Characterization of FBK-irst 3D Double Side Double Type Column …personalpages.to.infn.it/~rivero/tesi/Master_Thesis_Fabio_Rivero.pdf · MASTER THESIS Characterization of FBK-irst

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UNIVERSITÀ DEGLI STUDI DI TORINO

A.A. 2008-2009

Characterization of

FBK-irst 3D Double Side

Double Type Column

Silicon Sensors

Candidate: Rivero Fabio

M A S T E R T H E S I S

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UNIVERSITÀ DEGLI STUDI DI TORINO

FACOLTA’ DI SCIENZE MATEMATICHE, FISICHE E NATURALI

Corso di Laurea Specialistica in Fisica Ambientale e Biomedica

MASTER THESIS

Characterization of FBK-irst 3D Double Side Double Type

Column Silicon Sensors

Candidate: Rivero Fabio

Supervisor: Prof. A.M. Solano

Co-supervisor: Prof. G.-F. Dalla Betta

Co-supervisor: Dott. A. La Rosa

A.A. 2008-2009

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Abstract: 3D pixel silicon detectors are being investigated because of their promising properties for

experimental physics experiments and other applications. Their main advantages with respect to traditional

silicon detectors are the high radiation hardness and the possibility of having active edges, reducing the

dead zones in the sensor. After an introduction into this field of research, this thesis focuses on the

characterization of 3D Double Side Double Type Column pixel silicon detectors developed at the

Fondazione Bruno Kessler (FBK-irst) in Trento, Italy, with laboratory characterization, test beam and

irradiation of these detectors at CERN.

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Table of contents

1 - Introduction .......................................................................................................................................... 11

2 – Physics of Semiconductor Detectors ..................................................................................................... 15

2.1 – Ionizing radiation ............................................................................................................................ 17

2.2 – Interaction of electromagnetic radiation with matter ..................................................................... 17

2.2.1 –Photoelectric effect .................................................................................................................. 19

2.2.2 – Compton scattering ................................................................................................................. 20

2.2.3 – Pair production ........................................................................................................................ 20

2.3 – Interaction of charged particles with matter ................................................................................... 20

2.3.1 – Stopping power ....................................................................................................................... 20

2.3.2 – Energy loss by heavy charged particles .................................................................................... 21

2.3.3 – Energy loss by light charged particles ...................................................................................... 24

2.4 –Physics and behaviour of semiconductors........................................................................................ 25

2.4.1 – Conduction in a solid ............................................................................................................... 25

2.4.2 – Classification of semiconductors .............................................................................................. 26

2.4.3 – Silicon ..................................................................................................................................... 27

2.4.4 – Doping of silicon ...................................................................................................................... 27

2.4.5 – Generation and recombination of charge carriers .................................................................... 28

2.4.6 – Charge transportation ............................................................................................................. 29

2.4.7 – PN junctions ............................................................................................................................ 30

2.4.8 – Diffusion across the junction.................................................................................................... 30

2.4.9 – Biasing the junction with forward bias .................................................................................... 31

2.4.10 – Biasing the junction with reverse bias .................................................................................... 32

2.4.11 – I-V characteristic curve of a PN junction ................................................................................. 33

2.5 –Semiconductor silicon detectors ...................................................................................................... 34

2.5.1 – Capacitance ............................................................................................................................. 34

2.5.2 – Substrate and electrodes type ................................................................................................ 35

2.5.3 – Signal development ................................................................................................................ 35

2.5.4 – Photon detection ..................................................................................................................... 36

2.5.5 – Charged particle detection....................................................................................................... 36

2.5.6 – Functionality of silicon detectors ............................................................................................ 36

2.5.7 – Signal readout ......................................................................................................................... 37

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3 – Silicon Pixel Detectors .......................................................................................................................... 39

3.1 – Strip detectors ................................................................................................................................ 41

3.2 – Pixel detectors ................................................................................................................................ 42

3.2.1 – Pixel capacitance ..................................................................................................................... 43

3.2.2 – Cross talk, spatial resolution and charge sharing in pixel detectors .......................................... 43

3.3 – Planar and 3D pixel detectors ......................................................................................................... 44

3.3.1 – Active edges ............................................................................................................................ 46

3.3.2 – 3D detector concepts............................................................................................................... 47

