DIPLOMA THESIS Tests of semiconductor microstrip detectors of ...

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Nov 1, 2013 (3 years and 8 months ago)

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Charles University in Prague
Faculty of Mathematics and Physics
DIPLOMA THESIS
Pavel

Rezncek
Tests of semiconductor microstrip detectors
of ATLAS detector
Institute of Particle and Nuclear Physics
Supervisor:Dr.Zdenek Dolezal
Study programme:Physics
Study eld:Nuclear and Subnuclear Physics
I would like to thank to my supervisor Dr.Zdenek Dolezal for his leading of my
diploma thesis,for inspiring discussions and ideas.For help in building of the test setup I
would like to thank all the members of the VdGaccelerator lab at Institute of Particle and
Nuclear Physics MFF UK,especially to Dr.Peter Kodys who together with my supervisor
introduced me into the problematics of the tests of ATLAS microstrip detectors.
Many thanks belong to Bettina Mikulec and Rainer Wallny for their consultations
of radioactive source tests analysis and patience with testing my software during measure-
ments at CERN.Concerning computer simulations I'm very grateful to Szymon Gadom-
ski,the author of the simulation software,who instructed me how to use the software,
and to Grant Gorne for his help with Geant4 simulations.For the provided beam tests
data and discussions of features of the simulation I want to thank to Marcel Vos and
Jose Enrique Garcia Navarro.For help with experiencing the standard and beam module
tests I wish to thank to Gareth F.Moorhead,Monica D'Onofrio,Mariane Mangin Brinet,
Mauro Donega,Lars Eklund,Peter W.Phillips,the author of the standard software used
for module tests,and many other ATLAS SCT developers I met during my diploma thesis
training.
Finally I'm very grateful to many members and students of Institute of Particle and
Nuclear Physics MFF UK for their suggestive questions.
Prohlasuji,ze jsem svou diplomovou praci napsal samostantne a vyhradne s pouzitm
citovanych pramenu.Souhlasm se zapujcovanm prace.
I declare that I wrote my diploma thesis independently and exclusively with the use
of the cited sources.I agree with lending the thesis.
Prague,17
th
April 2003 Pavel

Rezncek
2
Contents
1 Introduction 5
2 ATLAS detector system 6
3 Semiconductor detectors 9
3.1 Comparison to other detectors.........................9
3.2 Silicon properties................................9
3.3 Drift and diusion...............................11
3.4 The P-N junction................................11
3.5 Reverse current.................................12
3.6 Interactions of particles in silicon.......................14
3.7 Microstrip detectors..............................16
3.8 Noise.......................................17
3.9 Radiation damage................................18
4 Detector modules 20
4.1 Construction..................................20
4.2 Read out system................................22
4.3 Standard QA tests...............................23
4.4 Beam tests....................................25
5 Simulations 28
5.1 Geant4 simulation................................28
5.2 SCT digitization................................29
5.3 Beam tests simulation and digitization....................32
6 Source tests 38
6.1 Radioactive source..............................38
6.2 Measurement setup...............................39
6.3 Analysis methods................................41
6.4 Measurement results..............................44
6.5 Source tests simulation.............................48
7 Conclusion 51
References 53
3
Nazev prace:Testovan polovodicovych stripovych detektoru pro detektor ATLAS
Autor:Pavel

Rezncek
Katedra (ustav):

Ustav casticove a jaderne fyziky
Vedouc diplomove prace:RNDr.Zdenek Dolezal,Dr.
e-mail vedoucho:Zdenek.Dolezal@m.cuni.cz
Abstrakt:Clem teto diplomove prace bylo provaden a vyvoj testu detekcnch modulu
vnitrnho detektoru ATLAS.V praci jsem se zameril na testy pomoc radioaktivnho


zarice.V Praze byla vyvinuta aparatura a napsan software pro meren a analyzu
dat.Smyslem techto testu bylo doplnen meren provadenych na svazku z SPS v CERNu,
tedy proveren skutecnych detektcnch vlastnost modulu.Vysledky testu se zaricem
a na svazku byly porovnany a byl nalezen vztah mezi merenymi signaly.Meren ukazala,
ze pomer stredn energie,kterou zaricem emitovany elektron ztrat pri pruchodu mod-
ulem,ku signalu zjistenemu z dat testu na svazku je 1.1090.070.Pro uplne pochopen
tohoto rozdlu byla provedena simulace obou typu testu.Simulaci meren na svazku
jsem pouzil k overen simulacnho softwaru.Vysledkem je dobra shoda trendu uhlovych a
jinych zavislost s daty,ovsemv absolutnch hodnotach dochaz k podhodnocen mereneho
signalu.Proto jsem provedl pouze relativn srovnan simulovanych odezev modulu z obou
typu testu.Simulace predpovda pomer strednch signalu z testu na svazku vuci testum
se zaricem:1.1170.020.Tyto testy se tedy,vzhledem k dobre denovanemu vztahu
jejich vysledku vuci vysledkum meren na svazku,staly vhodnym nastrojem pro overen
detekcnch vlastnost modulu.
Klcova slova:Krem

ikove stripove detektory,Testy zaricem,Testy na svazku,Geant4,
SCT,ATLAS
Title:Tests of semiconductor microstrip detectors of ATLAS detector
Author:Pavel

Rezncek
Department:Institute of Particle and Nuclear Physics
Supervisor:Dr.Zdenek Dolezal
Supervisor's e-mail address:Zdenek.Dolezal@m.cuni.cz
Abstract:The setup of system for testing silicon microstrip detectors with
90
Sr source
of electrons was developed.The aimof the measurements was to determine the median sig-
nal of particle passing through prototype modules for the ATLAS semiconductor tracker.
Comparison to beam tests results was performed to check the consistence of the source
tests results.The ratio of signals measured in beam tests to the source tests signal is
about 1.1090.070.To fully understand the results computer simulation of the setups
was performed.The beam tests simulation,used to validate the simulation software,
resulted in good description of trends of observed characteristics but in underestimation
of the signal.The source test simulation conrmed the relation of the beam tests results
to the source tests:the ratio of simulated median signal of beam tests to source tests was
about 1.1170.020.The dened relation of beam and source tests measurements made
the radioactive source tests usable for the signal determination.
Keywords:Silicon microstrip detectors,Source tests,Beam tests,Geant4,SCT,ATLAS
4
1 Introduction
The semiconductor detectors in high energy physics are mostly used for precise mea-
surement of particles'tracks.If placed in a magnetic eld the detectors provide high
accuracy momentum measurement.According to relatively high energy loss (hundreds
of eV/m) of charged particle passing through the semiconductor,low energy needed
to release free charge carriers (several eV for creation of electron-hole pair) and possibility
of creation of ne structures (in the order of m) of various properties,the semiconduc-
tor detectors can measure the position with an accuracy of several m.This makes the
detectors be able to detect secondary vertexes of decays of very short time living particles.
In the Center of European Nuclear Research (CERN) new hadron collider (LHC)
is being built.One of 4 detector systems at the LHC will be the ATLAS,described
in section 2.One part of it will be a semiconductor tracker consisting of silicon strips
detector modules.
This diploma thesis deals with tests and simulations of the SCT modules.The rst
parts of this thesis describe general properties and usability of semiconductors as detec-
tors,while the rest concerns SCT modules only.The standard quality assurance (QA)
procedure described in section 4.3 consists of detector tests and tests of readout electron-
ics.One of the main characteristics of SCT modules is the signal to noise ratio (S=N).
While the QA tests are able to nd the noise,signal can be determined by using real
particles only.For this purpose SCT modules were tested in beam on SPS at CERN (see
section 4.4).Because of the high cost and unavailability of beam tests,method using
the 

