1
E.G.Villani
STFC Rutherford Appleton Laboratory
Particle Physics Department

2

3
Introduction
The Si detection chain
E
Sensing/
Charge creation
Charge transport and collection
Conversion
Signal processing
Data TX
Si physical properties Si device properties Si device topologies properties all the boxes of the detection chain process based upon Silicon
1 2
Silicon Detector physics:
Silicon Physical and Electrical properties
Charge Transport Mechanisms
Detection principles
Detector examples:
Conversion - pn junction
Microstrips
MAPS
Detector system issues:
Detection efficiency
Power

4
Silicon properties
After Oxygen, Silicon is the 2 nd in Earth’s crust (>25% in mass) most abundant element
Si
1.48A
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
•Polysilicon consists of small Si crystals randomly oriented; in α-Si there is no long range order.
Apart from its abundance, the key to success of Si is related to its oxide
SiO
2
, an excellent insulator (BV ~ 10 7 V/cm).
*Micro crystals but the flexible bond angles make SiO
2 effectively an amorphous: its conductivity varies considerably (charge transport in SiO
2 via polaron hopping between non-bonding oxygen 2p orbitals)

5
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
 
 u n , k
  e jk
 r  E n
~ a wave associated with free motion of electrons modulated by the periodic solution u n,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).
VB
CB
* The appearance of Energy BAND GAP, separating CB and VB (semiconductor)
* The 6 CB minima are not located at the center of 1 st Brillouin zone, Indirect BAND GAP

Silicon electrical properties
6
Ph
: D
Q~10 7 m -1
D
Q~10 10 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

7
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
 

 2 k
2
2 m
*
0
 g

 
2 p
0
2 
3 /
3
2
E

E o
E

 2 k
2 m *
0
2
 v

1

 k
E

 k m *
0

 p
 m *
0
 dk dt
  d
 p
 dt
   r
V

F
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.

8
CB
Silicon electrical properties
The carrier density is calculated from:
• The density of states g(E);
• The Fermi distribution function F(E);
At equilibrium the carrier density in CB and VB is obtained by integrating the product:
VB n
D
  g
D
    dE

N
C / V e


Ec

Ev

/ kT
 n i
 p i
3
2
1
F

1 pn
 n i
2
1
 exp
 kT

N
C
N
V e

  g
/ kT
E
F

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 10 12 atoms is ionized
The density of states g
D
(E) depends on the dimension

9
Silicon electrical properties
Conduction of Si intrinsic @ T = 300K:
σ = q(μ n
+
μ p
) n i
= 3.04x10
-6 mho-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: 10 12 to 10 20
In crystalline Si ~ 5*10 22 atoms cm -3 cm -3
In equilibrium the relationship between carrier concentration and E is the same as in the intrinsic case: pn
 n i
2

N
C
N
V e

 
/ kT 
10
20
@ T

300 K e .
g .
: N
D

10 17
 pn
 pN
D
 p
 n i
2
N
D

10 3

10
Charge transport
Charge transport:
The charge transport description relies on semi-classical Boltzmann Transport
Equation (BTE, continuity equation in 6D phase space)
 f
 t

1

 k
E
 
  r f
 r , k , t


F

  k f
 r , k , t


 f
J n
 

1
V k
 f
 r , k , t

W
 
  q
V k
 v
   r , k , t
 r
 

1
V k

E
   r , k , t

Q conservation
P conservation
E conservation
 t coll

S
 r , k , t

The distribution function f(r,k) can be approximated near equilibrium:
 f
 t coll
  f

 f f
0
Near equilibrium equilibrium
0 k

11
Charge transport
Under (many) simplifying assumptions the 1 st moment of BTE gives the Drift Diffusion model
(DD, in many textbooks ‘The semiconductor equations’):
Drift term
Diffusion term J n
J p

 qn
 qp
 n p
E
E
 
 

 qD n
 n qD p
 p
 n
 t

1 q
 
J n

U n
 p
 t
 
   
V
1 q
 

J p

 p

U 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)

12
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

13
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 1/10 th in semiconductors compared to gas)
•
Higher density of semiconductor means higher charge signal;
•
High carrier mobility can improve radiation hardness;
•
Very well developed semiconductor technology implies higher reliability and lower cost;
•
Can be operated at room temperature;
Silicon detectors are commonly used in HEP (i.e. E > 1 GeV) used to localise charged particle trajectories by stacking them onto several layers

14
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
VB
Quantized levels

15
Detection principles
Ionization energy loss (/ density) : Bethe formula for charged particles through matter due to interaction with electrons
0.2 <

< 1

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
T max
: max energy transfer

: density correction term c: speed of light
Losses due to relativistic stretch, bremsstrahlung emissions
16

Bethe formula valid if velocity of particle is larger than orbital electrons velocity
Nuclear stopping dominates low energy collisions

17
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

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
18
In a typical 300 μm thick sensor:
* 32000 electrons / holes pair generated on average
* 21700 electrons / hole generated most probable
MPV of energy loss normalized to the mean loss of a
MIP

19
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.

20
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.

21
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.