3.4 – Devices under test .......................................................................................................................... 49

3.4.1 –FBK-3D sensors ......................................................................................................................... 49

3.4.2 – Hybrid Pixel Detectors ............................................................................................................. 51

3.4.3 – Single Chip Assembly (SCA) ...................................................................................................... 52

3.4.4 – Current ATLAS Silicon Pixel detectors ....................................................................................... 52

3.4.5 – Front-End Electronics description ............................................................................................ 54

3.4.6 – Single channel.......................................................................................................................... 56

3.4.7 – FE-I3 calibration ....................................................................................................................... 57

4 – Characterization and Test of FBK-3D Pixel Silicon Sensors ................................................................... 59

4.1 – Sensor properties and performance tests ....................................................................................... 61

4.2 – TurboDAQ setup ............................................................................................................................ 61

4.2.1 – Hardware description .............................................................................................................. 63

4.2.2 – Software description ............................................................................................................... 64

4.2.3 – Fixed setup at CERN Lab 161 .................................................................................................... 65

4.3 – The SCAs and their characterization ................................................................................................ 67

4.4 – I-V measurements .......................................................................................................................... 68

4.4.1 – Measurements results on FBK-3D and planar sensors .............................................................. 69

4.4.2 – Leakage current from Monleak Scan ........................................................................................ 72

4.5 – Threshold and noise ....................................................................................................................... 73

4.5.1 – Measurements results on FBK-3D and planar sensors ............................................................. 74

4.5.2 – Noise versus bias voltage of the sensor .................................................................................... 76

4.6 – Time over Threshold (ToT) measurements and internal calibration of the detector ........................ 78


4.7 – Gamma source measurements with 241Am and 109Cd ..................................................................... 81


4.8 – Beta source measurements with 90Sr ............................................................................................. 84

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4.9 – Test Beam ..................................................................................................................................... 87

4.9.1 – The experimental setup ........................................................................................................... 88

4.9.2 – Selected events ....................................................................................................................... 90

5 – Irradiation............................................................................................................................................. 91

5.1 – Radiation-induced effects on silicon ............................................................................................... 93

5.1.1 –Bulk damage ............................................................................................................................. 93

5.1.2 – Leakage current and annealing ................................................................................................ 94

5.1.3 – Effective doping and fluence dependence ................................................................................ 96

5.1.4 – Charge trapping ....................................................................................................................... 98

5.1.5 – Surface effects ......................................................................................................................... 98

5.1.6 – Consequences of irradiation damage on sensor operation ....................................................... 98

5.2 – PS irradiation facility overview ........................................................................................................ 99

5.3 – Irradiation of FBK-3D and planar sensors ...................................................................................... 101

5.3.1 – Irradiation of FE-I3 ................................................................................................................. 101

5.3.2 – Irradiation of SCAs - Setup ..................................................................................................... 103

5.1.3 – Irradiation of SCAs - Results .................................................................................................. 105

6 – Conclusions ........................................................................................................................................ 111

7 – Appendixes ........................................................................................................................................ 115

Appendix 1 – FE-I3 ................................................................................................................................ 117

Appendix 2 - TurboDAQ ........................................................................................................................ 118

Appendix 3 – Complete plots collection................................................................................................. 125

References ............................................................................................................................................... 135

Acknowledgements ................................................................................................................................. 141

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Chapter 1 – Introduction

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CHAPTER 1 INTRODUCTION


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ew sensor concepts and materials are currently being investigated in the field of particle detection,

mainly due to the proposed luminosity upgrade of the LHC at CERN, when tracker detectors will

have to cope with high density of events and survive very high radiation fluences up to 1016

protons per cm2. 3D silicon pixel detectors can be a possible answer to these uprising needs, and at present

are being fully investigated, tested and characterized within ATLAS. This thesis focuses on the

characterization of a particular type of 3D pixel silicon detectors, the DDTC ones developed and produced

at the Fondazione Bruno Kessler (FBK-irst) in Trento, Italy, in comparison to the current planar silicon pixel

detectors mounted inside the ATLAS inner tracker.

Chapter 2 gives an introduction to the theoretical aspects of particle (electromagnetic, light and heavy

charged particles) interactions with matter. In the second part of the chapter, semiconductors and in

particular silicon detectors are described.

