
10 μW/pixel x 1012 = 107W
Assuming Vcc=2V
current
6
consumption: 5*10 A
Radiation damage
In HEP and space applications the detectors are exposed to high level of dose of radiation:
LHC: 10’s Mrad (100kGy) over 10years of operation
N.B.: 1 rad/cm3 Si ~1013e/h pairs
Lethal dose: 500 rad Total Body Irradiation
42
Radiation damage
Radiation environment in LHC experiment
ATLAS Pixels
ATLAS Strips
CMS Pixels
CMS Strips
ALICE Pixel
LHCb VELO
TID
Fluence
50 Mrad
7.9 Mrad
~24Mrad
7.5Mrad
250krad
-
1.5 x 1015
2 x 1014
~6 x 1014 *
1.6 x 1014
3 x 1012
1.3 x 1014/year**
All values including safety factors.
43
1MeV n eq. [cm-2] @ 10 years
Radiation damage
Microscopic effects: Bulk damage to Silicon :
Displacement of lattice atoms
V
EK>25 eV
Atoms scattered by incoming particles leave behind vacancies or atoms in
interstitial positions (Frenkel pairs).
Low energy particle ~ point defects
High energy particles ~ cluster defects
44
I
Vacancy
+
Interstitial
Radiation damage
Energy
deposition
Atoms
displacement
altered
Lattice
periodicity
generation recombination
Donor levels +++
Band gap
Spurious
states
trapping
-
Altered
Electrical
characteristics
Conduction band
compensation
Band gap
Acceptor levels
Valence band
The appearance of spurious band gap states affects the electro/optical characteristics of the device:
• Thermal generation of carriers (increased leakage current)
• Reduced recombination time ( quicker charge loss , reduced signal)
• Charge trapping
• Scattering
• Type conversion
45
Radiation damage
Macroscopic effects:
Charge Collection Efficiency (CCE) is reduced by trapping
Noise increases because of increase leakage current

Depletion voltage increases because of type inversion
Qe ,h (t )  Q0 e,h exp  
1
  eff e ,h


t


1015 1MeV n-eq.
1
 eff e,h
46
 N defects
Radiation damage
To increase the Radiation Hardness of Sensors:
• Operating conditions (cooler – lower leakage)
• Material engineering ( OFZ - Diamond detectors)
• Device engineering (n in n/p – 3D detectors)
• Electrodes in the bulk – lateral collection reduces the
drift distance
• Lower depletion voltage – less power consumption
• difficult to manufacture
•3D DDTC similar to 3D but easier to manufacture; also
Better mechanical strength.
n+
F
47
p+
Conclusions
The field of semiconductor detectors encompasses different fields:
solid state physics, nuclear and particle physics, electrical engineering, …
Some of the issues relevant to modern radiation semiconductor detectors:
• Development of new detection techniques based on novel and well established semiconductor
material: ( phonon-based detectors, quantum detectors, compounds, low dimensional)
• Integration with electronics (monolithic solution to achieve more compactness and reduce cost)
3D structures
• Topologies optimization (power reduction is crucial for future large HEP experiments)
• Radiation hardness
48