Introduction to Silicon Detectors
G.Villani
STFC Rutherford Appleton Laboratory
Particle Physics Department
1
Outlook
• Introduction to physics of Si and detection
• Examples of detectors
• Conclusions
2
Introduction
The 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
Detector examples:
Silicon physical and electrical properties Microstrips
Detection principles
CCD
Transport mechanisms
MAPS
Detector physics:
Conversion
3
Detector system issues:
Detection efficiency
Power
Introduction to Silicon
After Oxygen, Silicon is the 2nd most abundant element
in Earth’s crust (>25% in mass)
The crystalline structure is diamond cubic (FCC), with lattice spacing of
5.43 A
Polysilicon consists of small Si crystals randomly oriented; in α-Si there
is no long range order.
Si
1.48A
4
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)
Introduction to Silicon
Silicon Band structure
The electronic band structure calculation can be done ab-initio using variational approach (DFT) or
empirical methods (kp) that solve 1 electron SE in a periodic potential neglecting electrons interaction.
The approximate solution of many-body SE in presence of periodic potential of the crystal lattice are in
the form of Bloch functions:
T  U 
 E   n,k r   un,k r e jkr  En k 
It can be regarded as a traveling 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 1st unit WS cell of the reciprocal lattice (the Brillouin zone).
The band diagram look complicated:
5
Introduction to Silicon
1st Brillouin zone of Diamond lattice
CB
VB
The appearance of Band Gap, separating CB and VB
The 6 CB minima are not located at the center of 1st Brillouin
zone, INDIRECT GAP
CB
Anisotropy in surface of E
6
VB-H
VB-L
Introduction to Silicon
The detailed band structure is too complicated: quasi-equilibrium simplifications are
needed to study the of mechanism 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
2 
E  Eo
the effective mass approximation takes into account the periodic potential of the crystal
by introducing an effective carrier mass (in 3D an average over different longitudinal
and transverse masses):
2
2 k
1
k  p
E k  
 v   k E 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 mobility of a particle is inversely related to its effective mass (or proportional to
the curvature of E(k)).
Similar approach used to calculate the E(k)
for phonons.
7
Introduction to Silicon
Once the band structure and simplified density of states is
known, it is possible to determine the carrier density. This
is essential to study the charge transport.
CB
• The density of states g(E);
• The distribution function F(E);
Only partly filled bands can contribute to conduction: carrier
density in CB and VB.
At equilibrium the carrier density 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
0
pn  ni2  N C NV e
 
 E g / kT
Fermi level: energy level @ 50% occupancy
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
The density of states gD(E) depends on the dimension
8
1
 E  EF 
1  exp

 kT 
Introduction to Silicon
Conduction of Si intrinsic @ T = 300K:
σ = q(μn +μp) ni = 3.04x10-6mho-cm ->329kOhm-cm
By adding atoms of dopants, which require little
energy to ionize, we can change by many odg the
carrier concentration.
Doping concentration: 1012 to 1018 cm-3
In crystalline Si ~ 5*1022atomscm-3
In equilibrium and for non degenerate case
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 
ni2
 103
ND
Thermal energies at ambient temperature
(~40meV) is enough to ionize the dopants
9
Detection
Detection principles:
A: Ionization: by imparting energy to break a bond, electrons are lifted from VB to CB then
made available to conduction. Well established concept ( ionization chambers, microstrip,
hybrid pixels, CCD, MAPS…)
α
MIP
Photon interaction
Bethe-Bloch formula for stopping power gives the rate of energy loss/unit
length for charged particles through matter
10
I z   I o e   E z
Detection
Ph: DQ~107 m-1
DQ~1010 m-1
/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
11
Detection
MIP charge density
n
I z   I o e   E z
dE 1 1

 3 1015 cm 3
2
dx  i   R
R
 v
I
 110nm
A MIP forms an ionization trail of radius R
when traversing Si, creating ~ 80e-/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;
Carrier dynamics does not need QM
The generated charge is too small to affect the internal electric field
12
Photoelectric charge density
z  

n
Pin
   z
  e
 5.6 106 e  / m
h
An optical power of -60dBm (= 1nW) of 1keV
photons generates ~ 6*106e-/μm
High injection regime:
Plasma effects
The internal electric field can be affected by
the generated charge
Detection
The variance in signal charge σi associated to the ionization process is related to the phonon excitation
i 
Eo
i
E pn   i

  1
Ei  Ei 
Fano factor ~0.1 in Si
High resolution requires smaller band gap (εi ),
direct or small phonon excitation energy
Intrinsic resolution of Si and Ge based detectors
13
Detection
B: Excitation: Charge or lattice (acoustic or optical phonons) some IR detectors, bolometers
60meV
Poly Si
SiO2
Si
Ec
EF
~10’s meV
EV
EF
Eigenvalues separation in quantized structures ~ 10’s meV
Dispersion relation for phonons in Si
Phonon excitation energy ~ 10 meV : much lower threshold
14
Charge transport
Charge transport:
Once the charge has been created in the material, the next step is its collection:
The charge transport description relies on semi-classical 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 