Chapter 3 describes pixel silicon detectors, and in particular FBK-3D pixel detectors and their

characteristics, explaining the differences between 3D and planar sensors. Moreover, a description of the

front-end electronics (ATLAS FE-I3 chip) used to readout signals coming out of the sensor is given.

In Chapter 4 the work done for this thesis on the characterization of FBK-3D detectors is presented, starting

from the electronics tests and coming to calibration of SCAs (Single Chip Assembly) and source tests to

verify the correct performance of the detectors. The 3D May 2009 Test Beam, to which I contributed for

data acquisition is also described.

Finally, Chapter 5 focuses on irradiation of FBK-3D detectors, showing preliminary results from a first

irradiation with the 24 GeV/c proton beam of the CERN PS (Proton Synchrotron), at which I have worked

from July to November 2009.

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CHAPTER 2 PHYSICS OF SEMICONDUCTOR DETECTORS

Chapter 2 – Physics of Semiconductor Detectors

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his chapter is meant to describe the physics behind interaction of radiation with matter, its

consequences and the principles applied in semiconductor silicon detector technology. Particles and

electromagnetic radiation are detected through their interaction with matter, with different

interaction processes for photons, charged particles and neutral particles. In semiconductor detectors

mainly interactions that create free charge carriers are of relevance, because they produce signals that can

be collected by appropriate electronics.

2.1 – Ionizing radiation

Referring to the way in which it ionizes a material, radiation can be distinguished in directly and indirectly

ionizing. All charged particles that lose their energy by directly exciting or ionizing atoms and molecules of

the traversed material by electromagnetic processes belong to the first category, while the second class

groups neutral particles (neutrons) and electromagnetic radiation (photons), because they interact with

matter generating secondary particles that can lead to excitation and ionization. Moreover, a particle

travelling through matter can lose energy gradually (losing energy nearly continuously through interactions

with the surrounding material), or catastrophically (moving through with no interaction until losing all its

energy in a single collision). Gradual energy loss is typical of charged particles, whereas photon interactions

are of the "all-or-nothing" kind.

2.2 - Interaction of electromagnetic radiation with matter

Depending on their energy and on the nature of the material, photons interact with matter in three main

ways: with the Photoelectric Effect (or Photoelectric Absorption), the Compton scattering and the Pair

Production. It is also important to mention the Rayleigh Scattering, which consists in the diffusion of the

photons over the electrons of atoms, without ionization or excitation of the atoms.

The absorption of a beam of photons, all with the same energy and all travelling in the same direction, is

described by an exponential law:

𝑁 𝑥 = 𝑁0𝑒−µ𝐿𝑥

that accounts for the exponential decrease of the number of particles N(x) at x given depth into the

material starting from the initial number 𝑁0, where µL is the linear absorption coefficient1 given by:

𝜇𝐿 =𝜍𝑁𝐴𝜌

𝐴

with ς cross-section, NA Avogadro’s constant, ρ the density of the material, A the molecular weight. The

average distance travelled by a photon before being absorbed is given by λ, the attenuation length or mean

free path, that is the inverse of the linear absorption coefficient:

𝜆 = 1

µ𝐿

The absorption of photons depends on the total amount of material in the beam path, and not on how it is

distributed, because the probability for a photon to interact somewhere within the matter depends on the

total amount of atoms ahead of its path (since they interact only with a single atom). Therefore, it is useful

1 It gives a measure of how fast the original photons are removed from the beam (if of high values the original photons are removed after travelling only small distances)

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to describe the absorption process factorizing the dependence on the density of the material from the type

of material. This is obtained by introducing the mass absorption coefficient μm, which relates the linear

absorption coefficient to the density of the material ρ:

µ𝐿 = µ𝑚𝜌

This means, for example, that the mass absorption coefficient is the same for ice, liquid water and steam,

whereas the linear absorption coefficients differs greatly. The total attenuation effect of a given material

slab can be described by quoting the mass attenuation coefficient, which depends on the material's

chemical composition and the photon energy, together with the material's density and thickness. The

product ρx, the areal density, is often quoted instead of the geometrical thickness x. If an absorber is made

of a composite material, the mass absorption coefficient is readily calculated by summing the products of

the mass absorption coefficients and the mass proportions (α) each element present in the material:

µ𝑚 𝑇𝑂𝑇𝐴𝐿 = (𝛼 µ𝑚 )

If the radiation changes, degrades in energy, it is not completely absorbed or if secondary particles are

produced, then the effective absorption may decrease, and so the radiation penetrates more deeply into

matter. It is also possible to have an increasing number of particles with depth in the material: this process

is called build-up, and has to be taken into account when evaluating the effect of radiation shielding, for

example.

