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8/6/2019 Khaled BEKHOUCHE : Measurement of Charge Transfer Efficiency of a Silicon Particle Detector Based on a Charge-
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Examination committee:
Full Name Title Quality University
Dehimi Lakhdar Pr Chairman Biskra
Sengouga Nouredine Pr Supervisor Biskra
Saidane Abdelkader Pr Examiner Oran
Debilou Abderrazak M.C.A Examiner Biskra
Melaab Djamel M.C.A Examiner Batna
by : Khaled BEKHOUCHE
Thesis
Submitted in fulfilment of the requirements of the degree of Doctor of Science in Electronics
Entitled:
Measurement of Charge Transfer Efficiency of a Silicon Particle
Detector Based on a Charge-Coupled Device
Democratic and Popular Republic of Algeria
Ministry of Higher Education and Scientific Research
Mohammed Khider University
Faculty of Sciences and TechnologyDepartment of electrical engineering
November 2010
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Abstract
The X-ray technique is used to measure the CTI in a CCD. The source is a 55Fe and the CCD
is a T-type Column Parallel (CPC-T) which has 4 channels, 500 pixels each. The CTI is
measured for one channel since they are identical. A LABVIEW software is used to acquire
data via an ADC converter while a MATLAB code is used to analyse the measured data and
extract the CTI. The CTI is calculated for two number of frames, 1000 and 10000. This
allows the study of the effect of the statistical errors. Smaller statistical errors are obtained
with 10000 frames. For an unirradiated CPC-T, the CTI is only a few 10 -5. An analytic model
is used to fit the experimental results and found to be in good agreement when a low density
of two electron traps located at 0.37 eV and 0.44 eV below the conduction band is considered.
The measured noise has a parabolic-like shape which indicates that the trap distribution has
the same shape too. Using a simple analytic model, the estimated occupancy is in good
agreement with the measured one except at the edges of the CCD. It was found that for each
clock voltage value there is an operating window where the CTI is low. Beyond this window,
the CTI increases rapidly and the electrons can not reach the sense node. The lower is the
clock voltage the lower is the energy consumption but the narrower is the operating window.
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Acknowledgements
All my thanks to Allah my lord
This work was carried out in the Laboratory Particle Physics of the University of Oxford.
Many people have contributed to the work presented in this thesis. I would like to thank them
for their help and support. First, I would like to thank my thesis advisor, Professor Nouredine
Sengouga and my co-advisor Professor Andr Sopczak from Lancaster University for the
guidance and encouragement. I would like to thank doctors Andrei Nomerotski and Rui Gao
for the great help in carrying out the measurements. I would like to thank Professor LakhdarDehimi and Aoulmit Salim for their invaluable help throughout the study. I would like also to
thank all LCFI members for their critical remarks and suggestions. Lastly but not least I
would like express my sincere appreciations for the Ministry of Higher Education and
Scientific Research and the University of Biskra for providing long term grant to Lancaster
and Oxford University.
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CONTENTS
Introduction .....................................................................................................................1
Chapter I Particle Detectors..........................................................................................3
I. 1 Radiations sources ......................................................................................................3
I. 2 Radiation detectors......................................................................................................4
I. 2. 1 Detector operation modes....................................................................................4
I.2.1.1 Current operation mode..................................................................................5
I.2.1.2 Mean Square Voltage operation mode ...........................................................5
I.2.1.3 Pulse operation mode .....................................................................................5
I.2.2 Pulse height spectra and energy resolution............................................................7
I.2.4 Dead time.............................................................................................................10
I.3 Radiation damage in particle detectors......................................................................11
I.3.1 Surface damage....................................................................................................11
I.3.2 Bulk damage........................................................................................................12
I. 4Trapping and generation-recombination at deep levels ............................................15
Chapter II Charge Coupled Devices..........................................................................19
II. 1 CCD operation.........................................................................................................19
II.1.1 Four-phase CCD ................................................................................................19
II.1.2 Three-phase CCD ..............................................................................................20
II.1.3 Two-phase CCD ................................................................................................21
II. 2 CCD array architecture...........................................................................................21
II.2.1 Linear arrays ......................................................................................................22
II.2.2 Full frame array .................................................................................................22
II.2.3 Frame transfer....................................................................................................24
II.3 Readout time requirement for the vertex detector at the Future International Linear
Collider (ILC)..................................................................................................................25
II. 4 Metal-Oxide-Semiconductor capacitor theory ........................................................26
II.4.1 P-MOS capacitor................................................................................................27
II.4.2 N-P MOS capacitor............................................................................................29
II.5 Charge generation.....................................................................................................32
II.6 Charge collection......................................................................................................34II.7 Charge transfer .........................................................................................................35
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II.7.1 Self-induced drift ...............................................................................................37
II.7.2 Fringing field drift .............................................................................................37
