khaled bekhouche : measurement of charge transfer efficiency of a silicon particle detector based on...

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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15

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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16

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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17

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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18

>=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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80

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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81

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

khaled bekhouche : measurement of charge transfer efficiency of a silicon particle detector based on...

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