The total interaction probability of the photons is given by the sum of the single effect cross-sections, which

are summarized in Figure 2.1 for silicon:

𝜍 = 𝜍𝑃𝑕𝑜𝑡𝑜𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐 + 𝜍𝐶𝑜𝑚𝑝𝑡𝑜𝑛 + 𝜍𝑃𝑎𝑖𝑟

For silicon (Z=14), and for energies of photons under 100 keV, the dominant effect is the photoelectric one,

whereas for over 10 MeV it is the pair production. The absorption coefficient for a photon coming from the

decay of 241Am, which produces X-rays of 59.5 keV, is 0.3 cm2g-1, and the probability of detection in 300 µm

Figure 2.1 – Probability of photon absorption for 300 µm silicon as function of the photon energy, indicating the contribution for different processes and a comparison with total probability for 300 µm CdTe [2-1]


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silicon is only of 2%. This because of the fact that cross-sections for photons are low, and consequently also

the probability of detection are low. Nevertheless, gamma sources are suited for calibrating silicon

detectors because the whole photon energy can be detected in the sensor with the assumption that

electrons from photoelectric effect do not escape from the detector. The exponential attenuation law does

not describe what happens to the energy carried by the photons removed from the beam, which possibly

may be carried through the medium by other particles, including some new photons.

2.2.1 - Photoelectric effect

This process consists in the absorption of a photon with consequent expulsion of an electron from the hit

atom. In order to remove a bound electron from an isolated atom, a threshold energy for the photon is

needed: it is the ionization potential, and it varies depending on the atomic shell the electron occupies. If

the energy of the photon, Eγ, exceeds the ionization potential (also called EB , binding energy2), an electron

will be emitted, carrying energy Ee given by the following formula:

𝐸𝑒 = 𝐸𝛾 − 𝐸𝐵

The ionization potential depends on the square of the nuclear charge Z of the atom (and so on the

dimension of the atom), and the cross-section for the photoelectric effect is also a strong function of Z:

𝜍𝑃𝑕𝑜𝑡𝑜 ∝ 𝑍𝑛

with n varying between 4 and 5 depending on the photon energy [2-2]. This process is dominant at low

photon energies (in silicon below 100 keV); for this reason high-Z materials (e.g. Cadmium Telluride CdTe)

are preferred for X-ray detection. In this thesis the photoelectric effect has been used in order to calibrate

3D silicon detectors, trying to reproduce the photoelectric peaks of some known gamma radioactive

elements (241Am and 109Cd).

When other atoms are present, as in molecules and solids, the electronic energy levels and the

photoelectric cross sections will be very different. For solids, the threshold can be ≈ 1 eV and it depends on

the crystalline structure and on the nature of the surface. The ionization potential in this case is usually

called work function. Photon absorption efficiencies approach 100% in the visible and ultraviolet, but the

overall device efficiencies are limited by the electron escape probabilities. In a semiconductor, a photon

can be thought as ”ionizing” an atom, producing a ”free” electron which remains in the conduction band of

the lattice. Thresholds are of order 0.1–1 eV for intrinsic semiconductors and of order 0.01–0.1 eV for

extrinsic semiconductors. The latter photon energies correspond to infrared photons. In the end, the

escaping electron produces a redistribution of the atomic electrons, that can lead to Fluorescence (emission

of photons) or Auger Effect (emission of characteristic X-ray radiation).

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2.2.2 - Compton scattering

Compton scattering takes place when a photon scatters off a free (or a quasi-free) electron, yielding a

scattered photon with a lower frequency and a new direction. For an unbound electron initially at rest, it is

possible to write the following equation:

𝑕𝜈 ′ = 𝑕𝜈 1 + 𝑕𝜈

𝑚𝑒𝑐2 (1 − cos 𝜃)

−1

with hν and hν’ initial and final energy, θ photon angle change, me electron mass and c speed of light. The

Compton cross section is given by the Klein-Nishina formula [e.g. 2-1]. The absorption cross section is small

at low energies, rises to a peak for photon energies around 1 MeV and declines at higher energy.