II.7.3 Thermal diffusion ..............................................................................................38
II.8 Charge measurement ................................................................................................38
II.8.1 Charge conversion .............................................................................................38
II.8.2 Correlated Double Sampling .............................................................................39
II.9 Noise sources............................................................................................................40
Chapter III Experimental setup and CTI calculation .............................................42
III. 1 Experimental setup.................................................................................................42
III.1.1 Hardware part ...................................................................................................45
III.1.1.1 CPC-T motherboard...................................................................................46
III.1.1.2 Temperature controller ..............................................................................47
III.1.1.3 ICS-554 Analog-To-Digital Converter......................................................48
III.1.2 Software part ....................................................................................................49
III.1.2.1 Bias tab ......................................................................................................50
III.1.2.2 Sequencer tab.............................................................................................51
III.1.2.3 Amplifier tab..............................................................................................52
III.1.2.4 DAQ system tab.........................................................................................52
III.2 Charge Transfer Inefficiency Calculation............................................................55
Chapter IV Charge Transfer Inefficiency results and discussion ..........................58
IV. 1 Introduction............................................................................................................58
IV. 2 Charge transfer inefficiency measurement ............................................................58
IV.2.1 Low statistics....................................................................................................58
IV.2.2 High statistics...................................................................................................61
III.3 Charge Transfer Inefficiency analysis.....................................................................64
III.4 Distribution of X-ray events....................................................................................66
III.5 Noise effect .............................................................................................................68
III. 6 OFFSET of the pedestal voltage and clock voltage effects ...................................69
Conclusion and Outlook ..............................................................................................70
Bibliography ...................................................................................................................72
Appendix A .....................................................................................................................75
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IntroductionOver the years, the technologies of optical imaging (still largely based on photographic films)
and particle tracking (increasingly using electronic detectors such as spark chambers and
multi-wire gaseous chambers) drifted apart. However, the invention of the Charge-Coupled
Device (CCD) in 1970 started a revolution which is still having profound effects in the fields
of optical imaging, particle tracking, X-ray detection, analog storage devices, etc [1-3].
Charge coupled devices have been successfully used in several high-energy physics
experiments over the last 20 years. Their small pixel size, excellent precision and high
quantum efficiency (QE) over a wide wavelength range going from the X-rays to the far
infrared [4] provide a superb tool for studying short-lived particles and understanding their
nature at a fundamental level. Over the last few years the Linear Collider FlavourIdentification (LCFI) collaboration has developed Column-Parallel CCDs (CPCCD) and
CMOS readout chips, to be used for the vertex detector at the International Linear Collider
(ILC). The CPCCDs are very fast devices capable of satisfying the challenging requirements
imposed by the beam structure of the superconducting accelerator [5]. Another type of a
CCD-based device is In-Situ Storage Image Sensor (ISIS). In ISIS, each pixel has an internal
memory implemented as a small CCD register. The charge is collected under a photogate and
is transferred to a few-pixel storage CCD inside the same pixel [6].Physics studies continuously show that extremely precise vertexing will be needed to uncover
the interactions at a future TeV-scale e+e- linear collider. A very good vertex detector is
crucial for the high quality b and c tagging, required to further explore the physics at high
energies. CCD-based vertex detectors have proven their potential for such studies, which was
shown in the excellent results of the vertex detector VXD3 at the Stanford Large Detector
(SLD). The excellent gain uniformity, high precision and small layer thickness of the CCD
are still difficult to achieve with other semiconductor sensors [7, 8]. The transfer
characteristics of charge-coupled devices have been investigated theoretically and simulated
experimentally since the invention of these devices [9-12].
Using analytic models, the charge transfer inefficiency is determined then compared to TCAD
simulations and/or to experimental results [13, 14].
In this work, the results of the CTI measured at the test stand at Oxford University are
presented. It is an unirradiated Column Parallel CCD (CPCCD) called CPC-T. The setup is
controlled by a Laboratory Virtual Instrumentation Engineering Workbench (LABVIEW)
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software [15]. The binary file, containing data, generated by the latter is then analysed by a
MATrix LABoratory (MATLAB) code [16] to calculate the CTI.
This thesis is organized as follows:
Chapter I: The general definitions and aspects in particle detectors domain are presented in
some details. This includes radiation sources which have a great effect on the detector
performances depending on their nature. Common operation modes of a particle detector are
explained in brief. Then, the characteristics and performances of the detectors are emphasised
such as the detection efficiency. Finally, the effect of radiation on creating defects in the
detector is studied.
Chapter II: This chapter concentrates on charge-coupled devices. First the three usual
operations of a CCD are explained: two, three and four-phase operation systems. Then, the
different architectures of the CCD are mentioned. As CCDs will be used in the inner vertex
detector of the future ILC, time requirement for this project is given in brief. The theory of P-
MOS and NP-MOS capacitors is given in some details because they are the element cells in
the CCDs. The three processes (charge generation, charge collection, charge measurement)
involved to properly convert the photo-generated electrons to an electric signal are presented.
