Transcript Document

Summary of what seen so far
Overview of charged or neutral particle interaction in matter
Overview of detectors providing precise time measurement -> scintillators
Need them for
trigger
lifetime measurement
identification of particles
Overview of detectors providing precise space measurement ->
gaseous tracking chambers
Need them for
direction, angle measurement
momentum measurement
identification of particles (using dE/dx differences)
Gaseous tracking chambers
Typical resolution ?
200 micrometers
space point
resolution
is quite typical
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Gaseous tracking chambers
What is the typical size (radial, longitudinal) at a collider experiment?
Hint : what particle property do we want to measure ?
and what polar angle distribution do we want to observe ?
Radial : momentum measurement
s=0.3 L2 B / 8 pT
e.g. s=0.15 cm for pT =10 GeV (150 micrometers is resolution)
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so typically need L~ meters
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Longit. : have as much acceptance as possible to measure eg. differential
cross sections, etc.. Depends on the goals of experiment.
Typically ~ meters
Gaseous tracking chambers: literature
W.Leo pages 119 - 146
D. Green pages 151 - 176
Peter’s notes on ISIS web site (all lecture slides are there !)
Problem for today
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Qu i c k T i m e ™ a n d a
TIF F (U n c o m p re s s e d ) d e c o m p re s s o r
a re n e e d e d to s e e th i s p i c tu re .
BaBar detector at Stanford Accelerator PEPII
B0
electron
positron
B0
Ecms=10 GeV
Y(4S) -> BB
=0.56
Problem will be about evaluation of BaBar detector design
Babar physics goals which concern us today :
- Measure very precisely the travel distance of the two B mesons
- Measure very precisely the momentum of the particles coming
from B meson decays
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Pros and cons ? Is the design appropriate to the physics goals?
Can we suggest improvements?
B mesons (hadrons containing b quarks) have a mean lifetime = 1.5 picoseconds.
At the PEP collider B mesons are produced with a boost factor  ~ 0.5
> This means that they will travel on average a distance “L” = ?
The B meson travels a distance L and then decays into particles a and c
a

r
c
L
b
z
> The impact parameter “b” particle “a” also carries information about the lifetime
of the B meson. so it is important to be able to measure that too. What is the
expected value for “b” ? (hint: assume  small)
> What is the resolution needed to observe the decay length “L” and the impact
parameter “b” ? We are happy if L / error(L) is > 3
A:
L=average distance travelled in mean lifetime by B meson =
 c  = 0.56 * 1.5 ps * 3 108 m/s= 230 micrometers
a

b ≈ L if  is small
c
 = pT /p
L
b
of decay particle B ~ MB/2 / pB/2 ~ 1/()B
=> b ~ c  = 450 micrometers
to observe L at least a 3 sigma significance , meaning that L/error(L) >3,
we need maximal resolution to be 70 micrometers. For b is 150 micrometers.
Asking for 3 sigma is really the minimum, one should need more.
So we need a different tracking device than the gaseous
Ones, whose resolution is too coarse. Which one ?
We need
> Smaller resolution (electronic readout with higher granularity)
> particles should loose little energy compared to initial energy
> produce electronic signal high enough to detect particle and also
fast enough to be readout before next collision event occurs
Which one?
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silicon
Goals of the lecture
Silicon detectors
Reference: D.Green, pages 177-201. W.Leo, pages
Example of silicon detectors in past and current experiments
Reference: slides (and web links)
Exercise : Pros and cons of the BaBar detector?
Vertex reconstruction and kinematic fitting.
Reference : slides (and web links)
Identification of heavy quarks
Reference: slides (and web links)
Semiconductors devices
(besides book reference, veryy usefull to browse here
http://jas.eng.buffalo.edu/index.html
)
Solid state or semiconductor detectors are made of crystalline
semiconductor material, typically silicon or germanium
Development really started in 1950’s
At first used for high resolution energy measurement and were
adopted in nuclear physics for charged particle detection and gamma
spectroscopy
Last 20 years, gained attention in high energy physics for high
resolution fast tracking detectors.
Basic operating principle is similar to gaseous devices: charged particle
ionizes and creates electron-hole pairs which are the collected by an
electric field. Photons will also be detected in solid state detectors,
via photoelectric effect and then electron ionizes.
Basic SemiConductor properties
When isolated atoms are brought together to form a lattice, the discrete atomic states shift to
form energy bands as shown below. Affects only the outer energy levels of atoms.
Intrinsic conductivity of semiconductors
Thermal excitation of charge carriers across gap
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http://jas.eng.buffalo.edu/education/semicon/fermi/functionAndStates/functionAndStates.html
http://jas.eng.buffalo.edu/education/semicon/fermi/levelAndDOS/index.html
n = density of electrons in the conduction band = 1/V
∫ f(E) g(E) dE
Where
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n
(density of states)
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And similarly for holes
(Reference : http://britneyspears.ac/physics/basics/basics.htm)
ni = AT 3/2 e (-Eg/2KT)
ni= concentration of e (holes).