2.2.3 - Pair production

Photons with energies in excess of 2mec2 produce electron-positron pairs, and interaction with a nucleus is

needed in order to balance momentum. The pair production cross section starts at 1.022 MeV and then

rises to an approximately constant value at high photon energy, in the gamma ray region of the spectrum

of electromagnetic radiation. Cross sections scale with the square of the atomic number, and complete

equations describing the cross-section are Bethe-Heitler equations [e.g. 2-3].

2.3 - Interactions of charged particles with matter

The most common way in which charged particles can interact with matter is the electromagnetic

interaction, that can involve inelastic collisions with electrons in the absorbing material or elastic collisions

with nuclei. Inelastic collisions lead to continuous loss of energy by incident particles. When atoms or

molecules are given energy by an incident particle that brings them at an excited state, the process is called

Excitation3; alternatively, when the released energy is enough to form electron-ion pairs, the process is

called Ionization. Emitted electrons can have higher kinetic energy than the material’s ionization potential,

so they can furthermore ionize the atom, creating secondary energetic electrons called δ rays. Elastic

collisions cause lateral diffusion of the incoming particle (Multiple Scattering), without noticeable loss of

energy. This effect is higher when the mass of the hitting particle is small, so it is particularly relevant for

light particles such as the electrons. When small masses are involved, other electromagnetic processes such

as Bremsstrahlung, Cerenkov Effect and Transition Radiation become relevant. So it is important with

charged particles to split light charged particles, such as electrons and positrons, from heavy charged

particles, such as pions, ions, protons and muons.

2.3.1 - Stopping power

The mean value of energy loss for ionization per path length is known as stopping power, Sl, also known as

dE/dx (where E is the particle energy and x is the distance travelled):

𝑆𝑙 = − 𝑑𝐸

𝑑𝑥

It is commonly measured in MeV∙m-1, and depends on the charged particle's energy, on the density of

electrons within the material, and hence on the atomic number of the atoms. A more fundamental way of

3 Energy is then lost with the emission of photons (Auger effect) or vibration or rotation


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describing the rate of energy loss is to specify the rate in terms of the density-thickness, rather than the

geometrical length of the path, with the quantity called mass stopping power:

𝑆𝑚 = − 𝑑𝐸

𝑑(𝜌𝑥)= −

1

𝜌 𝑑𝐸

𝑑𝑥

where ρ is the density of the material and ρx is the density-thickness.

2.3.2 - Energy loss by heavy charged particles

The mean energy loss of a charged particle through matter can be described by the Bethe-Bloch formula [2-

1]:

𝑑𝐸

𝑑𝜉 =

1

𝜌

𝑑𝐸

𝑑𝑥= 𝐷

1

𝛽2𝑧2

𝑍

𝐴{1

2ln

2𝑚𝑒𝛾2𝛽2𝑐2

𝐼2 −𝛽2 −

𝛿

2−

𝐶

𝑍}

𝐷 = 4𝜋𝑟02𝑚𝑒𝑐

2𝑁𝐴 = 0,307 𝑀𝑒𝑉 𝑐𝑚2

𝑔

with ρ the density of the material, x the depth into the material, β and γ the relativistic parameters of the

particle, z the charge of the particle, Z the atomic number of the material that is traversed, A the atomic

weight of the material, me the mass of the electron, c the speed of light, I average ionization energy of the

material, δ and C the relativistic corrections of the formula, r0 the classical electron radius, NA Avogadro’s

constant.