Finally, we present the theory of the generation-recombination processes resulting from the
presence of the defects.
Chapter III: We present the setup used in this work to measure the CTI. It is composed of two
parts: hardware and software. Then, the method used to analyse data and calculate CTI is
explained.
Chapter IV: This chapter and the previous one are the heart of this work. In this chapter we
present the results obtained after measuring the CTI of an unirradiated CCD. An analytic
model is used to fit the CTI-T characteristics. Some other parameters are estimated such as:
noise and occupancy. The effect of temperature and pixel number on the CTI is also studied.
This thesis terminates by a conclusion in which the results obtained are summarized and a
possible future work is suggested. An appendix for the MATLAB code developed is also
included.
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Chapter I
Particle Detectors
I.1 Radiations sourcesRadiations can be categorized into four general types. Fast electrons and heavy charged
particles are considered as charged particle radiation. Electromagnetic radiation and neutrons
are considered as uncharged radiation. Fast electrons are energetic electrons emitted in
nuclear decays or produced by any other process. Alpha particles, protons, fission products or
the products of many nuclear reactions are parts of heavy charged particles. The
electromagnetic radiation includes X-rays emitted in the rearrangement of electrons shells of
atoms, and gamma rays that originate from transitions within the nucleus itself. Neutrons
generated in various nuclear processes are divided in slow neutrons and fast neutrons
subcategories. Radiations differ in their ability to penetrate into a material. This property is of
considerable concern in determining the physical form of radiation sources or the structure
and the physical parameters of the detector. Soft radiations, such as alpha particles or low-
energy X-rays, penetrate only a few micrometers of depth. Beta particles are generally more
penetrating; up to a few tenths of a millimeter of depth can usually be achieved. Harder
radiations, such as gamma rays or neutrons, can penetrate to a depth in millimetres orcentimetres without seriously affecting its properties [17]. A radiation source is characterized
by its activity which is defined as the sources rate of decay and is given by:
Ndt
dNdecay = (I.1)
whereN is the number of radioactive nuclei and is defined as the decay constant. The SI
unit of activity is the Becquerel (Bq) defined as one disintegration per second. The historical
unit of activity has been the Curie (Ci), defined as 10107.3 disintegrations per second. Thus
Ci10703.2Bq1 11= (I.2)
The specific activity of a radioisotope source is defined as the activity per unit mass of
radioisotope sample and it is given by
M
A
ANM
N v
v
===
/mass
activityactivitySpecific (I.3)
where Mis the molecular weight of the sample,Av is Avogadros number and is given by
1/2T/)2ln(=
(I.4)where T1/2 is the half-life of the radiation source.
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I.2 Radiation detectors
The net result of the radiation interaction in a wide category of detectors is the appearance of
a given amount of electric charge within the detector active volume. A simplified detector
model assumes that a charge Q appears within the detector at time t= 0 resulting from the
interaction of a single particle or quantum of radiation. Next, this charge must be collected to
form the basic electrical signal. Typically, collection of the charge is accomplished through
the imposition of an electric field within the detector, which causes the positive and negative
charges created by the radiation to flow in opposite directions. The time required to fully
collect the charge varies greatly from one detector to another. The sketch in Fig.I.1 illustrates
one example for the time dependence the detector current might assume, where tc represents
the charge collection time.
Fig.I.1: An illustration of the time dependent of the detector current during charge collection time tc.
The total charge generated in that specific interaction is equal to the time integral over the
duration of the current, thus
=ct
dttiQ0
)( (I.5)
I.2.1 Detector operation modes
There are three general modes of operation of radiation detectors: the current mode, the pulse
mode and the mean square voltage mode (abbreviated MSV mode, or sometimes called
Campbelling mode). Pulse mode is the most commonly applied of these, but current mode
also finds many applications. MSV mode is limited to some specialized applications that
make use of its unique characteristics.
Time
i(t)
tc
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I.2.1.1 Current operation mode
In the current mode, a current-measuring device (practically a picoammeter) is connected
across the output terminals of a radiation detector as shown in Fig.I.2. The current mode
operation is used with many detectors when event rates are very high.
Fig.I.2: Radiation detector in current mode. (a) Current-measuring device (picoammeter) connected across the
output terminals of a radiation detector. (b) Recorded signal from a sequence of events.
I.2.1.2 Mean Square Voltage operation mode
The MSV mode of operation is most useful when making measurements in mixed radiation
environments when the charge produced by one type of radiation is much different than that
from the second type. In this mode, the average current I0 is blocked. Then, by providing
additional signal-processing elements, the time average of the squared amplitude of the
fluctuations is computed. The processing steps are illustrated in Fig.I.3.