radioactive source for signal measurement has been developed and results of sev-
eral modules shown in section 6.4 were compared to the results of ATLAS simulation and
digitization software described in sections 5.1 and 5.2.The simulation and digitization
software has been validated on the beam-tests data in section 5.3,that were analyzed
by other SCT groups [10].Because of very high luminosity of the LHC,SCT modules
will operate in high radiation environment.So the tests were focused on measurement
of properties of modules irradiated to dose equivalent to the dose after 10 years of oper-
ation of the ATLAS detector system.Most of the tests were done on irradiated forward
modules,however several were performed on unirradiated as well.
5
2 ATLAS detector system
The ATLAS (A Toroidal LHC ApparatuS) detector system [1] is general-purpose de-
tector which is designed to exploit the full discovery potential of Large Hadron Col-
lider (LHC).The LHC properties (energy of interacting protons 7 TeV,expected lumi-
nosity 10
34
cm
2
s
1
) oer a large range of physics opportunities.The major ATLAS
interest is the origin of mass at the electroweak scale based on spontaneous symmetry-
breaking.One of the possible manifestation of spontaneous symmetry-breaking mecha-
nism is the existence of standard model Higgs boson or of a family of Higgs particles.
Alternative manifestation could involve a strongly interacting Higgs system.Other goal
are the searches for heavy W- and Z-like objects.Considering their leptonic decays,high
resolution lepton measurements and charge identication are needed even in the range
of few TeV.For supersymmetric particles searches hermecity and missing transverse en-
ergy E
T
capability of the detector is necessary.Another class of signatures of a new
physics like the composition of the fundamental fermions can be provided by very high
transverse momentum p
T
jet measurements.An important chapter of the LHC will be
a high rate b- and t-quark factory.The main emphasis in B-physics will be on precise
measurement of CP violation,determination of the angles in CKM unitary matrix and
general spectroscopy of states with b-quarks.
The set of ATLAS physics goals demonstrates that sensitivity to a variety of nal states
signatures is required.The basic design considerations lead to the following ATLAS de-
tector systems:electromagnetic calorimetry for electron and photon identication and
measurement,hermetic jet and missing E
T
calorimetry,tracking for lepton momentum
measurement,for b-quark tagging,for electron and photon identication and for tau and
heavy- avour vertexing.The other features are stand-alone,precision muon momentum
measurements,large acceptance in -coverage and triggering and measurements of parti-
cles at low-p
T
thresholds.The ATLAS detector system is shown in gure 1 and described
below.
The ATLAS magnet system consists of a solenoid and air-core toroids.The 2 T
solenoid is positioned in front of the barrel electromagnetic (e.m.) calorimeter.In order
to avoid degrading the e.m.calorimeter performance the thickness of the solenoid had to
be minimized.The superconducting coil is integrated into vacuumvessel of the calorimeter
barrel cryostat to eliminate the material and space of independent vessel walls.The di-
mensions of the solenoid are 1.22 m in radius and 5.3 m in length.The superconducting
toroid magnet system consists of 26 m long barrel part with outer diameter 19.5 m and
inner bore of 9.4 m,and of 2 end-caps with length 5.6 m and bores of 1.26 m.Magnetic
induction varies from 3 Tm
1
to 8 Tm
1
.The curved trajectories of charged particles
in the magnetic eld allow momentum measurement using the inner detector and muon
chambers tracking data.
The calorimetry of ATLAS consists of an inner barrel cylinder and end-caps using
liquid argon (LAr) technology,that is intrinsically radiation resistant,and hadronic scin-
tillator tile calorimeter surrounding the LAr one in full length.The barrel part of the liquid
calorimetry includes a presampler detector for correction to the in uence of solenoid coil
of the thickness of 0.83X
0
at normal incidence.The minimal thickness of the e.m.barrel
calorimeter is 26X
0
,while in case of end-caps calorimeters the minimal thickness is 27X
0
.
The hadronic scintillator tile calorimeter is based on a sampling technique with plastic
scintillator plates (tiles) placed in plane perpendicular to the beam axis and embedded
in iron absorber and read out by wavelength shifting bers.The outer radius of the whole
calorimetry system is 4.23 m and total length is 6.7 m.This high performance system
must be capable of reconstructing the energy of electrons,protons and jets as well as
6
measuring missing E
T
.
The muon detector system involves 3 layers of chambers in the barrel part and 3 or
4 layers in the end-cap part.In the barrel region 2 muon chamber planes are attached
to the magnetic toroids and the third one is in the mid-plane to measure the sagitta.
In the forward region the chambers are placed at the front and back faces of the toroid
cryostats,with a third layer against the cavern wall to maximize the lever armof the point-
angle measurement.Every chamber consists of detectors for the precision measurement
and for the triggering.In the barrel part,2 multilayers of drift tubes are used for pre-
cision measurement while in the end-cap part cathode strip chambers are used in addi-
tion.For triggering resistive plates are used in the barrel region and thin gap chambers
in the end-cap region.The basic measurement in each muon chamber is a tracks segment,
providing a vector for robust pattern recognition and momentum determination.
Figure 1:The ATLAS detector system.
The inner detector system [2] shown gure 2 and covering range of pseudorapidity
jj < 2:5 is composed of 3 dierent detectors:semiconductor pixel detector,semiconductor
strip detector and transition radiation tracker.The nearest one to the beam pipe is
the pixel detector.It is designed to provide a very high-granularity and high-precision
set of measurements as close to the interaction point as possible.The system consists
of 3 layers in the barrel part and 4 disks in the end-cap part,and oers 140 million
detector elements,each 50 m in the R direction and 300 m in the z.The maximal
radius of barrel layer is 14 cm and of forward disk is 20 cm.The total length is 2.2 m.
The furthest part of the inner detector system is the transition radiation tracker based
on straw tubes.Electron identication capability is added by employing xenon gas to
detect transition radiation photons created in radiator between the straws and by using
2 independent thresholds for tracking hits and transition radiation hits.The technique
allows typically 36 measurements to be made on every track.The diameter of every straw
is 4 mm and drift-time measurements give a spatial resolution of 170 m.The maximum
7
straw length is 150 cm.In the barrel region straws are parallel to the beam direction and
perpendicular in the end-cap region.The middle part of the inner detector is the silicon
strip detector - semiconductor tracker (SCT) - consisting of 4 barrel layers and 9 forward
wheels.The SCT system is designed to provide 4 precision measurements per track
in the intermediate radial range and contributing to the momentum,impact parameter
and vertex position measurement.The maximum radius of the barrel layer is 52 cm
and 56 cm of the forward wheel.The system requires very high dimensional stability,
cold operation of the detectors and evacuation of heat generated by the electronics and
detector leakage current.
Forward SCT
Barrel SCT
TRT
Pixel Detectors
Figure 2:The inner detector.
The group of VdG accelerator at Institute of Particle and Nuclear Physics (IPNP)
of Faculty of mathematics and physics at Charles University in Prague has been involved
in working places where QA tests of 200 SCT forward detector modules will be performed.
8
3 Semiconductor detectors
3.1 Comparison to other detectors
Semiconductor detectors are in high energy physics mostly used for precision tracking
that allows detection of secondary vertexes of very fast decaying particles.The advantages
of semiconductor detectors compared to the others being used for tracking are following:
 The gap energy between valence and conduction band is 1.11 eV in silicon and so
the average energy for creation of electron-hole pair (e-h) is 3.6 eV.That is approx-
imately 10 times lower compared to the ionization energy of gases used in propor-
tional chambers,drift chambers,time projection chambers etc.
 Due to high density of semiconductors,the average energy loss per unit of length
is also higher according to the energy loss in gases.In case of silicon and minimum
ionizing particle (MIP) the value is 390 eV/mwhile for the gases the loss is 3 orders
of magnitude lower.Consequently the thickness of semiconductor detectors can be
very small which minimizes the multiple Coulomb scattering.Usual thickness is
around 300 m.
 Another advantage connected to the high density is the reduction of range of ener-
getic secondary electrons that leads to good spatial resolution.
 The present advanced technology of silicon detector production allows creation
of very ne structures on them (in the dimensions of micrometers).The dimensions
of the structures (usually strips or pixels) then mainly contribute to the resolution
of the semiconductor detectors.
 Since the readout electronics is usually based on semiconductor technology,the de-
tectors and electronics can be integrated together.Noise of such a module is than
reduced.
 These detectors are mechanically rigid and so not complicated supporting structures
are needed.
 High mobility of the charge carriers results in high rate of reading and lower dead
time.Typical width at half maximum (FWHM) of the read out pulse is 20 ns.
But the semiconductor detectors have beside their high cost also one disadvantage
compared to the gaseous detectors.It is the absence of multiplication of the amount
of primary generated charge carriers and so the signal is only a function of the detector
thickness.
3.2 Silicon properties
Silicon is an element of IV group of the group of elements and has 4 electrons on the va-
lence shell.All the conductivity is realized by electrons excited from the valence band
into the conducting one.Such an excitation leads to a generation of hole - empty state
that left after the electron excitation and that behaves as a positively charged particle.
In the silicon without impurities the densities of electrons and holes are the same.By re-
placing some of the silicon atoms by atoms from the III or V groups the p- or n-type
materials are obtained.Elements from the III group (acceptors) have 3 valence electrons
and easily attach an electron from silicon atoms.Elements from the V group (donors)
9
have one very weakly bound electron that can be easily excited to the conduction band.
The"binding"energy of electrons in n-type and of holes in p-type silicon semiconductor
is approximately 45 meV.Very heavily doped semiconductors are marked n
+
or p
+
re-
spectively.In both n- and p-type semiconductors there are the other type carriers as well,
due to thermal excitations,called minority carriers.
The density of intrinsic charge carriers is [4]:
n(T) =
Z
1
E
g
D
e
(E;T)f
e
(E;T)dE (1)
where D
e
(E) is the state density [3]:
D
e
(E) =
1
2
2