Eg= energy gap at 0 Kelvin
equilibrium
Constantly :
• e/h pairs are generated by thermal energy.
• e and holes recombine.
n electron= n holes in pure semiconductor
? e -Eg/2KT ~ 10-9
T=0, no conduction
T=300 K, pure Si, 1.5 10
10 cm-3
(Remember there are 1022 atoms cm-3)
-> Silicon is a poor conductor
If one applies a electric field E to a semiconductor, e and holes start moving.
Drift velocity :
ve = e E , vh = h E
=mobility=f(E,T)
T=300K , E<103 V/cm :  is constant
E ~ 103 - 104 V/cm :  ~ E-1/2
E >104 V/cm
:  ~ 1/E
saturation v=107 cm/s
 ~ T-m m=2.5 for e, 2.7 for holes in Si
e = 1350 cm2/Vs in Silicon -> v= 1.3 106 cm/s (gas was 105 cm/s)
J = current = e ni (e + h ) E
Conductivity ~ 1/ resistivity
Recombination and trapping
e can fall back into valence band, but need
exact energy -> rare
Nonetheless lifetime for e and holes is ~ ns
-> what happens ?
Impurities or defects in the semiconductor !
additional levels in the forbidden gap
Recombination centre:
This center can capture electron from conduction band and either release it back to the
conduction band after a while or collect also a hole and e-hole annihilate
Trapping center:
This center can only trap an electron or a hole. They hold it and then release it after a
while.
http://jas.eng.buffalo.edu/education/semicon/recombination/indirect.html
time electron is free should be >> time takes to collect electron out of detector
-> impurity concentration should typically be < 10 10 impurities cm-3
Doped SemiConductors
P-Type
N-Type
P, As, Sb
5 electrons in the M-shell
1 electron with binding energy 10-50 meV
B, Al, Ga
3 electrons in the M-shell
1 electron missing
.. When doping is actually good :)
0.05 eV
in Si
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Fermi level
much closer to
conductive band
or valence band
Amount of dopant is quite small typically (10 13 cm-3).
ND + n= NA + p
In n type NA=0 , ND~n
p= ni2 / ND
-> conductivity is = e ND e
Donor concentration determines
conductivity
… but how can we use a piece of Silicon for
detecting a high energy particle … ?
+ +
- -
V
Is this going to
work?
Can you foresee any
Problems ?
We don’t like the thermal current !
Intrinsic silicon will have electron density = hole density ~ 1010 cm-3
In the volume above 4.5 108 free charge carriers
But : only 3.2 104 produced by MIP (dE/dx in 300um Si divided by 3.6 eV).
So, to use silicon as particle detector, we need to decrease number of free
carriers
How?
- Reduce temperature ( need cryogenics, more expensive)
- Create a free zone in the semiconductor
Reverse pn
There must be
a single Fermi
level
junction
Deformation of
band level
http://jas.eng.buffalo.edu/education/pn/pnformation3/index.html
Potential
difference
Difference in concentration
starts diffusion
Perfect candidate for
detector region
Do we know an example of what a pn junction can be usefull for?
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Solar cell
V  d2
A
C    V 1/ 2
d
V is potential in figure f) of pn junction
http://jas.eng.buffalo.edu/education/pn/pnformation3/index.html
Field in a p-n junction is not intense enough to provide efficient charge
collection
thickness of the depletion zone will not be enough to detect
high energy particles
Solution: By applying an external voltage, we can enlarge the depletion
zone and therefore the sensitive volume for radiation detection.
The capacitance, hence the electronic noise, will also decrease
Reversed biased junctions
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http://jas.eng.buffalo.edu/education/pn/biasedPN2/BiasedPN2.html
The higher external voltage also helps increasing efficiency of charge
collection.
Max voltage appliable depends on the resistivity of the semiconductor.
At some point junction will breakdown and begin conducting.
In Si n-type, with V=300V a depletion d=1mm can be obtained
Bigger d
bigger resistivity (to postpone breakdown)
Basic scheme for operating a pn junction
-V
1 m Al
~ 1018 /m3
Electrons
Depleted
Layer
Holes
p+ implant
Si (n type)
n+ implant
Signal
from
incoming
particle
Is readout
1 m Al
+V
p+n junction, depletion region all in the n region (as seen)
To collect charge, electrodes must be placed on both ends. But the ohmic contact
cannot be made by directly depositing metal on the semiconductor (else a
rectifing junction extending into the semiconductor is formed).
So heavily doped layers of n+ or p+ are used between the semiconductor and the
metal.
Typically, a preamplifier of charge-sensitive type, with low noise characteristics,
is used to collect the charge out of the detector (~ 30000 eh pairs in 300 micrometers, need ampl.)
Leakage current
Reverse biased pn junction does not conduct, ideally.