Fig.I.3: The processing steps using in a detector operating in the mean square voltage (MSV) mode.
I.2.1.3 Pulse operation mode
Most applications are better served by preserving information on the amplitude and timing of
individual events that only pulse mode can provide. The nature of the signal event depends on
the input characteristics of the circuit to which the detector is connected (usually a
preamplifier). The equivalent circuit can often be represented as shown in Fig.I.4.
Detector pA
Time
i(t)
Ion chamber Squaring circuitAveraging
Output
Variance computing circuit
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Fig.I.4: The equivalent circuit of both, detector output and the input of the circuit connected to it.
Figure I.5.a shows the signal pulse produced from a single event in a detector operated in
pulse mode. Two separate extremes of operation can be identified that depend on the relative
value of the time constant of the measuring circuit. In the case where the time constant, given
by =RC, is kept small compared with the charge collection time, so the signal voltage V(t)
produced under these conditions has a shape nearly identical to the time dependence of the
current produced within the detector as illustrated in Fig.I.5b. Radiation detectors are
sometimes operated under these conditions when high event rates or timing information ismore important than accurate energy information. But it is more common to operate detectors
in the opposite extreme in which the time constant of the external circuit is much larger than
the detector charge collection time as illustrated in Fig.I.5c.
Fig.I.5: (a) The signal pulse produced from a single event in a detector operated in pulse mode. (b) The case of a
small time constant load circuit. (c) The case of a large time constant load circuit.
Detector C R V(t)
i(t)
Time
V(t)
Time
V(t)
Time
= dttiQ )(
(a)
(b)
(c)Case 2 :RC >> tc
Vmax = Q/C
Case 1 :RC
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I.2.2 Pulse height spectra and energy resolution
The pulse amplitude distribution is a fundamental property of the detector output that is
routinely used to deduce information about the incident radiation or the operation of the
detector itself. The most common way of displaying pulse amplitude information is through
the differential pulse height distribution. Figure I.6 shows an example of such distribution.
The abscissa is a linear pulse amplitude scale in volts or analog to digital converter (ADC)
counts. The ordinate is the differential number dN of pulses observed with an amplitude
within the differential amplitude increment dH, divided by that increment.
Fig.I.6: An example of differential pulse height spectra.
The number of pulses whose amplitude lies between two specific values, H1 andH2, can be
obtained by integrating the area under the distribution between those two limits, as shown by
the cross-hatched area in Fig.I.6. Peaks in the distribution, such as H4, indicate pulse
amplitudes about which a large number of pulses may be found. On the other hand, valleys or
low points in the spectrum, such asH3, indicate pulse amplitudes around which relatively few
pulses occur. The physical interpretation of differential pulse height spectra always involves
area under the spectrum between two given limits of the pulse height.
In many applications of radiation detectors, the objective is to measure the energy distribution
of the incident radiation. These efforts are classified under the general term radiation
spectroscopy. One important property of a detector in radiation spectroscopy can be examined
by noting its response to a monoenergetic source of that radiation. Under these conditions, the
differential pulse height distribution is called the response function of the detector for the
energy used in the determination as illustrated in Fig.I.7. The energy resolution of the detector
H2H1 H4H3 Pulse height
dN/dH
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is conventionally defined as the full width at half maximum (FWHM) divided by the location
of the peak centroidH0, thus
0
FWHM
HR = (I.6)
For peaks whose shape is Gaussian with standard deviation , the FWHM is given by
35.2 . The energy resolutionR is thus a dimensionless fraction conventionally expressed as
a percentage. It should be clear that the smaller the figure for the energy resolution, the better
the detector will be able to distinguish between two radiations whose energies lie near each
other.
Fig.I.7: An example of response function and definition of detector resolution.
I.2.3 Detection efficiency
The detection efficiency depends on the type of radiation. For charged radiation such as alpha
and beta particles, they will form enough ion pairs along its path to ensure that the resulting
pulse is large enough to be recorded. The detector is said to have a high counting efficiency.
On the other hand, uncharged particle such as gamma rays and neutrons can travel large
distances between interactions. The detector in this case has less counting efficiency. It then
becomes necessary to have a precise figure for the detector efficiency.