2m
e
h
2

3=2
(E E
g
)
1=2
(2)
and f
e
(E) the Fermi-Dirac function for system of fermions:
f
e
(E) =
1
e
EE
F
kT
+1
(3)
The used symbols are the energy of electrons E,the Fermi level E
F
,the gap energy E
g
,
the temperature T,the Boltzmann constant k,the Planck constant h and the eective
electron mass m
e
connected to the second derivative of energy as a function of momentum.
Application of equations (2) and (3) in (1) and use of similar relations for the density
of holes p(T) results in:
n(T) = 2

m
e
kT
2h
2

3=2
e
E
F
E
g
kT
(4)
and
p(T) = 2

m
h
kT
2h
2

3=2
e
E
F
kT
(5)
In Si without any impurity both densities are equal (n
i
) and do not depend on the Fermi
level:
n(T)p(T) = n
2
i
= 4

kT
2h
2

3
(m
e
m
h
)
3=2
e
E
g
kT
(6)
In doped silicon of densities of N
A
acceptors and N
D
donors the relation (6) still holds
since compared to intrinsic semiconductor it is the Fermi level E
Fe
that changes only.
The extrinsic carrier densities follow equations coming from zero net charge density [5]:
n = n
i
e
E
Fe
E
F
kT
=
1
2
h
N
D
N
A
+
q
(N
D
N
A
)
2
+4n
2
i
i
 N
D
(7)
and
p = n
i
e
E
F
E
Fe
kT
=
1
2
h
N
A
N
D
+
q
(N
D
N
A
)
2
+4n
2
i
i
 N
A
(8)
where the approximations are valid when N
D
 N
A
;n
i
,(n  p) and N
A
 N
D
;n
i
,
(p n) respectively.
Properties of silicon material are written in table 1.Particle passing through the de-
tector ionizes the Si atoms and so eectively creates the e-h pairs.For typical thickness
of silicon detector 300 m the number of generated e-h pairs by MIP passing perpendicu-
lar through the detector (see section 3.6) is 3.210
4
which is 4 orders magnitude lower than
the total number of free carriers in intrinsic silicon of a surface of 1 cm
2
and the thickness
mentioned above.In doped material the S=N ratio would be even smaller.One way to
increase the ratio,is to cool the semiconductor.Another way is to deplete the detector
of free carriers through a reverse biases P-N junction.The second way is the principle
of operation of a silicon radiation detectors.
10
Atomic number
14
Atomic weight
28.08
Atomic density
4.9910
22
cm
3
Density
2.33 g/cm
3
Dielectric constant
11.6
Gap energy
1.11 eV
Eective states density in conduction band
2.8010
19
cm
3
Eective states density in valence band
1.0410
19
cm
3
Electron mobility
1350 cm
2
V
1
s
1
Hole mobility
480 cm
2
V
1
s
1
Electron Hall mobility
1670 cm
2
V
1
s
1
Hole Hall mobility
370 cm
2
V
1
s
1
Electron diusion constant
34.6 cm
2
s
1
Hole diusion constant
12.3 cm
2
s
1
Intrinsic carrier density
1.4510
10
cm
3
Breakdown eld
30 V/m
Diamond type lattice spacing
0.5431 nm
Mean energy for e-h pair creation
3.63 eV
Fano factor
0.115
Table 1:The physical properties of silicon at room temperature.
3.3 Drift and diusion
Drift of charge carriers is their movement under external eld
~
E.The speed ~v of such
a movement is proportional to the external eld:
~v = 
~
E (9)
where the coecient  of the proportionality is mobility of electrons and holes respectively.
Movement of charge carriers under magnetic eld
~
B results in change of the movement
direction by Lorentz angle#
L
:
tan#
L
= 
H
B (10)
The coecient 
H
is Hall mobility.
For silicon with inhomogeneous carriers density the mean movement of the carriers
of charge q is,due to thermal uctuations,nonzero and follows the opposite direction
of the density n gradient:
~
F = D
~
rn (11)
This equation expresses the proportionality of ow
~
F to the density gradient
~
rn using
the diusion coecient D.This coecient is related to the mobility by Einstein equation:
D =
kT
q
 (12)
coming from the zero value of sum of drift and diusion ows.
3.4 The P-N junction
As mentioned above,reverse biased P-N junction reduces the number of free carriers.
Due to gradient of electrons'and holes'densities in the junction of n- and p-type semi-
conductors,the free charge carriers diuse and recombine.The result is net positive and
11
negative charge in the n- and p-type materials respectively.This region of net charge
called depletion region causes built-in potential barrier that,assuming N
A
;N
D
n
i
,can
be calculated from [5]:
V
D
=
E
FA
E
FN
q
=
kT
q
ln

N
A
N
D
n
2
i

(13)
with E
FA
and E
FN
being the Fermi levels in n- and p-type crystals respectively.
The depletion region can be widened by applying reversed potential V
bias
on the P-N
junction.The barrier height would than be V
B
= V
bias
+V
D
.The electric eld distribution
can be obtained by solving a one-dimensional Poisson equation:
d
2
V
dx
2
= 
qN

(14)
Let W
A
and W
D
be the width of depletion layers where uniformnet charge densities are N
A
and N
D
in the p and n regions respectively.Considering the neutrality of the crystal
(N
A
W
A
= N
D
W
D
) the solution of the Poisson equation is [5] (see gure 3):
W
A
=
s
2V
B
qN
A
(1 +N
A
=N
D
)

s
2V
B
qN
D

N
D
N
A
(15)
and
W
D
=
s
2V
B
qN
D
(1 +N
D
=N
A
)

s
2V
B
qN
D
(16)
where  is the permitivity of silicon.Choosing the material so that N
A
 N
D
(see
the approximation),the depletion region is wide on the n-side and shallow on the p-side.
Since there is a voltage dependent charge increment dQ = qNdW that appears on ei-
ther side of the junction as a result of the widening of the depletion region on that side dW,
caused by an increase of the barrier voltage dV
B
,then it is possible to dene junction
capacitance [5]:
C
j
=
dQ
dV
B
=
dQ
dW

dW
dV
B
=
s
qN
A
N
D
2(N
A
+N
D
)V
B

s
qN
D
2V
B
(17)
The capacitance decreases with rising bias voltage until depletion layer reaches the back
of the crystal.Such a V
B
is called depletion voltage V
dep
.
3.5 Reverse current
The depletion region is free of majority carriers,but under equilibrium conditions e-h
pairs are generated continuously anywhere within the volume of the crystal.In opposite
to non-biased detector,the created carriers have little chance to recombine.The pairs
are separated and electrons and holes drift under the in uence of the electric eld.This
current is called leakage or reverse current.Depending on where the e-h pair is generated
there are 2 components:a generation current of density j
gen
caused by charge generated
within the depletion region and a diusion current j
di
coming from charge generated
in the neutral silicon and diusing to the depletion region.
Assuming very low charge densities n;p  n
i
in the depletion zone of width W and
eective life time 
0
of minority carriers [5]:
j
gen
=
1
2
q
n
i
(T)

0
W(V
bias
) (18)
12
Acceptor ion
hole
Donor ion
electron
P N
x [mm]
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
Charge density [C/m]
-0.0015
-0.001
-0.0005
0
0.0005
0.001
x [mm]
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
Electric field [V/m]
-1
-0.8
-0.6
-0.4
-0.2
0
x [mm]
-0.15 -0.1 -0.05 0 0.05 0.1 0.15
Potential [V]
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Figure 3:The charge density,electric eld (intensity) and potential in the P-N junction.
13
The temperature dependence is only through n
i
(T).Considering equation (6) n
i
(T)
increases by factor of 2 with a temperature increase of 8 K.The current is proportional
to
p
V
bias
,when V
bias
is lower than depletion voltage,and constant above it.
Pairs e-h generated in the neutral region in the proximity of depletion one have
a chance to diuse into it before recombination.Denoting by 
e
and 
h
the lifetimes
of electrons and holes in the n- and p-type region respectively,the width of the layer
from which carriers would diuse is [5]:
L =
p
D (19)
where D is the diusion coecient for proper free carriers of density n.The diusion
current can be than calculated from:
j
di
= q
n

L (20)
3.6 Interactions of particles in silicon
There are two mechanisms of energy loss of charged particles in solids:the ionization
and the bremsstrahlung.Important part of the ionization process is the release of high
energy electrons (-electrons) that increase the mean energy loss.Another important
eect is the Coulomb scattering resulting in beam divergence after passing through the
detector.
The mean energy loss due to ionization of particle of charge z,mass M and velocity
(in units of speed of light c)  =
p
1 
2
,is described by Bethe-Bloch formula:


dE
dx

ion
=
Z
T
max
T
min
Tn
e
d
Ruth
dT
dT = 2 
2
2
h
2
z
2
m
e

2
Z
A
N
A
 ln

T
max
T
min

(21)
where T is the energy loss,n
e
is the density of electrons of mass m
e
in material of atomic
number Z,atomic weight Aand density ,
Ruth
is the Rutherford scattering cross-section,
 is the ne structure constant and N
A
is the Avogadro constant.The minimum energy
loss T
min
is equal to the ionization potential I
0
 16  Z
0:9
[6],while the maximum energy
loss is:
T
max
=
2m
e
c
2