In reality a small current always exists : leakage current.
Appears as noise at the detector output.
Sources:
1. Movement of minority carriers (nanoAmpers/cm2)
2. Thermally generated e/h due to impurities in depletion region
(microAmp/cm2)
3. Largest source: leakage current through surface channels.
depends on a lot of factors (surface chemistry, contaminants, etc.)
clean encapsulation is usually required
http://jas.eng.buffalo.edu/education/pn/biasedPN/index.html
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Intrinsic efficiency and sensitivity
Basically 100%. Limiting factor on sensitivity is noise from leakage current (I)
and noise from associated electronics ( C ) and thermal noise ( KT/R )
which sets a lower limit on the amplitude that can be detected
Very important to choose correct depletion thickness, to ensure good signal
To summarize
often require cooling to be operated, adds to material budget of detector
Silicon based detectors
Silicon microstrip detectors
pitch
Voltage roughly 160 V
Q: Formula for resolution on position
strip detector with pitch P=50 micrometers
P
y
Q: what is the position resolution if the information saved is: which strip is hit ?
Q: If one saves also the information: charge collected at each strip ,
can one think of improving the resolution ?
A:
P
y
2  <(y - <y>)2 > = ∫ (y - <y>)2 dy / ∫ dy between -P/2 and P/2 (continuous form)
assume uniform illumination
given <y>=0
2 = ∫ y2dy /∫ dy = P2 /12
So if P=50m, then  = 15m
Reading out amplitude (of charge signal) at each strip, and weigthing
positions with this, we can get better precision on position
The position of the particle = the center of gravity of the charges collected
at several readout strips.
Charge liberated by a charged particle is collected at the electrodes within 10 ns .
Signals picked up at the strips measure the position with a precision dependent
on the pitch of the strips.
Detector with 20m pitch, readout
every 6 or 3 strips. Resolution
r is respectively
:
When Magnetic field applied !
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Magnetic field (typically applied in high energy particle physics detectors)
worsens the resolution and introduces a bias.
Holes less mobile -> less angle
One can improve by reading out more strips (every one, eg.).
Simplified readout in this case if possible, to put on detector the electronics
associated with each strip
Not optimal
How to get
2-dim information
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fake
real
Solid state pixel detectors
Avoids problem
with combinatorics
and gives precise
3-D information
Precise 3D information : 20 x 20 x 20 micrometers pixels
Indeed we can clearly resolve decay distance “L” and impact parameter “b”
Disadvantage:
Added material due to
cryostat
SLD
Other examples of silicon detectors
Reconstructed B decays
DELPHI
In both SLD and DELPHI detector we have mentioned the resolution on
impact parameter “b” seen at start
z
a

c
L
b
r
 b = a + const/ (p sin  3/2)
- do we understand why ?
- how does the resolution on “b” influence the choice of design ?
r2
r1
b
z1 z2
z
(z2-b) / r2 = (z2-z1) / (r2-r1)
b= (r2 z1 -r1 z2)/(r2-r1)
 b 2= (r2 2  z1 2 + r12  z2 2) / (r2 -r1) 2
Resolution on b
indeed resol. on b is a constant, depends on point resolution of detector
 b 2= (r2 2  z1 2 + r12  z2 2) / (r2 -r1) 2
If
r1=1cm and r2=1m and  z1 =10microns and  z2 = 200 microns
(case of SLD vertex detector and gaseous tracking chamber)
then clearly  b is good because the “near” measurement is good.
-> it is a good idea to insert a high resolution detector close to the
interaction point and eg. B decay point
how close one can get depends on radiation damage suffered (see later)
if after z1 particle suffers multiple scattering then
z2’ = z2 + (r2-r1)* ms so
 z2 2 =>  z2 2 + (r2-r1)2 const / p2 so we get now the term on
 b dependent on p
Moore's Law for Silicon Detectors
50
cost/area ($/cm2)
4''
Wafer size
6''
10
< 2 $/cm2
2
Blank wafer price 6''
1
DATA From H.F-W. Sadrozinski, UC-Santa Cruz
Now affordable also to cover large volume with silicon.
Any disadvantages in using only silicon for tracking devices at
collider experiments ?
:(
more multiple scattering
:( more material, more energy loss
:( Probability of brehmstrahlung for electrons is higher in Si
(~Z^2 vs ionization that goes like Z), and
also photons will convert in pairs more easily
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CMS
All silicon
Inner tracking
Detector
(two single sided strip
detectors, mounted
back to back)
Radiation damage
At the moment silicon detectors are used close to the interaction region in most
collider experiments and are exposed to severe radiation conditions (damage).
The damage depend on fluence , particle type (,,e,n,etc)
and energy spectrum. It affects both sensors and electronics.
Three main consequences seen for silicon detectors :
(1) Increase of leakage current
(2) Change in depletion voltage, problematic
(3) Decrease of charge collection efficiency (less and slower signal)