It is convenient to subdivide counting efficiencies into two classes: absolute and intrinsic. The
absolute efficiency is defined as
sourceby theemittedquantaradiationofnumber
recordedpulsesofnumber=
abs (I.7)
dN/dH
HH0
Y/2
Y
FWHM
Resolution :R = FWHM/H0
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The intrinsic efficiency is defined as
detectoron theincidentquantaradiationofnumber
recordedpulsesofnumberint = (I.8)
The two efficiencies are simply related for isotropic sources by
=
4int abs (I.9)
where is the solid angle of the detector seen from the actual source position. A commonly
encountered circumstance is shown in Fig.I.8. It involves a uniform circular disk source
emitting isotropic radiation aligned with a circular disk detector, both positioned
perpendicular to a common axis passing through their centers. The solid angle is given by the
following approximate equation calculated numerically [17]
( ) ( )
+
+
+ 2
31
22/52/1 18
3
1
112 FF
(I.10)
where
( ) ( ) 2/92
2/71164
35
116
5
+
+=F ;
( ) ( ) ( ) 2/133
2/11
2
2/92 11024
1155
1256
315
1128
35
++
+
+=F
2
=
d
s ;
2
=
d
a
This approximation becomes inaccurate when the source or detector diameters become too
large compared with their spacing.
Fig.I.8: A uniform circular disk source emitting isotropic radiation aligned with a circular disk detector, both
positioned perpendicular to a common axis passing through their centers.
d
a
s
Source Detector
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I.2.4 Dead time
Dead time is defined as the finite time after the registration of an event, before the detector is
able to accurately register another incident event [18]. Dead time is the minimum amount of
time that must separate two events in order that they be recorded as two separate pulses. Two
models of dead time behaviour of counting systems have come into common usage:
paralyzable and nonparalyzable response. The fundamental assumptions of the models are
illustrated in Fig.I.9. At the center of the figure, a time scale is shown on which six randomly
spaced events in the detector are indicated. At the bottom of the figure is the corresponding
dead time behaviour of a detector assumed to be nonparalyzable. A fixed time is assumed to
follow each true event that occurs during the live period of the detector. True events that
occur during the dead period are lost and assumed to have no effect whatsoever on the
behaviour of the detector. In the case of non-paralyzable detectors and electronics, the
expression giving the recorded events rate m as a function of delivered events rate or true
interaction rate n can be calculated for random time distributions of the events for a given
dead time as
n
nm
+=
1(I.11)
For paralyzable systems (dead time adds up for subsequent events) the rate of recorded events
readsnenm = (I.12)
Fig.I.9: An illustration of two assumed models of dead time behaviour for radiation detector. (a) Paralyzable
model. (b) True events in detector. (c) Nonparalyzable model.
Time
Time
Time
Dead
Live
(a)
(b)
(c)
Dead
Live
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I.3 Radiation damage in particle detectors
Semiconductor devices are sensitive to radiation, both ionizing and non-ionizing. It was
found, that the degradation of the parameters of bipolar and MOS devices is caused by
radiation-induced surface effects at the Si-SiO2 interface, as well as by defects in the bulk
silicon [19].
I.3.1 Surface damage
The passage of an ionising radiation in the depletion region in silicon detectors creates
electron-hole (e-h) pairs that are collected by the electric field at the electrodes and form the
signal. In the undepleted bulk of the semiconductor, where there is no electric field, the high
carrier density allows the deposited charge carriers to recombine. Therefore, the
semiconductor does not show permanent traces of the passage of a charged particle that loses
energy by ionisation.
On the contrary, the passage of an ionising radiation in the oxide causes the built up of
trapped charge in the oxide layers of the detector [20]. If an MOS structure (Fig.I.10) is
exposed to a short radiation pulse while under an applied bias voltage, electron-hole pairs are
generated in the oxide. Under the applied bias, the electrons that escape early recombination
with the holes are rapidly (within picoseconds) swept out of the oxide and leave behind an
instantaneous, essentially uniform distribution of relatively immobile holes. This positive
charge distribution causes an initial negative voltage shift, V(O+), in the capacitance voltage
(C-V) characteristic of an MOS capacitor or the current- voltage (I-V) characteristic of the
equivalent MOSFET [20]. In terms of the continuous time random walk (CTRW) model [21],
holes then begin to move under the influence of the applied bias to either the gate or the Si02-
Si interface by a slow polaron-hopping process that requires many decades in time. As the
transporting holes reach the interface most of them are removed, causing the voltage shift,
V(t), to decrease with time. Figure I.10 shows schematically the expected behaviour of the
voltage shift as a function of time for a sample irradiated under positive bias (a) and negative
bias (b).
In addition to the trapped charge, the ionising radiation also produces new energy levels in the
band gap at the SiO2-Si interface. These levels can be occupied by electrons or holes,
depending on the position of the Fermi level at the interface and the corresponding charge can
be added or subtracted to the oxide charge.
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Fig.I.10: Contributions of holes to voltage shift in MOS structures. Dotted curves correspond to the transporting
holes. Dashed curves correspond to the trapped holes at interface. Continue curves correspond to the total. (a)
Positive bias. (b) Negative bias.