2

2
1 +2
m
e
M
+(
m
e
M
)
2
(22)
The factor of 2 in relation (21) accounts for such eects as atomic excitation.Modication
of the formula (21) for fast electrons was found to be [9]:


dE
dx

ion;e

=
2
2
h
2
z
2
m
e

2
Z
A
N
A

ln

m
2
e
c
4

2

2I
2
(1 
2
)

ln2

2


1

2

+
1

2
+
1
8

1 
1


2

(23)
The statistical uctuations around the mean energy loss in a layer of thickness x are
described by Landau,Vavilov or Gaussian theory,depending on ratio ,that is propor-
tional to the ratio of mean energy loss to the T
max
:
 =

T
max
=
2
2
h
2
N
A
z
2
Z
m
e

2
A

x
T
max
(24)
The assumptions on Landau theory are that the ratio =I
0
1 and that the typical energy
loss is small compared to T
max
and is large compared to the binding energy of the most
tightly bound electrons.The Landau distribution function is shown in gure 4.The rst
restriction is removed in the Vavilov theory.According to the assumptions,Landau
14
Energy loss [keV]
50 100 150 200 250 300
Number of events
0
50
100
150
200
250
300
350
400
Figure 4:Simulated energy loss of 180 GeV negative pions using Geant4 and distribution
function of Landau theory (solid curve).
theory can be used when  < 0:01,while the Vavilov theory is used when 0:01 <  < 10.
In the region of  > 10 which describes non-relativistic particle energy loss,Gaussian
distribution can be applied,assuming a large number of collisions involving the loss of most
of the incident particle energy,
The tail in the region of high energy loss in Landau distribution is caused by high
energetic electrons (-electrons) released by the incoming particle and resulting in sig-
nicantly higher average energy loss than the most probable value.Since the range
of the -electrons is in the order of 10 m (40 m for 100 keV electron),they can cause
displacement of the measured track position.The number of -electrons of energy higher
than T

is [8]:
dN

dx
=
2
2
h
2
z
2
m
e

2
Z
A
N
A

x
T

(25)
A -electron of kinetic energy T

is produced at an angle 

determined by relation [8]:
cos 

=
T
e
p
e

p
max
T
max
(26)
where p
max
and p
e
are momenta corresponding to the kinetic energies.
Another mechanism of energy loss important for e

is the electromagnetic radiation
(bremsstrahlung) described by formula [9]:


dE
dx

brem;e

=

2
h
2
Z(Z +1)N
A

137m
e
A

4 ln(2 ) 
4
3

(27)
The relative in uence of ionization and bremsstrahlung in solids is described by critical
energy [8]:
E
c
=
610
Z +1:24
 MeV (28)
Assuming thickness of the layer being passed through x  X
0
,with X
0
= 9.36 cm
being the radiation length in silicon,the mean number of radiated photons with energies
15
between E
min
and E
max
is [8]:
N

=
x
X
0

4
3
ln

E
max
E
min


4(E
max
E
min
)
3m
e
c
2

+
(E
max
E
min
)
2
2(m
e
c
2
)
2

(29)
The coulomb scattering at small angles [8] of particle of momentum p passing through
a thin layer is described by RMS of Gaussian distribution of de ection angles:
P() =
1
q
2
2
RMS
 exp


2

2
RMS

d (30)

RMS
=
z  21MeV
cp
s
x
X
0
(31)
3.7 Microstrip detectors
Schematic diagram of n-type microstrip detector is shown in gure 5.The main
part of the depletion region is in the weakly doped n-type material (see formula (16)).
Particle traversing through the detector creates e-h pairs along its path.The number
of the pairs is proportional to the energy loss described in section 3.6.Since the detector
of thickness d is reverse biased the generated carriers drift along the electric eld E(x) [7]
towards the strips and backplane:
E(z) = 
V
bias
+V
dep
d
+
2V
dep
d
z
d
(32)
The carriers diuse in the direction ~x perpendicular to the electric eld.The distribution
of number of holes and electrons after drift to the strips and backplane respectively follows
the Gaussian law:
dN =
1
q
2[2Dt(z) +
2
]
 exp


x
2
4Dt(z) +2
2

N(z)dzdx (33)
where dN is the charge in the element dx,at distance x from the track,and com-
ing from the charge N(z)dz generated in the element dz of the track at distance z
from the strips.N(z) is the linear density of the generated charge.The other used
symbols are diusion coecient D,width of the track  and the time of charge carriers
drift t(z) from the place of generation to the strips and backplane.The drift time can be
calculated combining denition (9) and relation (32):
t
h
(z) =
d
2
2V
dep