Figure 2.2 - Energy loss of µ on Cu [2-4]


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Figure 2.2 shows the behaviour of energy loss for a µ particle as function of its momentum, while Figure 2.3

shows the same for different particles. Figure 2.4 shows the energy loss for heavy charged particles in

different materials, pointing out the fact that the minimum of the curve varies from 1.15 MeV for Pb to 2

MeV for He, with the exception of the H2. These graphs are plots of the energy-loss rate as a function of the

kinetic energy of the incident particle. It is important to notice that in Figure 2.4 the stopping power is

expressed using density-thickness units. As for photon interactions, it is found that when expressed as loss

rate per density-thickness, the curve is nearly the same for

most of the materials. To obtain the energy loss per path

length one needs to multiply the energy loss per density-

thickness, shown in Figure 2.4, by the density of the

material. There is, however, a small systematic variation;

the energy loss is slightly lower in materials with larger

atomic numbers. At high incident energies there is also

some variation with density, because a higher density of

atomic electrons protects the more distant electrons from

interactions with the incident particle. This results in lower

energy loss rates for higher densities. Figure 2.5 shows the

silicon behaviour.

For low energies the stopping power varies approximately as the inverse of the particle's kinetic energy.

The rate of energy loss reaches a minimum, then starts to increase slowly with further grow in kinetic

energy. Minimum ionization occurs when the particle's kinetic energy is about 2.5 times its rest energy, and

its speed is about 96% of the speed of light in vacuum. At minimum ionization the energy loss is about 2

MeV cm2 g-1 (= 3 × 10-12 J∙m2∙kg-1 in SI units), which slightly decreases with the increasing atomic number of

the absorbing material. Given that the minimum of the curve is almost the same for all particles in all

materials, it is common to define this value as due to a Minimum Ionizing Particle (MIP), used to quantify

the minimum signal that can be expected as detector response without referring to a specific particle. For

silicon, the <dE/dx>min≈1.66 MeV cm2 g-1, as shown in Figure 2.6.

The probability distribution for the energy lost by a particle in a single hit follows a Landau curve, because

events with a high energy release can happen but are less probable. Experimentally, a Gauss curve is

obtained only when the thickness of the material allows to have many of hits with atomic electrons. For

Figure 2.3 - Energy loss for different particles [2-4] Figure 2.4 - Energy loss for heavy charged particles in

different materials [2-4]

Figure 2.5 - Energy loss in silicon [2-4]


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thin depths, hits with atoms are not many, and hits with high energy loss can produce a tail in the

distribution through high energies.

A charged particle leaves a track in the material formed by ion-electron pairs and photons produced by de-

excitation. For every material there exists an energy value for the production of pairs, independent of the

particle energy:

𝑊 = Δ𝐸

𝑛𝑇

with ∆E energy transferred by the incident particle, nT number of pairs created. In the definition of nT are

included the primary nP and secondary nS pairs as:

𝑛𝑇 = 𝑛𝑃 + 𝑛𝑆

In silicon the mean energy loss of a MIP is 1.66 MeV cm2 g-1, and the density is 2.33 g cm-3, which implies

that the energy loss is 390 eV/μm. Since to generate a hole-electron pair an energy of 3.6 eV is needed, it

follows that a MIP creates ~110 pairs per μm in silicon. For a thickness of 250 μm, a MIP creates about

20000 hole-electrons pairs, with 27000 as mean amount and 19400 as most probable value (MPV), that is

the peak of the Landau curve, as shown in Figure 2.6.

The loss of energy for a heavy charged particle as a function of the depth in the material follows a

characteristic behaviour: first the loss of energy is almost constant (or grows really slowly), and then, when

the particle’s speed is significantly reduced, there is a maximum peak (Bragg Peak) where most of the

particle’s energy is released before it stops. This allows to define the range of a particle in a material as the

distance travelled before being totally absorbed.

Figure 2.6 - Mean and Most Probable Value of energy loss of a MIP in 250 µm of silicon [2-4]


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2.3.3 - Energy loss by light charged particles

Electrons lose energy in matter both with ionizing collisions with electrons and with radiative loss

(bremsstrahlung) due to accelerations in the electric field of the nuclei. The mean value of the energy is

given by the sum of the two contributions:

𝑑𝐸

𝑑𝑥 =

𝑑𝐸

𝑑𝑥 𝐵𝑟𝑒𝑚

+ 𝑑𝐸

𝑑𝑥 𝐼𝑜𝑛

Since radiative loss is much stronger for lighter particles, it is much more important for beta particles

(electrons and positrons) than for protons, alpha particles, and heavier nuclei (but it happens also for

them). Bremsstrahlung starts to become important only at particle energies well above the minimum

ionization energy (for particle energies below about 1 MeV the energy loss due to radiation is very small

and can be neglected). The radiative energy loss is described by:

−1

𝜌 𝑑𝐸

𝑑𝑥 𝐵𝑟𝑒𝑚

=𝐸

𝑋0

with

1

𝑋0=

4𝑍(𝑍 + 1)𝑁𝐴𝑉

137𝐴𝑟0

2 ln183

𝑍13

X0 is called radiation length, which is the distance over which the energy of an electron is reduced by a

factor e due to only radiation losses. At relativistic energies the ratio of energy loss by radiation to energy

loss by ionization is approximately proportional to the product of the particle's kinetic energy and the

atomic number of the absorber:

𝑑𝐸𝑑𝑥

𝐵𝑟𝑒𝑚

𝑑𝐸𝑑𝑥

𝐼𝑜𝑛

=1

580 𝑍𝐸

where E is the energy and Z is the mean atomic number of the absorber. The kinetic energy at which the

energy loss by radiation equals the energy loss by collisions is called critical energy, Ec, and is approximately

𝐸𝑐 ≈580 𝑀𝑒𝑉

𝑍


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2.4 – Physics and behaviour of semiconductors

From now on we will concentrate on semiconductors, and focus on the interaction of MIP particles with

silicon sensors to discuss the behaviour of silicon detectors for particle tracking. They can be used for

particle detection because they are materials with a little number of free charges, and particles passing

through them can easily produce a detectable quantity of electron-hole pairs. Semiconductor devices are

also widely used in electronics because of their specific electrical conductivity, σ, which is between that of

good conductors (>1020 cm-3 free electron density) and that of good insulators (<103 cm-3 free electron

density).

2.4.1 - Conduction in a solid

The structure of an isolated atom shows countable states of the electrons surrounding the nucleus,

characterized by a definite energy En4. In a solid the entire number of atoms that constitutes the lattice has

to be taken into account: the electron states become so dense to make them forming a continuous band of

allowed energy. These bands are separated by forbidden gaps that electrons cannot occupy (in Figure 2.7

the case of Silicon). Electrons fill the states starting from the lowest energy level available, filling the energy

bands up to a maximum energy.

Qualitatively, there are two possible configurations: one with the last band partially filled, and the other

with the last band completely filled. The partially filled (or empty) band is called conduction band, while the

band below is referred to as valence band. In the case of a partially filled band, the solid is a conductor,

because when an electric field is applied the electrons can freely change state in the conduction band. In

the case of completely filled bands, the gap width between the valence and the conduction band can make

the solid an insulator (Φ ~10 eV) or a semiconductor (Φ ~1 eV). The conduction band can be accessed by

thermal excitation and in fact the thermal energy available at T ≈ 300 K is sufficient to bring some electrons

into the conduction band if the gap is of the order of 1 eV. To calculate the number of electrons with an

energy above a given value E0 , one must apply Boltzmann statistics, which gives the number n of electrons

having energy greater than E0. From this it follows:

𝑛 𝐸 > 𝐸0 = 𝑒−

𝐸0𝑘𝐵𝑇

where kB = 1.3807 ∙ 10−23 𝐽 ∙ 𝐾−1 is the Boltzmann constant.

4 n is a set of integer numbers

Figure 2.7 – Band structure of Silicon


26

2.4.2 - Classification of Semiconductors

Although there is a large variety of semiconductor materials, there is one that stands out from the group:

Silicon. Its properties are well known, it is quite easy to find and to manage practically, and – last but not

least for the productive processes – inexpensive. Nevertheless, depending on the chemical composition,

each kind of semiconductor has different properties, and so is used for different applications. Elementary

semiconductors are located in the IV-A group of the Periodic Table of Elements (see Table 2.1), and they are

the Silicon (Si), the Germanium (Ge), the Grey Tin (α-Sn), and the Carbon (C), that can solidify in two

different structures (graphite and diamond, which is an insulator but with the same crystal structure as Si,

Ge and α-Sn).