I.3.2 Bulk damage
While in the silicon crystal itself ionization is a reversible process, and therefore does not
cause any damage, the energy transfer to crystal atoms which is the non-ionizing energy loss
(NIEL) of the incident particle causes displacement damage [22]. The bulk damage is caused
by the NIEL interactions of a primary particle with mass mp and energy Ep with a lattice
silicon atom with mass MSi. The energy transferred in the interaction is, in the non-relativistic
case:
( ) pSipSip
EMm
MmE
+=
2sin4 2
2
(I.13)
where is the scattering angle. Displacement damage occurs when the energy transferred to
the silicon atom is sufficient to remove it from the crystal lattice. The atom is then called
primary knock-on atom (PKA). The minimum threshold energy for the displacement is
eV15 in silicon. The vacancy-interstitial (V-I) silicon created is called a Frenkel pair. The
minimum energy for particles like neutrons or protons, with mass u1 , required to create a
Frankel pair is eV110 . The same threshold energy for electrons is keV260 . The energy
of the particle used for the irradiation studies reported in the present work is several orders of
magnitude higher than the threshold level, as it will be in the background radiation in theinner detectors of the Large Hadron Collider (LHC) [19].
Gate (+) Gate (-)
SiO2 Si SiO2 Si
1.0
0V
V
0
Log(t)Log(t)
0V
V
1.0
0
(a) (b)
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The recoil energy of the PKAs can be up to 130 keV and therefore they can remove other
atoms from the crystal lattice, giving rise to a PKA cascade. It has been estimated that about
50% of the energy of the recoil atom is deposited via ionisation and the displacement
dominates when the recoil atom loses its final 5-10 keV. The fraction of energy going to the
non-ionising interaction is described by the Lindhard partition function. The cascade results in
the formation of two or three terminal clusters of 50 linear dimension with high
concentration of Frankel defects. About 90% of the vacancies recombine with interstitials,
leaving no net damage in the crystal. Some vacancies can form stable divacancy (or multi-
vacancy) defect complexes and the remaining vacancies and interstitials diffuse through the
crystal and react with other defects or impurity atoms always present in the silicon crystal (O,
C, P, B) to form stable complexes. The introduction rate of vacancies (V) and divacancies
(V2) have been determined to be1cm5.01.2 =V and
1cm4.07.4 =V for 1 MeV
neutron irradiation. Figure I.11 shows an example of the final damage due to aggregation of
point defects (V2, VP).
Fig.I.11: A diagram of some defects in the n-type silicon crystal lattice due to point defect complexes.
Closely situated multiple displacements, which can interact electrically is called defect
cluster. Light particles, such as electrons generate mostly point defects, and need more than 5
MeV to produce clusters. The energy threshold for electrons to displace a Si atom has been
estimated to 260 keV, whereas only 190 eV is required for a neutron to do the same effect.
Heavy particles easily create clusters because of the high energy of the primary recoil Siatom. Neutrons, protons and pions need only about 15 keV to create clusters and generate
DivacancyVacancyInterstitiel silicon(self interstitiel)
Interstitielimpurity
Phosphorus Substitutional impurity Vacancy-phosphorus
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point defects as well. The final radiation damage is due to the thermally stable defects formed
by the reaction of primary defects (V, interstitial) with other defects or atomic impurities.
Some of the possible reaction have been identified and are reported in Table I.1 [19]. Some of
the stable complexes are electrically active, therefore the changes of the electrical properties
of detectors are correlated with the electrical activity of the stable damage. Several defects
have been identified by means of different measurement techniques, such as electron
paramagnetic resonance (EPR), photoluminescence, current or capacitance deep level
transient spectroscopy (I-DLTS, C-DLTS), thermally stimulated current (TSC). Table I.2 lists
some of the identified defects, their charge states and their associated energy levels in the
band gap [19]. Most of these energy levels situate in the deep region of the silicon band gap,
close to the middle.
I reaction V reaction Ci reaction
I + Cs Ci V + V V2 Ci + Cs CC
I + CC CCI V + V2 V3 Ci + O CO
I + CCI CCII V + O VO
I + CO COI V + VO V2O
I + COI COII V + P VP
I + VO O
I + CV2V
I + VP P
Table I.1: A few defect reactions in silicon. The subscript i stands for interstitial, s for substitutional, I for Siinterstitial, V for vacancy, C for carbon, O for Oxygen and P for phosphorus.
Defect Energy level Defect type
VO EC-0.17 acceptor
V2O EC-0.50 acceptor
V2
EC-0.23
EC-0.42
EV+0.25
acceptor
acceptor
donor
VP EC-0.45 acceptor
CC EC-0.17 acceptor
CO EV+0.36 donor
Table I.2: Identified defect states with their energy levels in eV.