h
ln

(V
bias
+V
dep
)d
(V
bias
+V
dep
)d 2V
dep
z

(34)
for holes and:
t
e
(z) =
d
2
2V
dep

e
ln

(V
bias
+V
dep
)d 2V
dep
z
(V
bias
V
dep
)d

(35)
for electrons respectively.The product of D t(z) is independent of  and so is the width
of the distribution.
When measuring the amplitude of the signal on each strip (analog readout),partial
reconstruction of the distribution is possible,which results in much better localization
precision compared to strip pitch p:
x 
p
S=N
(36)
16
When binary readout is used,signal on the strips is compared to a given threshold and
the RMS of the measured and real track position x
2
can be calculated,assuming no
charge loss,from formula:
x
2
=
1
p
Z
+p=2
p=2
x
2
dx =
p
2
12
(37)
The charge division between the strips can be realized in resistive or capacitive way.
The resistive one leads to noise generation.The capacitive one is naturally realized
by interstrip capacitance,but there is a non-linearity and charge loss due to strip-by-strip
and strip-ground capacitance.
As mentioned in section 3.1 one of the advantages of semiconductor detectors is the in-
tegration of the sensitive material and the read out electronics.There are 2 possible ways
of such integration:direct connection (see left part of gure 5) where reverse current ows
through the electronics or capacitive connection (see right part of gure 5) where only cur-
rent changes are detected by the electronics.The capacitor C can be easily implemented
on the detector using a layer of SiO
2
as well as the bias resistor R using polysilicon.
n
+
Al
p
+
p
+
Al Al
n
SiO
2
+ -
+ -
+ -
+ -
+ -
+ -
+ -
z
d
dx x
Front-end
electronics
particle
Front-end
electronics
R
C
Figure 5:The slice of n-type microstrip detector with DC-readout (left) and AC-readout
(right).
3.8 Noise
Referring to section 3.1 there is no multiplication of the amount of generated charge
carriers.In events with tracks crossing the detector between 2 strips or at large angles,
due to charge sharing,only a fraction of total charge is collected on each strip.To
distinguish the real signal,low noise is essential.The electronics and detector itself
contribute to the noise in dierent ways:
17
 The main contribution comes from the capacitance of the strip being read out to its
neighbours and to the backplane.It causes a signal loss and acts as a load capac-
itance C of the preamplier.For conventional charge sensitive amplier the elec-
tronics noise is calculated as equivalent noise charge (ENC) from the formula:
ENC
load
= A+B  C (38)
where A and B are constants depending on the preamplier.
 Another contribution is the equivalent noise referred to the input of the amplier
from the leakage current I and is given by:
ENC
leak
=
e
q
s
qIT
p
4
(39)
where e is natural logarithm base,q is the electron charge.and T
p
is the peaking
time equal to the integration time of a CR-RC shaper.The peaking time diers
from the integration time for other types of shapers.
 Bias resistor R contribute to the noise as well by following formula:
ENC
bias
=
e
q
s
T
p
kT
2R
(40)
with k being the Boltzmann constant and T temperature.
The error in measurement of the signal caused by all these contributions can be ob-
tained as their sum in squares:
ENC =
q
ENC
2
load
+ENC
2
leak
+ENC
2
bias
(41)
3.9 Radiation damage
As ATLAS will operate in high radiation environment,changes to the properties parti-
cles with the nuclei in the lattice may lead to permanent material changes due to following
processes:
 Displacement of lattice atoms leading to interstitials and vacancies
 Nuclear interactions
 Secondary processes from energetic displacement lattice atoms leading to possible
defect clusters
Most of the primary defects are mobile at room temperature and will therefore par-
tially anneal.However,there are also stable defects:combination of vacancy and oxy-
gen (A-center),a vacancy phosphorus complex (E-center) and 2 vacancies next to each
other (divacancy).Although the primary interaction of radiation with silicon is strongly
particle-type and -energy dependent,due to smoothing out by secondary interactions and
considering non-defect-producing interactions with electrons,it is possible to use scaling
by the non-ionizing energy loss (NIEL) of 1MeV neutrons.
The defects can act as trapping centers reducing signal and as recombination centers
leading to an increase of the leakage current.They can change the resistivity of undepleted
18
regions and charge density in the depleted region,thus requiring an increase of depletion
voltage.In case of n-type detector,long term radiation leads to eective type inversion.
Damage in electronics has dierent eect as induced change in doping concentration is
not important due to much higher doping densities than in detectors.The most important
eects are the damage on silicon oxide layers in metal-oxide-semiconductor eld eect
transistors (MOSFET) and the decrease of minority carriers lifetime in case of bipolar
and junction eld eect transistors (JFET).The eects lead to decrease of amplication
characteristics of transistors and increase of noise.
19
4 Detector modules
4.1 Construction
Every SCT module consists of 2 or 4 silicon strips detector wafers connected by fan-ins
to a hybrid with 12 readout chips.The detectors are glued on a mechanical basement.
The typical surface of the sensitive wafers is 66 cm
2
.There are 4 types of the SCT
modules (see gure 6):a barrel module and 3 forward modules diering in the number
of detectors and their geometry.In modules with 4 silicon wafers,the detector wafers are
bonded to 2 pairs and so providing eectively 2 sensitive wafers of length approximately
12 cm.
Figure 6:The barrel module (top left),forward outer module (bottom left),forward
middle module (bottom right),forward inner module (top right).
All the silicon wafers are single sided p-in-n detectors,285 mthick and containing 768
Al strips 23 m wide.Every module has 2 parallel detector planes and thus 1536 readout
channels.The 2 planes are rotated by an angle of 40 mrad to provide 2D track position
measurement by combining the hit strips numbers.The strip pitch of barrel detectors
is constant:80 m.Thus taking into account the cylindrical coordinate system (R,,z)
with z direction parallel to the beampipe,the point resolution is 23 m(see formula (37)).
Combining the 2 points from both detector planes gives precision of 16 m in the R-
direction and 580 m in the z-direction.The forward detectors dier from the barrel ones
by non-parallel strips converging to one point close to the beam line for easy extraction
of the (R,,z) coordinates of the measured tracks.The strip pitch varies from 54 m
up to 95 mand consequently the point resolution is position dependent.While the plane
of the barrel detectors is parallel to the beam direction,the forward modules'detector
planes are perpendicular to it and so the last mentioned precision is not in the z-direction
but in the R-direction for forward modules.
20
Readout buffer
Compression
Format
Control
128 strips x 132 cells
pipeline
Data Out
Calibration
pulse
Threshold
Discriminator
Comparator
Preamplifier
Shaper
Front-end electronics
Detector
Strips
Figure 7:The FE and readout electronics.
The ATLAS SCT readout electronics is responsible for supplying the hits information
to the ATLAS 2
nd
level trigger and data acquisition system.To ensure low noise opera-
tion,front-end (FE) electronics is mounted immediately at the strips'electrodes.There
are 12 readout chips on hybrid of every module and every chip reads out 128 channels
(strips).The chips on the rst and second module side are marked M0 S1 S2 S3 S4 E5
and M8 S9 S10 S11 S12 E13 respectively (see gure 8).The ATLAS SCT uses binary
Detectors
Mechanical
basement
Bonds
Chip S3
Chip S4
Chip E5
Chip S2
Chip S1
Chip M0
Fan-ins
Hybrid
Figure 8:Module description.
readout (signal on strips is compared to a given threshold) to reduce the amount of data
to be transmitted and stored.The schematics diagram [11] of FE architecture is shown
in gure 7.The data from the strips are every 25 ns (LHC bunch crossing rate) stored
into chips'pipelines and are held there for the duration of the level 1 trigger (L1) la-
tency waiting for the decision to transmit the data or discard it.The average trigger
rate of the FE electronics operation is 100 kHz.If the data are to be read out,they
are compressed and transmitted out using optical bers.To suppress noisy hits (clusters
of channels where read signal is greater than set threshold),certain type of data readout
and compression based on special timing pattern recognition can be applied.Important
feature of the electronics is the calibration circuit allowing to associate threshold on dis-
criminator to an appropriate charge at the input of the preamplier.To obtain the best
21
possible uniformity of the calibration process,thresholds can be adjusted individually
for every channel.This process is called trimming.The chips and hybrid construction
allows to bypass non-functional chips and there is a redundant optical connection to x
possible failure of the standard one.
4.2 Read out system
The schematic diagram of the readout system for QA procedures for a single module
is shown in gure 9.The hardware is based on Versa Module Eurocard (VME) modules
of the following functionality:
PC
ROOT
VME controller
SCTLV3
SCTHV
MuSTARD
CLOAC
SLOG
PPR
VME crate
Clean room
Slow control system
Cooling
Module box
Support
card
Figure 9:The readout system for a single module.
 SCTLV3 module [12] provides low voltages (digital 4.0 V,analog 3.5 V) to the read-
out electronics and assures monitoring of the temperature and power consumption.
 SCTHV module [13] provides bias voltage for the detectors and monitors the leakage
current.
 MuSTARD module [14] reads out and stores the data from the hybrid
 CLOAC module [15] and SLOG module [16] generate command sequences like trig-
ger,calibration and reset signals.The latest ones resend conguration to the chips
to correct possible loss of threshold and other settings.The CLOAC module allows
use of external triggers (for example from a scintillator in beam tests) and can fan-
out the command sequences that were sent to the readout electronics.The later
mentioned feature can be used to trigger a laser.
 VME controller assures communication of the modules with personal computer.
 The PPR together with the support card are passive components connecting data
links from the hybrid and the VME modules.
The data acquisition (DAQ) software [18] is based on ROOT [17] - a C++ interpreter
with additional classes for easy data manipulation and visualization.The software con-
tains a buttons control panel,ROOT interactive window and a basic information panels
showing data control system (DCS) monitoring and the occupancy of the strips after
applied a burst of triggers,results of performed scans etc.
22
As the silicon modules have to be tested in a clean environment,clean room was built
for this purpose at IPNP [28].Typical readout system for QA allows to test up to 6
modules in parallel.Since the modules have to be cooled during the tests and humidity
reduction by owing a dry air on the modules is needed to prevent shorts at the detector,
the tested devices are placed into special boxes.The monitoring of the environment
conditions,data backup and solving of accidents like power failure,is assured by slow-
control system [26].
4.3 Standard QA tests
The standard QA procedure includes tests of the detectors and functionality tests
of the readout electronics.The quality of the detector wafers is checked by measure-
ment of the leakage current as a function of bias voltage.Example of this IV-curve is
in gure 10.Accounting the dependence of depletion layer width on the bias voltage,
the relation (18) for generation current is valid up to 300 V,where the avalanche eects
start to modify the shape of the IV-curve,and the depletion voltage is around 60 V.Ap-
plying in the relation (18) 
0
= 1 ms [4] gives the generation current of 2 A.This value
is consistent in the order with the measured one.Precise comparison is complicated due
to 
0
dependence on the temperature and number of impurities in the silicon.The used
value of 1 ms is a very rough approximation for weakly doped n-type silicon.In addition
the diusion current j
di
was neglected.
0 50 100 150 200 250 300 350
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
Bias [V]
Leakage current [A]µ
0 100 200 300 400 500
0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
Bias [V]
Leakage current [A]m
Figure 10:The IV-curve of unirradiated (left) and irradiated (right) module.Monitored
temperatures on the hybrids were around 25 Celsius degrees on the unirradiated module
and 0 Celsius degrees on the irradiated one.
The tests of the readout electronics involve bypass and redundancy tests,but the most
important part is the calibration process including trimming and noise occupancy mea-
surement.Another issue is the long-term stability test lasting 24 hours.Since the SCT
readout is binary,it is not possible to nd the amplitude of the signal directly by one
measurement,but integral of the spectrum of the signal can be obtained by scanning
the threshold to which the signal is being compared.If the signal is generated by charged
particle passing through the detector,one obtains integral of the Landau curve,while
for signal coming from the calibration circuit,the result is an error function,because
the charge provided by calibration circuit has a narrow Gaussian distribution.The real
measured sigma of the Gaussian function is higher and is equal to the noise (see sec-
tion 3.8) assuming Gaussian distribution of the noise with given sigma equal to ENC and
zero mean.Example of such an error function is shown in gure 11.The noise occupancy
measurement (see gure 12) is a simple high statistics threshold scan with no calibra-
tion charge applied.The trimming (see gure 13) is done for selected calibration charge
23
Amplitude [fC]
-2 -1 0 1 2 3 4
Spectrum
0
0.2
0.4
0.6
0.8
1
Threshold [fC]
1 1.5 2 2.5 3 3.5 4 4.5 5
Number of hits
0
200
400
600
800
1000
Figure 11:The threshold scan (right) of single channel with 0.2 fC step and with zero-
width calibration charge of 3 fC - see dashed curve in gure (left).For every set thresh-
old,the calibration pulse was applied and signal was read out 1000 times.The his-
togram (right) shows the number of events when the read out signal was greater than
the threshold.The dashed curve corresponds to ideal readout with no noise,while the full
one is the smeared by Gaussian distribution of the noise (left).
by scanning the threshold and tuning the readout chips'settings so that the threshold
of 50% eciency (median) is uniform over all channels as much as possible.The calibra-
tion process consists of scanning the calibration charge and calculating the appropriate
median of threshold scan for every setting of the charge.Example of such a dependence
called response curve is shown in gure 14.The derivative of the response curve deter-
mines gain of the FE preampliers.The aim of these tests is to check whether the module
matches the specications (see section 4.4) on the rate of noisy hits and the purpose
of the calibration is to nd the threshold of around 1 fC,where the eciency should be
high enough.
Channel number
100 200 300 400 500 600 700
Threshold [mV]
0
20
40
60
80
100
120
140
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
Threshold [mV]
0 20 40 60 80 100 120 140
Noise occupancy
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
1
4.88E-006
Figure 12:The noise occupancy scan of KB-105 module.The left gure shows the oc-
cupancy separately for every channel,while the on the right average noise occupancy
of the 6 chips (1 side of the module) is shown.The marked point is the noise occupancy
at 1 fC threshold.
The radiation damage in uences properties of both the sensitive wafers and the read-
out electronics.The latter mentioned can be seen in an increase of the leakage current
24
and consequently the noise occupancy,depletion voltage increases as well.Fromthe beam
tests (see section 4.4) decrease of the amount of collected charge is obvious.In the elec-
tronics the radiation aects noise and gain.The irradiation of the modules is performed
at CERN PS by 24 GeV protons to the dose of 310
14
protons/cm
2
during approximately
2 weeks.The typical characteristics for both the irradiated and unirradiated modules
of 4 detector wafers are summed in table 2.Note the higher noise occupancy,leakage
current and bias voltage needed for operation of irradiated modules compared to unirra-
diated ones.In spite of the fact that the median collected charge in irradiated detectors
is lower and so is the eciency,the average size of strips clusters (see section 4.4) is
the same as for the unirradiated ones.This is due to stronger charge sharing in the ir-
radiated detectors.The lower gain of the FE electronics conrms the eects of radiation
on the electronics described above.
Channel number
100 200 300 400 500 600 700
Pulse amplitude [mV]
40
60
80
100
120
140
160
Channel number
100 200 300 400 500 600 700
Pulse amplitude [mV]
40
60
80
100
120
140
160
Figure 13:The points of 50 % eciency from threshold scan of all channels of KB-105
module before (left) and after trimming (right) showing better uniformity of the measured
signal amplitudes after trimming.
Calibration charge [fC]
0 1 2 3 4 5 6 7 8
Gain [mV/fC]
0
10
20
30
40
50
60
70
80
90
100
Calibration charge [fC]
0 1 2 3 4 5 6 7 8
Median [mV]
0
100
200
300
400
500
600
Calibration charge [fC]
0 1 2 3 4 5 6 7 8
ENC
0
500
1000
1500
2000
2500
Figure 14:The results of M0 chip calibration of module KB-105:response curve (left),
FE electronics gain (center) and ENC (right).
4.4 Beam tests
To verify the eciency of the modules in detecting particles,prototypes of the modules
were tested in beam of SPS at CERN.The schematic diagram of the beam tests setup is
shown in gure 15.The modules were placed in a light-tight box with integrated cooling
system.To nd the eciency of the tested devices,positions of the particles'tracks must
25
Quantity
Unirradiated modules
Irradiated modules
Eciency [%]
99.5
99.0
Noise occupancy
10
6
..10
5
10
4
..10
3
Cluster size
1.27
1.26
Median [fC]
3.4
2.7
Leakage current [A]
1
2000
FE gain [mV/fC]
50
35
Used bias voltage [V]
150
350
Table 2:The characteristics of SCT modules:unirradiated modules,irradiated modules.
The presented values are given at 1 fC threshold and cluster size at incidence angle 16 de-
grees.The values are typical as they vary from module to module.The leakage currents
correspond to measurements with monitored temperatures on the hybrids around 0 Cel-
sius degrees.
be known.This information is provided by 4 silicon strip detectors of strips pitch 50 m
and analog readout.The precision of this telescopes is up to 5 m(see formula 36).There
are 3 important characteristics of the measurements:
 Eciency - the number of events when there is a cluster of neighbouring strips
with read signal greater than the threshold and the track given by the telescopes is
not too distant (<150 m) from the position of the center of such a cluster of strips.
 Median - the threshold where the eciency reaches 50% (see section 4.3).
 Noise occupancy - probability that there will be a signal on a strip greater than
the threshold and the position of the strip is far from the track in the detector
determined by the telescopes.
 Cluster size - an average width of the hit strips clusters that are assumed to be caused
by the particle passing through the detector (see the denition of the eciency).
Light-tight box
B
Tested modules
Analogue
telescopes
Beam
Scintillators
in coincidence
Analogue
telescopes
&
trigger signal
Figure 15:The beam tests setup.
There are 3 possible eects that lead to the existence of 2- and more-strips clusters:
 -electrons with range sucient to reach also the strips neighbouring to the nearest
one.
26
 Charge sharing between strips due to possible non-perpendicular incidence angle and
due to diusion of the generated charge carriers as they always drift to the nearest
strip (see gure 17).
 Cross-talk between strips due to their capacitive coupling.
The region of interest is at around 1 fC threshold where eciency has to be suciently
high (>99%) and noise occupancy low (<510
4
) as dened in the Technical Design Re-
port (TDR) [2] to provide the expected reconstruction capability.Another important
characteristics are the dependence of the median (and consequently the eciency) and
cluster size on the incidence angle and change of the response in magnetic eld of 1.56 T.
The precise information about the track positions allowed to study the characteristics
at the edges of the detectors and to measure the median and cluster size dependence
on the relative position () of the track position with respect to the position of the strips.
Results of the beam tests can be found in [10].
27
5 Simulations
To understand the results of beamtests and their dierence to the source tests,simula-
tion of SCT modules functionality was performed.The whole simulation is divided into 2
parts:Geant4 [22] simulation and digitization under standard ATLAS SCT software [23].
5.1 Geant4 simulation
Geant4 is used to calculate the energy loss of particle passing through the module.
The output is a particle track divided into several segments with deposited energy in them.
This information is than used by the digitization software described in section 5.2.
The Geant4 simulation accounts following processes of particle's interactions in matter.
For electrons ionization including -electrons production,bremsstrahlung and multiple
scattering is applied.For positrons annihilation is used in addition and for muons,pair
production is considered as well.Photons interact through photo-electric eect,Compton
scattering and conversion to electron-positron pair.For hadrons ionization and multiple
scattering is used only.
The ionization is divided into 2 parts:ionization process with local energy deposition
and creation of -electrons.There is an energy cut T
cut
in Geant4 given by minimal
distance,that particle of energy E and mass m has to pass in material in order its energy
loss not to be involved into local energy deposition.So the local energy deposition is given
by [22]:


dE(Z;E;T
cut
)
dx

ion
= n
e
Z
T
cut
0
d
ion
(Z;E;T)
dT
dT (42)
where 
ion
(E;T) is the cross-section of particle's interaction with electrons in the material.
The cross-section of release of -electrons with kinetic energy T greater than T
cut
comes
from the cross-section 
ion
(Z;E;T):


(Z;E;T
cut
) =
Z
T
max
T
cut
d
ion
(Z;E;T)
dT
dT (43)
Compared to equations (21) (23) Geant4 ionization involves density eect correction that
takes into account material polarization,when high energetic particle passes through
it.The second correction is the shell one that involves lower probability of particle's
interaction with electrons on inner atomic shells (K,L,...).
Analogically the bremsstrahlung is divided into 2 parts:local energy deposition and
photon radiation if the photon has sucient energy E

(greater than E
cut
) to pass
in the material the predened minimal distance.The local energy deposition is given
by equation:


dE(Z;E;E
cut
)
dx

brem
= n
e
Z
E
cut
0
d
brem
(Z;E;E

)
dE

dE

(44)
And the cross-section for radiation of photons with energy greater than E
cut
can be
calculated from:


(Z;E;E
cut
) =
Z
Emc
2
E
cut
d
brem
(Z;E;E

)
dE

dE

(45)
To calculate energy loss at distance x in the material,Geant4 slices the track into N
segments x
i
:
E =
N
X
i=1