Interactions of photons
Detection principles
22
10 eV 1 keV 1 MeV 1 GeV .1 TeV

23
Detection
MIP charge density n
R

 dE dx


I

 v
1
 i
 p
1

R 2
110 nm

3

10
15 cm

3
A MIP forms an ionization trail of radius R when traversing Si, creating ~ 100 e /
μm
 
L
 h
2
 m

E

10
0 .
5

1

10

7 cm

15 cm
Photoelectric charge density
I

I o e
    z n 

P in h

   e
  z 
5 .
6

10
6 e

/
 m
An optical power of -60dBm (= 1nW) of 1keV photons generates ~ 6*10 6 e-/
μm
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
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
Conversion
24
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
•…
Si physical properties
Charge transport:
Big devices, DD adequate;
Small injection, electric field as static;
Si device properties
Charge generation:
Ionization: Small injection, QM not needed;
Stopping power, average ionization energy, fluctuations

26
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.
PN junction
Strip / pixel detectors
HEP, Scientific applications
Monolithic Active Pixel Sensors (MAPS)
Consumer and scientific applications
Charge Coupled Devices (CCD)
Imaging, scientific and consumer applications

Detectors examples
27
 Almost all HEP experiments use Si detectors:
The high density track region usually covered by pixel detectors; by strip at larger radius (cost reason)

28
F
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
• 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
0
 qp
 p
E
 qD n
 n

 qD p
 p
 n
 p

D  n
0 e
V t p
0 e

D 
V t
• 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

29
W
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
• 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

2

V b q
N a
N a

N d

N d
Capacitance C
= q e
2 V b
N a
N a
×
N d
+
N d
×
A

The full depletion voltage is the minimum voltage at which the bulk of the sensor
(over depletion).
Signal conversion: The pn junction
High-resistivity material (i.e. low doping) requires low depletion voltage.
 To achieve large W high field region:
• Low doping (high resistivity)
• Large voltages
• typical values:
N a
= 10 15 cm -3 ,N
W (0V) ≈ 23 μm d
= 10 12
22 May 2011 resistivity r
[kOhm cm]
Depletion voltage vs. resistivity
Thomas Bergauer (HEPHY Vienna) 40
30

Strip detectors
Detectors examples
80 μm
(high res)
F
Q transversal diffusion
V bias
~ 100’sV
31
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)

768 Strip Sensors
Detectors examples
12 RO ASIC
ATLAS SCT RO ASIC (ABCD3TA)
128 channels/ASIC
RAD-HARD DMILL technology
ASICS glued to hybrid
40 MHz Ck
32
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

33
ATLAS SCT
61 m 2 of Si
6.3 * 10 6 channels
50 kW total power consumption
1 barrel
4 layers
2100 modules
2 endcaps
9 disks/each
988 modules
2 T solenoidal field
Detectors examples

34
Detectors examples
ATLAS Tracker overview
Pixel: (n+ on n) 1.8m
2 , 80M channels
SCT: 6.3M 61 m 2 channels
TRT: 0.4M channels

35
Detectors examples
Barrel insertion in the ATLAS Cavern

36
Detectors examples

37
Detectors in operation

38
Detectors in operation

MAPS detectors
≈1’s  m
Detectors examples
39
RO electronic
3T ( 3MOS) MAPS structure
2 D array of pixels
 Monolithic solution : detector and readout integrated onto the same substrate

MAPS detectors
Electronics
0.’s μm
Active region
‘s μm
Mechanical substrate
100’s μm
Detectors examples
V bias
~V’s
N ++ (low res)
P + (low-med res)
P ++ (low res)
40
 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

Detectors examples
Example of MAPS detectors:
10 -7
41
 n
 t

D n
 2 n

U n
 t coll
 l
2
D n
Charge collection time (s) in MAPS vs. perpendicular MIP hit
TPAC 1 pixel size 50x50 μm 2
Chip size ~1cm 2
Total pixels 28k
>8Meg Transistors approximately 2000 m 2 of Silicon
 10 12 pixels

10 μW/pixel x 10 12 = 10 7 W
Assuming V cc
=2V current consumption: 5*10 6 A

42
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/cm 3 Si ~10 13 e/h pairs
Lethal dose: 500 rad Total Body Irradiation

43
Radiation damage
Radiation environment in LHC experiment
TID Fluence
-2
ATLAS Pixels
ATLAS Strips
CMS Pixels
CMS Strips
ALICE Pixel
LHCb VELO
50 Mrad
7.9 Mrad
~24Mrad
7.5Mrad
250krad
-
1.5 x 10 15
2 x 10 14
~6 x 10 14 *
1.6 x 10 14
3 x 10 12
1.3 x 10 14 /year**

Radiation damage
Microscopic effects: Bulk damage to Silicon :
Displacement of lattice atoms
E
K
>25 eV
V
I
V acancy
+
I nterstitial
44
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

Radiation damage
Energy deposition
Atoms displacement altered
Lattice periodicity
Band gap
Spurious states
Altered
Electrical characteristics generation recombination trapping Conduction band
Donor levels
+++
Band gap
Acceptor levels
Valence band
The appearance of spurious band gap states affects the electro/optical characteristics of the device:
45
• Thermal generation of carriers (increased leakage current)
• Reduced recombination time ( quicker charge loss , reduced signal)
• Charge trapping
• Scattering
• Type conversion

46
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
Q e , h
( t )

Q
0 e , h exp

 eff
1 e , h
 t
10 15 1MeV n-eq.
 eff
1 e , h

N defects

47
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.
F n+ 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