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I.4. Trapping and generation-recombination at deep levels
If the energy levels introduced in the forbidden gap of a semiconductor lie greater than 0.1 eV
from the valence or the conduction band-edges, the level is commonly referred to as a deep
level. Deep levels can be formed by either introduction of impurities or be the result of
inherent crystal defects. They may be, for example, large foreign atoms positioned
substitutionally or interstitially, vacancies, host atoms on the wrong site in compound
semiconductors (anti-site defect), defect due to dislocations or damages induced by irradiation
or ion-implantation.
Deep levels may behave as carrier traps or as generation recombination centres if they are
near to mid-band-gap. As traps they can capture the free carriers supplied by the dopant
atoms, thus compensating the shallow levels, reducing the effective doping density and
increasing the resistivity of the material. Deep levels, behaving as recombination centres,
provide a path for the generation and recombination of electron-hole pairs across the band-
gap. Deep levels may be characterized by three parameters: the activation energy (Et) which is
related to the position of the level in the band-gap, its concentration (Nt) and its capture cross-
section () for carriers which provides a measure of the ability of the deep level to trap
carriers.
A theory describing the generation and recombination (g-r) processes has been established by
Shockley, Read and Hall [23, 24]. More details on g-r processes can be found in the literature
[25, 26]. Therefore, the effect is throughout the literature referenced as Shockley-Read-Hall
(SRH) generation/recombination. Four sub-processes are possible:
a) Electron capture. An electron from the conduction band is captured by an empty trap
in the band-gap of the semiconductor. The excess energy ofEc Et is transferred to
the crystal lattice (phonon emission).
b) Hole capture. The trapped electron moves to the valence band and neutralizes a hole
(the hole is captured by the occupied trap). A phonon with the energy Et Ev is
generated.
c) Electron emission. A trapped electron moves from the trap energy level to the
conduction band. For this process additional energy of the magnitude Ec Ethas to be
supplied.
d) Hole emission. An electron from the valence band is trapped leaving a hole in the
valence band (the hole is emitted from the empty trap to the valence band). The energy
necessary for this process isEtEv.These four processes are illustrated in Fig.I.12.
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Fig.I.12: The four sub-processes in the Shockley-Read-Hall generation/recombination process. (a) Electron
capture. (b) Hole capture. (c) Electron emission. (d) Hole emission.
The process (a) i.e. capture of electrons by the deep centre from the conduction band has the
following equation
npnpR TnTthnna =>
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npnedt
dnTnTn += (I.18)
Similarly the net rate of holes leaving the valence band is given by
pnpedt
dpTpTp += (I.19)
Thus the net rate of increase of density of filled deep levels is given by
pnpenpne
dt
dp
dt
dn
dt
dn
TpTpTnTn
T
+++=
=
(I.20)
Using the total density of traps TTT pnN += , we get
( ) ( ) TppnnTpnT nececNecdt
dn++++= (I.21)
where cn and cp are the capture rates of electron and hole, respectively.
According to the detailed balance principle, in thermal equilibrium, the rate of any physical
process and its reverse must balance each other. Thus, in this case, the rates for holes
emission and capture must be equal. Similarly the rate of emission of electrons and the
corresponding capture rate must also exactly cancel. One can obtain the electron and hole
thermal emission rates from a deep level using the detailed balance principle and the Fermi
Dirac distribution function. The probability of an electron occupying an energy level Et isgiven by
+
=
kT
EEEf
Ft
t
exp1
1)( (I.22)
The emission and capture rates for electrons and holes are equal according to the balance
principle, thus
ca RR = (I.23.a)
db RR = (I.23.b)
The number of filled traps is given by
TtT NEfn )(= (I.24)
The density of electrons in the conduction band is given by
=
kT