dE
dx

i
x
i
(46)
28
The directions of track segments include multiple scattering given by equation (30) and
also the lengths x
i
are corrected to the multiple scattering.
The geometry used for the simulation is written directly in Geant4 and is shown
in gure 16.While the detector wafers were implemented in the geometry,the hybrid
with readout electronics was not because both in the beam and source tests,that were
simulated,the particles weren't crossing the area of the hybrid.
Figure 16:Geometry of the Geant4 simulation of the beamtests.The geometry for source
tests diers only in dierent source (point) and in one case in aluminum plate between
the module and scintillator.
5.2 SCT digitization
The digitization software simulates the drift and diusion of the generated charge
carriers inside silicon and the function of the readout electronics.The software is described
in [24] and the used physical processes in [25].The purpose of the digitization is to provide
relatively fast and acceptable response of the SCT modules according to the geometrical
and electrical settings used in the beam tests.
The software reads the output of the Geant4 simulation described in section 5.1.
The segments of the track can be linearly divided to get vernier segmentation.For every
such segment its position,direction and energy loss in it is known.As the average energy
needed to create e-h pair is well known,it is possible to associate an appropriate generated
charge to every segment.The holes drift to the strips for time given by (34).The electrons
drift to the backplane of the detector and so their contribution to the signal on the strips
is not taken into account.Current induction on the strips coming from the movement
of the holes is neglected and so the signal is assumed to appear precisely when the holes
reach the side of the detector with the strips.This approximation can be used as the eld
is the strongest near the strips and so the high drift velocity of the holes causes the most
signicant induction on the strips.The eld approximation by formula (32) in the detec-
tor volume is not valid near the strips.Using simple numeric method to solve the Poison
29
"Surface drift"
to the nearest strip
z
d
particle
Strip
B
q
L
Drift time
t (z+d/2)
h
Pulse shape
Amplifier
Noise
Threshold
Arrival position
on the surface:
gaussian distribution
(diffusion)
d-electron
Geant4
simulation
h=0 h=1
Figure 17:The principal scheme of the digitization.
equation results in eld shown in gure 18.The arrival position of the holes on the surface
of the detector is shifted from the segment position due to diusion by random distance
z [mm]
0
0.05
0.1
0.15
0.2
0.25
x [mm]
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
E(x) [kV/mm]
-1.5
-1
-0.5
0
0.5
1
1.5
z [mm]
0
0.05
0.1
0.15
0.2
0.25
x [mm]
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
E(z) [kV/mm]
-1.8
-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
-0
Figure 18:Electric eld in microstrip detector.The coordinates x and z match the selec-
tion in gure 5.The eld coordinate in the direction along strips is zero.The strips are
located at x = 0 mm and x = 0.08 mm in the plane z = 0 mm.
with Gaussian distribution given by (33).Accounting the electric eld in the detector
shown in gure 18,such a surface charge is than supposed to be collected on the near-
est strip.The process is symbolically shown in gure 17.The digitization than simulates
the readout electronics:the noise,shaping of the signal on the strips,comparing the pulse
height at given time (see gure 19) to a set of thresholds and nally producing the digits
- the map of strips with the signal greater than the threshold.The software contains
several free parameters mostly concerning the electronics like gain and oset correlation
of the ampliers or peaking time of the shaper,but there are also physical parameters like
30
Time [ns]
0 10 20 30 40 50 60 70 80 90 100
Signal [fC]
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
Time [ns]
0 10 20 30 40 50 60 70 80 90 100
Logical pulse
0
0.2
0.4
0.6
0.8
1
Figure 19:The pulse shape (top) and output of the comparator (bottom) (see gure 7)
when the threshold was set to 2 fC (dashed line).
temperature,ENC or magnetic eld.To simulate the response of the modules in magnetic
eld,the eld is not applied in Geant4 because its in uence on the momentum direction
of the primary particle is not measurable (for 180 GeV pions in magnetic eld of 1.56 T
the Lorentz angle - the particle movement direction deviation due to magnetic eld dur-
ing going through the detector - is approximately 0.7 rad).Because the magnetic eld
considerably in uences the movement of the generated free charge carriers inside the de-
tector,the magnetic eld is applied in the digitization software.The parameter that
denes the magnetic eld in the software is the Lorentz angle.
The standard outputs of the digitization for every scan-point (determined by threshold
and time of readout) are the same as in beam tests:
 Eciency - the maximum distance of the nearest cluster of strips is 50 m.The 3
times wider limit in the beam tests analysis is used because of the inaccuracy
of the telescopes determining the track position,while in the digitization the track
is known absolutely from the Geant4 simulation.Using the dependence of eciency
on threshold,median can be calculated.
 Noise occupancy - the only discrepancy from the beam tests analysis is analogi-
cally to the eciency denition the limit on the minimum distance of the noisy hit
from the track in the detector.
 Cluster size - see denition in section 4.4.Statistical error of cluster size is calculated
as well.
It was checked that the used limits (that are set in the software as default) provide,
accounting the statistical errors of the eciency and the noise occupancy calculation,
the same results as with the limits used in beam tests.
31
The existing version of the digitization of beamtests written by Szymon Gadomski [25]
does not write out the binary information (digits) from the strips,but calculate straight-
way the eciency etc.described above,so I made a slight modication to the software
to assure this feature.The map of digits is useful as it is possible to use it as real mea-
sured data in analyzing software of beam and source tests.Therefore this allows to test
the analyzing software and to perform comparison to the real data at the basic level.
5.3 Beam tests simulation and digitization
To validate the simulations software,beam tests conguration was set in Geant4 ge-
ometry.The validation was performed on simulation of a single barrel module,because
due to constant strip pitch the response simulation is simpler compared to forward mod-
ules.The important characteristics that the simulation should be able to reproduce are
the noise occupancy (simply determined by the free parameter ENC),the dependence
of the cluster size and the eciency (respectively the median) on bias voltage,incidence
Geant4
Particle


Particle's kinetic energy
180 GeV
Minimal step length
10 m
Minimal energy of secondary particles (-e

) in silicon
31.5 keV
Minimal energy deposited in scintillator
0 keV
Total number of simulated events
1000
Length of the track segments
80 m
Digitization
Module type
Barrel
Depletion voltage
70 V
Temperature
0
o
C
Length of the track segments
80 m (10 m)
Number of simulated charges'drifts per segment
10 (1)
ENC
1500 e

Number of bad channels
0
Surface drift time on the whole strip pitch
10 ns
Maximal distance from ecient hit to the track position
50 m
Minimal distance of noise hit from the track position
150 m
Peaking time
21 ns
Cross factor to neighbouring strips
0.10
Cross factor to backplane
0.07
FE electronics gain spread (RMS)
0.061
FE electronics oset spread
680 e

Oset and gain correlations
-0.60
Table 3:The conguration of Geant4 and the digitization software used for the beam
tests simulation.The values in brackets were used for 16 degrees incidence angle to
obtain vernier division of charges'positions with respect to the strips.
angle and magnetic eld.Very detailed validation can be performed by the -dependences
(see section 4.4) of the eciency and cluster size.The parameter  scales the track posi-
tion between strips to the strip pitch and so it has values between 0 and 1 and is chosen
32
so that the chips are located at =0 and =1.The simulation was compared to the results
of beam tests in 2001.
Angle [deg]
-15 -10 -5 0 5 10 15
Median [fC]
2.2
2.4
2.6
2.8
3
3.2
3.4
Angle [deg]
-15 -10 -5 0 5 10 15
Median [fC]
2.6
2.8
3
3.2
3.4
3.6
3.8
Angle [deg]
-15 -10 -5 0 5 10 15
Median [fC]
2.6
2.8
3
3.2
3.4
3.6
3.8
Angle [deg]
-15 -10 -5 0 5 10 15
Cluster size
1
1.1
1.2
1.3
1.4
1.5
Angle [deg]
-15 -10 -5 0 5 10 15
Cluster size
1
1.1
1.2
1.3
1.4
1.5
Angle [deg]
-15 -10 -5 0 5 10 15
Cluster size
1
1.1
1.2
1.3
1.4
1.5
Figure 20:The angular dependence of the median (top) and cluster size (bottom).Sim-
ulation is shown in the left gures and the beam tests results in the right.Open circles
correspond to results with magnetic eld of 1.56 T and full circles were obtained without
magnetic eld.The geometrical model is drawn by dashed curves.
In table 3 there is the conguration of Geant4 and the digitization used for the simula-
tion of the beam tests.The angular and magnetic eld dependence of median and cluster
size at 1 fC threshold is shown in gure 20.The simulation apparently underestimates
the median by approximately 0.4 fC and overestimates the cluster sizes.The shifts of ex-
tremes of the curves due to magnetic eld are in good agreement with the beamtests data,
because the shift is equal to the Lorentz angle - the parameter by which is the magnetic
eld dened in the digitization software.The charge generated by particle passing through
the detector at an incidence angle  is proportional to the path length in the sensitive
material and so it is inversely proportional to cos .The median decreases with the in-
cidence angle due to increasing charge sharing between strips.Assuming the charge to
be collected at the nearest strip,a simple geometrical model for median Q
med
and cluster
size n
cs
dependence on the incidence angle can be used.The results are superimposed
to the gures 20:
Q
med
=
Q
?
cos 

1 
d tan
4p

(47)
n
cs
= 1 +
d tan
p

1 2 cos  
Q
thr
Q
?