 S r , k , t 
coll
Q conservation
k
 
q
vk  f r , k , t 
V k
P conservation
 
1
E k  f r , k , t 
V k
E conservation
J r, t  
W r, t 
The distribution function f(r,k) can be approximated near equilibrium:
Near equilibrium
equilibrium
0
15
k

f r , k , t
t


coll
f  f0
f
Charge transport
Under (many) simplifying assumptions the 1st momentum of BTE gives the DD model
(The semiconductor equations):
J n  qn n E r   qDnn
J p  qp p E r   qDp p
Drift term
Diffusion term
n 1
   Jn Un
t q
p
1
    J p U p
t
q
  V   p  n  N D  N A 
DD expresses momentum conservation: it becomes invalid when sharp variation in energy
of carriers occur (due to F for example: deep submicron devices)
When feature size is 0.’sμm the DD model becomes invalid: higher momentum required
Even in low injection regime, a small F renders the drift term >> diffusion term
16
Half summary
The processes in the detection chain can be simplified:
E
Sensing/
Charge creation
Charge transport
and collection
Si physical properties
Si device properties
Physical characteristics:
Charge generation:
Charge transport:
Quasi equilibrium;
Ionization: Small
injection, QM not needed;
Big devices, DD
adequate;
Stopping power, average
ionization energy
Small injection, electric
field as static;
Homogeneity;
‘Room’ temperature;
Non degenerate Si;
17
Conversion
Under conditions of
• quasi stationary conditions
• non degenerate semiconductor
• not small feature size
• low injection
•…
Signal conversion: The pn junction
Homojunction: consider two pieces of same semiconductor materials
with different doping levels:
In equilibrium, the Fermi level equalizes throughout the structure
The thermal diffusion of charge across the junction leaves just
the ionized dopants : an electric potential develops
In equilibrium J = 0: using DD model
0  qnn E r   qDnn  n  n0e
D
Vt
0  qp p E r   qDpp  p  p0e
 0

D
Vt
Near the interface, the carrier concentration exponentially
drops: a depletion region (empty of free charge) is formed.
A ‘positive’ voltage increases (exponentially) the charge concentration: high
direct current.
A ‘negative’ voltage decreases it (down to leakage): the current reduces and at
the same time widens the depleted region.
Unidirectional of current characteristics
18
Signal conversion: The pn junction
An electric field F is present in the depletion region of a
junction, sustained by the ionized dopants
The electric field in the depletion region contributes to the
charge drift , when generated, and helps the collection process.
PN junction signal converter: A capacitor with a strong F across
W
A device with a large depleted region can be used to efficiently
collect radiation generated charge ( Solid state ionization
chamber)
W
2Vb N a  N d
q Na  Nd
To achieve large W high field region:
• Low doping (high resistivity) Silicon is needed
• Large voltages
Conversion: Q to V // Q to I
19
The bipolar transistor device
A bipolar transistor can be thought of as a two diode system,
connected in anti series;
•One is forward biased;
•The other is reverse biased
The bipolar transistor can be (and it is) used as a high gain
detector
Main limitations arising from speed: the minority carriers diffuse
through the base ( relatively low speed)
20
Detectors examples
Strip detectors
Scientific applications
Charge Coupled Devices (CCD)
Imaging, scientific and consumer applications
Monolithic Active Pixel Sensors (MAPS)
Imaging, consumer applications
RAL PPD has (is) actively involved with all these detector technologies
21
Detectors examples
Strip detectors
768 Strip Sensors
300μm
80μm
P++
N+ (high res)
F
Wires
RO electronic
Vbias ~10’sV
Power supply
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 transversal diffusion of charge implies a spread of signal over neighbouring strips
The high resistivity Si is not usually used in mainstream semiconductor industry:
Hybrid solution: detector connected (wirebonded) to the readout electronic (RO)
22
Detectors examples
module
768 Strip Sensors
RO
ATLAS SCT
4 barrel layers,2 x 9 forward disks
4088 double sided modules
Total Silicon surface 61.1m²
Total 6.3 M channels
Power consumption ~ 50kW
23
Detectors examples
High events rate require fast signal collection:
Estimate of charge collection time in strip detector:
z
1
1 z
t z   
dz  
 z0
z0 v  z 
1
dz
z 