EENn CFCexp (I.25)
Using equations (I.14), (I.16), (I.22), (I.23.a), (I.24) and (I.25), we get the thermal emissionrate of electrons
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>=l1 && xdataC2(i)maxy
maxy=ydataC2(i);
imaxy=i;
end
end
end
ipeak1=imaxy;
limit1nC2=xdataC2(ipeak1)-noisewidth/0.6*GV/Factor; %%%%Noise limit1
limit2nC2=xdataC2(ipeak1)+noisewidth/0.6*GV/Factor; %%%%Noise limit2
else
limit1nC2=fresult2C2.b1-3*fresult2C2.c1;
limit2nC2=fresult2C2.b1+3*fresult2C2.c1;
end
xdata2C2=[limit1nC2:Mbin:limit2nC2];
ydata2C2=(hist(data_col(:,M),xdata2C2));
fresult2C2=fit((xdata2C2(2:length(xdata2C2)-1))',(ydata2C2(2:length(ydata2C2)-1))','gauss1');
limit1xC2=fresult2C2.b1+xraynoise/0.6*GV/Factor-nsigma*fresult2C2.c1; %%%%X-ray limit1
limit2xC2=fresult2C2.b1+xraynoise/0.6*GV/Factor+nsigma*fresult2C2.c1; %%%%X-ray limit2
xdata3C2=[limit1xC2:Mbin:limit2xC2];ydata3C2=(hist(data_col(:,M),xdata3C2));
fresult3C2=fit((xdata3C2(2:length(xdata3C2)-1))',(ydata3C2(2:length(ydata3C2)-1))','gauss1');
if (PP>(Pend-MPX)) || (PP==(Pstart+Pend)/2) || (PP==(Pstart+MPX))
figure;
semilogy(xdataC2(2:length(xdataC2)-1),abs(ydataC2(2:length(ydataC2)-1)),'k-','LineWidth',1);
hold on;
semilogy(xdata2C2(2:length(xdata2C2)-1),fresult2C2(xdata2C2(2:length(xdata2C2)-1))','r-
','LineWidth',3);
hold on;
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semilogy(xdata3C2(2:length(xdata3C2)-1),fresult3C2(xdata3C2(2:length(xdata3C2)-1))','b-
','LineWidth',3);
axis([fresult2C2.b1-3*fresult2C2.c1 fresult3C2.b1+3*fresult3C2.c1 1 2*fresult2C2.a1]);
grid on;
xlabel('ADC codes');ylabel('Counts');
legend('Distribution of ADC codes','Fit noise','Fit X-ray');
end
limit1noise(2)=fresult2C2.b1-ms*fresult2C2.c1;
limit2noise(2)=fresult2C2.b1+ms*fresult2C2.c1;
limit1xray(2)=fresult3C2.b1-ms*fresult3C2.c1;
limit2xray(2)=fresult3C2.b1+ms*fresult3C2.c1;
for j=P1:P2
xrayC2(KK2)=0;
nxrayC2(KK2)=0;
noiseC2(KK2)=0;
nnoiseC2(KK2)=0;
for k=1:iframe
if ((datatot(k,j,M)>=limit1xray(2))&&(datatot(k,j,M)=limit1noise(2))&&(datatot(k,j,M)
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pixel_number
end
end
end
%%% Start: CTI determination %%%figure;
LLC2=length(XrayADC2);
plot(XpixelC2,XrayADC2,'b-','LineWidth',0.5);
fresult4C2=fit(XpixelC2',XrayADC2','poly1');
hold on;
plot(XpixelC2,fresult4C2(XpixelC2),'r-','LineWidth',3);
grid on;
axis([Pstart Pend fresult3C2.b1-fresult3C2.c1 fresult3C2.b1+fresult3C2.c1]);
xlabel('Pixel number (COL 2)');
ylabel('X-ray peak');
legend('X-ray peak','Linear fit');
CTI2=-fresult4C2.p1/fresult4C2.p2
errorsC2=confint(fresult4C2);
dp1C2=(errorsC2(2,1)-errorsC2(1,1))/2;
dp2C2=(errorsC2(2,2)-errorsC2(1,2))/2;
dCTIC2=abs(CTI2)*(dp1C2/abs(fresult4C2.p1)+dp2C2/abs(fresult4C2.p2))
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Publications related to this work
A. Sopczak et al., Measurements of Charge Transfer Inefficiency in a CCD With High-
Speed Column Parallel Readout,IEEE Trans. Nucl. Sci., vol. 56, no. 5, pp. 29252930,2009.
A. Sopczak et al., Comparison of Measurements of Charge Transfer Inefficiencies of a High
Speed Column Parallel CCD,IEEE Trans. Nucl. Sci., vol 57, no. 2, pp. 854859, 2010.
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55Fe .CCD))CTI
CTI.500 )CPC-T)T-type CPCCD
LABVIEW.
.CTI MATLAB ))ADC
CTI 100010000)Frame.( .
, CPC-T .10000
CTI10-5.
. 0.44eV0.37eV
Parabolic .
.CCD
.CTI )Clock voltage(
CTI )Sense node.(
. ,
Rsum
La technique des rayons X est utilise pour mesurer la CTI dans un CCD. La source est une55Fe et le CCD est un CPC-T (T-type column parallel CCD), qui dispose de 4 canaux, 500
pixels chacun. La CTI est mesure pour un seul canal, car ils sont identiques. LabVIEW est
utilis pour acqurir des donnes via un convertisseur ADC. Un code MATLAB est utilis
pour analyser les donnes mesures et extraire la CTI. La CTI est calcule pour deux nombres
de frames, 1000 et 10000. Cela permet l'tude de l'effet des erreurs statistiques. Les petites
erreurs statistiques sont obtenues avec 10000 images. Pour un CPC-T non irradi, la CTI est
de lordre de 10-5. Un modle analytique est utilis pour ajuster les rsultats exprimentaux et
sest trouvs en bon accord dans le cas dune faible densit de deux piges lectrons situ
0,37 eV et 0,44 eV en dessous de la bande de conduction. Le niveau de bruit mesur est de