(48)
where d is the detector thickness,p is the strip pitch,Q
thr
is the threshold at which
cluster size is calculated and Q
?
is the median at perpendicular incidence (3.9 fC).These
calculated angular dependences are as can be seen at the gures more sensitive to incidence
33
angle compared to the beam tests data.Better agreement of the calculated medians sizes
can be reached by lowering the detector thickness from 285 m to approximately 250m.
Bias [V]
100 120 140 160 180 200 220 240 260
Median [fC]
2.7
2.75
2.8
2.85
2.9
2.95
3
3.05
3.1
Bias [V]
100 120 140 160 180 200 220 240 260
Median [fC]
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
Figure 21:The bias voltage dependence of the median.Simulation is shown in the left
gure and beam tests results in the right.
The bias dependence is drawn in gure 21.The comparison of beam tests and simula-
tion shows dierences in the absolute values (the median is underestimated as mentioned
above),but the trends of the curves are in good agreement.The drop of the median with
low bias voltage is caused by 3 eects:
 If the bias is lower than the depletion voltage (approximately 70 V for unirradiated
modules - see table 3),then the sensitive area (depletion region) is narrower than
the detector thickness and so the total collected charge is lower,because only the free
charge generated by passing particle in the depleted region can be collected.
 The drift time of holes towards the strips can cause drop of median measurement
if the drift time is large compared to the width of shaper pulse (see gures 7,19).
In that case signals from holes generated near the strips and near the backplane are
too distant in the time to be composed in the optimal way - the pulse is wider but
with lower amplitude (the total charge is constant).The overall signal at the output
of the shaper is given by convolution of the raw signal on the strips and the shaper
pulse.The bias dependence of drift time through the whole thickness of the detector
is shown in gure 22.
 At low bias voltages due to long drift time the charge diuses into larger area (refer
formula (33)) and so is shared between strips.The dependence of the diusion sigma
of the distribution (33) for holes drifting from the backplane towards the strips is
shown in gure 22.
The 2 latter eects are involved in the digitization,while the rst one is not,because
it does not match real working conditions of the modules and because beamtests with bias
voltage lower than the depletion one have been never done.
The -plots of eciency and cluster size at incidence angle 16
o
are shown in gure 23.
The comparison of the simulation with the beam tests follows the conclusions of angular
and bias dependence simulation above - the absolute values dier,but the trends are
in good agreement.But the -plots for perpendicular (see gure 24) incidence dier
in the trend as well.The region of eciency drop and high cluster size is much narrower
compared to beam tests results.There are 3 causes of this discrepancy:
 The points in graph of beam tests results are averaged over a 6 m wide interval.
34
Bias voltage [V]
80 100 120 140 160 180 200 220 240
Drift time [ns]
0
5
10
15
20
25
30
35
Bias voltage [V]
80 100 120 140 160 180 200 220 240
Diffusion sigma [mm]
0.004
0.005
0.006
0.007
0.008
0.009
Figure 22:The drift time of holes through the whole thickness of the detector (left) and
the diusion sigma of Gaussian distribution of holes drifting from the backplane towards
the strips.
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Efficiency
0.2
0.4
0.6
0.8
1
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Cluster size
1
1.2
1.4
1.6
1.8
2
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Cluster size
1
1.2
1.4
1.6
1.8
2
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Cluster size
1
1.2
1.4
1.6
1.8
2
Figure 23:The interstrip position dependence of the eciency (top) at thresholds 1.5 fC,
2.0 fC,2.5 fC and 3.0 fC and cluster size (bottom) at 1 fC threshold.Simulation is shown
in the left gures and beam tests results in the right.The incidence angle is 16 degrees.
35
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Efficiency
0.2
0.4
0.6
0.8
1
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Cluster size
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Efficiency
0.2
0.4
0.6
0.8
1
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Cluster size
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Cluster size
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Relative interstrip position
0 0.2 0.4 0.6 0.8 1
Cluster size
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
Figure 24:The interstrip position dependence of the eciency (left) at thresholds 1.5 fC,
2.0 fC,2.5 fC and 3.0 fC and cluster size (right) at 1 fC threshold.Beam tests results are
located at the bottom,simulation with correction to track position uncertainties is shown
in the middle and pure simulation on the top.The particles incident perpendicularly.
36
 The precision of track position measurement is determined by the telescopes (see
section 4.4) and is up to 5 m.This adds uncertainty in the interstrip position
determination.
 Due to multiple scattering of beam particles in the modules and additional material
(PVC covers of the modules in their boxes) the real track of the beam particle
in a tested module diers from the track given by the telescopes.The distribution
of the deviations is approximately Gaussian with sigma around 6 m.
Application of these uncertainties of the interstrip position in the -plots for perpendicular
incidence is shown in gure 24.The shape of the modied curve is then in better agreement
with the beam tests data.The above described uncertainties in the track determination
in beam tests can be also responsible for the higher pedestal of the cluster size -plots
measured in beam tests.
37
6 Source tests
6.1 Radioactive source


radioactivity consists of neutron decay:n!p 
e
e

inside a nucleus.Assuming
zero mass of the antineutrino,the spectrumof electron energies can be derived using Fermi
theory [20] (in the equation (49) the speed of light and Planck constant are assumed to
be unity):
dw =
1
2m
n
j
M
fi
j
2

d
3
~p
p
(2)
3
2E
p

d
3
~p
e
(2)
3
2E
e

d
3
~p

e
(2)
3
2E

e
 (2)
4

(4)
(p
n
p
p
p
e
p

e
) (49)
dw
dT
e
= C  (T
e
+m
e
c
2
)(T
max
T
e
)
2
q
T
2
e
+2T
e
m
e
c
2
(50)
where C is a normalization factor,p is the momentum of the electron of mass m
e
,T is
its kinetic energy and E = T + m
e
c
2
.The half-width  of the decay is proportional
to the Fermi constant G
F
and maximal possible kinetic energy  of the emitted electron:
  
5
G
2
F
(51)
The real spectrum diers from the formula (50) due to in uence of the electromagnetic
eld of the decaying nucleus and electrons in the atomic shell on the emitted electron.
The correction is applied through Fermi functions F(Z;T) for
90
Sr and
90
Y that can be
reasonably approximated by formula [21]:
F(Z;T) =
2Z
1
1 e
2Z
1
(52)
with Z being the atomic number and c the velocity of electron:
(T) =
s
1 

m
e
c
2
m
e
c
2
+T

2
(53)
Kinetic energy [MeV]
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2
Number of events
0
200
400
600
800
1000
Figure 25:The spectrum of the radioactive source.
38
For the measurement of detector's charge collection capability the tests using radioac-
tive 

source
90
Sr was developed.The decay chain is following:
90
Sr!
90
Y 
e
e

and
90
Y!
90
Zr 
e
e

.The half-life of
90
Sr is T
1=2
Sr
= 28.5 years,while the half-life
of
90
Y is T
1=2
Y
= 68 hours.Because T
1=2
Sr
T
1=2
Y
the numbers of decays of
90
Sr and
90
Y
are equal.The normalization factors for the elements are:C
Sr
= 258 and C
Y
= 1.
The maximum energy of emitted e

coming from the decay of
90
Sr is 0.546 MeV [8] and
so accounting the spectrum of the e

energies,most of the electrons will hardly pass
through both detector wafers 285 m thick,as the mean energy of electrons with range
equal to 2 the detector thickness is around 500 keV,which can be found using the re-
lation (23).Since the maximum energy of the e

from
90
Y decay is 2.283 MeV,only
a minority of these electrons will stop in the silicon.The combined spectrum of the ra-
dioactive source is shown in gure 25.
6.2 Measurement setup
The measurement setup for 

source tests is shown in gure 26.The readout is
triggered by signal from photomultiplier to which a scintillator is connected.As the read-
out data have to go through the pipelines [11] (13225 ns) of the chips,it is important
to set proper delay between the trigger signal and readout of the data from the ends
of the pipelines.The photons created in the scintillator are transported by an optical
ber to a photomultiplier.The amplitude of pulse from the photomultiplier is compared
to a threshold on discriminator and the output logical pulse is sent to an external-trigger
input of the CLOAC VME module of the DAQ system (see section 4.2).The module and
scintillator are placed in a light-tight volume to prevent triggers caused by light photons.
The threshold on the discriminator is set so that there are reasonable high rate of real
triggers and low rate of fake ones.
CLOAC
VME crate
External trigger input
Aluminum plate
Hybrid
1. detector plane
2. detector plane
90 90
Sr ( Y) source
Scintillator
Photomultiplier
Discriminator
Figure 26:The setup of the source tests.
For source tests special software for DAQand analysis was written by myself.The soft-
ware is based on the DAQ system for standard QA tests.The main features of the DAQ
part are assured by macros for:
39
 adjusting the optional timing (delay between the external trigger pulse and readout
of the data),
 sending burst of external triggers that is done at each scan-point,
 performing a scan (for example scan of threshold),
 data storage and reading of already stored data to be analyzed.
The rest of the software assures the analysis and visualization:
 The analysis macro made for the timing scan nds and sets the optional timing
determined by maximum eciency.
 Analysis is also made for every scan-point (usually determined by the value of thresh-
old) where the most important characteristics and some plots are shown:
{ Eciency
{ Noise occupancy
{ Cluster size
{ Histogram of multiplicity (total number of channels with read signal greater
than the threshold) that is closely related to the noise occupancy
{ Histogram of cluster widths (mean value is the cluster size)
{ Monitored values of bias voltage,leakage current,set threshold,number of an-
alyzed events and some other parameters
{ Reconstructed prole of the beamof electrons that passed through both the de-
tector planes
{ Impact point position dependence of the eciency and the cluster sizes,which
can be used for adjusting the requested geometry of the source test,because
both the characteristics strongly depend on the impact direction of the elec-
trons
{ Check of correct connection between strips and channels of the readout elec-
tronics,using the rate of special types of hit-patterns (see section 6