Fo 1    F1
 W
For a detector thickness of 300um and overdepleted Vb = 50V and 10kohm
resistivity
tcoll(e)≈ 12ns
tcoll(h)≈ 35ns
The fast collection time helps the radiation hardness:
Radiation damage to the Si bulk increases the recombination rate. To
avoid signal loss the charge has to be collected quickly, before it
recombines.
24
Detectors examples
MAPS detectors
≈10’s m
RO electronic
RO electronic
3T ( 3MOS) MAPS structure
2D array of pixels
Monolithic solution:
Detector and readout integrated onto the same substrate
25
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
Different implants arrangements for charge collection optimization
Circuit topologies for low noise
26
Detectors examples
Example of charge collection in MAPS:
10-7
TPAC 1 pixel size 50x50um2
Chip size ~1cm2
Total pixels 28k
>8Meg Transistors
n
l2
2
 Dn n  U n  tcoll 
t
Dn
Charge collection time (s) in MAPS vs. perpendicular MIP hit
27
Detectors examples
Example of charge collection in MAPS: simulated MIP vs.1064nm laser 2x2um 5ns pulse
28
Detectors examples
CCD detectors
Once the charge has been generated, it accumulates in the potential well, under the capacitor.
The control circuitry shifts the accumulated charge to the end of the row, to the input of a charge
amplifier. The sensor is fabricated in a optimized, dedicated process and the RO on a separate
chip. Superior imaging quality but less integration and speed.
Nobel Prize 2009 for Physics to
inventors Boyle and Smith
29
Detectors examples
5 m
Global Photogate and Transfer gate
In-situ Storage Image Sensor: ISIS
ROW 2: CCD clocks
ROW 3: CCD clocks
On-chip logic
80 m
On-chip switches
ROW 1: CCD clocks
Imaging pixel
ROW 1: RSEL
Global RG, RD, OD
55
Fe  source Mn(K
RG RD
OD RSEL
Mn(Kb 
Column
transistor
30
CCD in CMOS process 0.18μm
Charge collection under a PG then
stored under a 20 pixels storage
CCD
Signal conversion: The unipolar MOS device
NMOS
SiO2
N++
P++
Metal Oxide Semiconductor device are unipolar
devices based on voltage modulation of charge.
The control gate is physically separated by the
active region where the charge moves by a thin
(nm) layer of SiO2.
By applying a voltage to the G with respect to the Substrate
an electric field develops across the SiO2: a charge channel
is formed between Source and Drain.
The Ids characteristics depends on the Vgs applied.
The CMOS process refers to the minimum feature size
achievable i.e. the channel length)
Currently 45nm: the modelling of the characteristics of the
device of this size is non-trivial:
•Quantization effects at the boundary;
•QM tunnelling across the gate;
•Hot carriers near the D/S junction;
•…
31
Sensor devices: The unipolar MOS device
LET in SiO2 for different particles
The SiO2 is a very good insulator: a strong electric
field can be applied to it and the charge
generated in SiO2 by ionizing radiation efficiently
collected
However SiO2 is a polar material: the recombination
processes are stronger than in Si. Furthermore, hole
Transport is non Gaussian (low ‘mobility’) and traps
form near Si interface.
32
Generation rate in SiO2 vs. electric field
Y ( Fox , T , ro )  K e
1 (  A ) (  K )
K
A
qFox ro
kT
rc
q2
, rc 
ro
4 SiO2 kT
e

Am   K l

 
m 0 m! n 0 l  m  n 1 l!
Sensor devices: The unipolar MOS device
Floating Gate
Control Gate
Si
O2
Si
O2
FG
FG
Addition of a Floating Gate (FG): the electrical characteristics of the device are controlled by the charge
stored in the FG. The electric field in the SiO2 due to the FG drifts charge towards/away from it.
The discharge of the FG alters the device electrical characteristics
Ids(A)
Pre-rad
Post-rad
Reprog
Radiation sensitivity
Chip #2
100Gy
<∆Vth >
0.6152
Std dev
0.00598
Conversion: Q to I
33
The MOS structure easily allows
excitation based radiation detection
Detector systems
Detection efficiency:
50μm
SF
CA
RC-CR
SF
Vth
MAPS pixel structure can host complex electronics
Estimated power consumption MAPS Calice:
10 μW/pixel x 1012= 107W Assuming Vcc=2V
10μW continuous -> 10μJ energy
Energy deposited by a particle: 0.2 – 10fJ
Noise occupancy 1% : hit pixel fires/100sec
Required energy/deposited energy >> 1010 !!!
Extremely huge energy inefficiency
34
5*106A
Detector systems
Power reduction at detector level
=
At pixel level, power consumption could be optimized by
using a non linear approach:
The positive feedback structure is biased near threshold
(variable)
A small signal triggers the structure
35
Detector systems
Power optimization at system level
Alternative powering schemes:
SP
DC2DC
The ATLAS SCT (semiconductor tracker) detector.
The thick red cables on show feed the detector with half of its
power – adding more will take up even more space
A serial powering or DC2DC approach can increase efficiency in
power distribution compared to a parallel approach
36
Conclusions
The field of semiconductor detectors encompasses different scientific and technology fields:
solid state physics, EM, QM, electrical engineering, nuclear and particle physics…
Some of the issues relevant to radiation 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, noise reduction)
• Radiation hardness
37
Backup slides
Quantization effects due to band bending in Si-SiO2 interface: excitation based detection
SiO2
Si-sub
Si-poly
Q-effects
A