Material a (nm) EG (eV) Structure

Diamond (C) 0.357 5.48 cubic Silicon (Si) 0.543 1.11 cubic

Germanium (Ge) 0.566 0.664 cubic

Grey Tin (α-Sn) 0.649 - cubic

White Tin (β-Sn) 0.583 0.318

- tetragonal

Table 2.1 - Lattice constant a, energy gap EG at 300 K and lattice structure of some group IV-A elements [2-5]

The main characteristic of the IV-A group elements is that they all have the outer shell of each atom exactly

half filled, and so by sharing the four electrons of the outer shell with other atoms it is possible to obtain a

three-dimensional crystal structure with no preferential direction (except for graphite), and it is also

possible to combine two IV-A group semiconductors in order to form useful compounds (such as SiC or

SiGe) with new properties (for example the SiC is a borderline compound between semiconductor and

insulator and can be useful for high temperature electronics). Also elements of group III (II) can be

combined with elements of group V (VI), with covalent bonds (but, in contrast with IV group ones, they

show also a certain degree ,~30%, of ionic bonds), to obtain semiconductors. Most of the III-V

semiconductors exist in the so-called zincblende structure (cubic lattice), and some in the wurtzite structure

(hexagonal lattice); GaAs and GaN are the most known and commonly used (for example for optical

applications, because they are direct gap semiconductors). It also exists a II-IV class of semiconductors,

characterized by an higher ionic bond percentage, ~60%, since the respective elements differ more in the

electron affinity due to their location in the Periodic Table of Elements, and a I-VII class, with larger energy

gap. There are other elementary semiconductors such as selenium and tellurium from group VI, the

chalcogenes, but only with two missing valence electrons to be shared with the neighboring atoms, so they

have the tendency to form chain structures. Finally, also some spare compounds can work as

semiconductors: they are the IV-VI (PbS, PbSe,PbTe), V-VI (B2Te3), II-V (Cd3As2, CdSb) compounds, a number

of amorphous semiconductors (the a-SI:H, amorphous hydrogenate silicon, for example, is a mixture of Si

and H), and the chalcogenide glasses (As2Te3, As2Se3, that can be used in xerography)[2-5].


27

2.4.3 - Silicon

Silicon is used in detector technologies because only 3.6 eV are needed to create an electron-hole pair. It

has four valence electrons, so it can form covalent bonds with four nearby atoms. When the temperature

increases electrons in the covalent bond can become free, generating holes that can afterwards be filled by

other free electrons, so effectively there is a flow of charge carriers. The energy needed to break off an

electron from its covalent bond is given by Eg (gap energy). There exists an exponential relation between

the free-electron density ni and Eg, given by the formula:

𝑛𝑖 = 2(𝑚𝑒𝑐

2𝑘𝐵

2𝜋(ℏ𝑐)2𝑇)

32 𝑒

−𝐸𝑔

2𝑘𝐵𝑇 [ 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠

𝑐𝑚3]

For example, at T=300 K ni = 1.45 x 1010 electrons/cm3, and at T=600 K ni = 1.54 x 1015 electrons/cm3[2-6].

These electrons determine an intrinsic current in the silicon material when a voltage is applied. In pure

silicon, so called intrinsic, at equilibrium the number of electrons is equal to the number of holes. Electron-

hole pairs are continually generated by thermal ionization, and in order to preserve equilibrium

continuously recombine. The intrinsic carrier concentrations ni are equal for electrons and holes, small and

highly dependent on temperature. Holes and electrons both contribute to conduction, although holes have

smaller mobility due to the covalent bonding.

2.4.4 – Doping of silicon

In order to produce either a silicon detector or a power-switching silicon device, it is necessary to greatly

increase the free hole or electron population. This is achieved by deliberately doping the silicon, adding

specific impurities called dopants. The doped silicon is called extrinsic and as the concentration of dopant

increases its resistivity ρ decreases. Pure silicon electrical properties can be changed by doping it with

group V elements of the periodic table, such as phosphourous (P), which create electrons (n-type silicon

doping, with free negative charges), or with group III elements, such as boron (B), which leave free holes (p-

type silicon doping, with free positive charges), as shown in Figure 2.8. A group V dopant is called a donor,

since it makes available an electron for conduction. The resulting electron impurity concentration is

denoted by ND (donor concentration). If the silicon is doped with group III atoms, such as B, Al, Ga or In,

which have three valence electrons, the covalent

bonds in the silicon involving the dopant will

have one covalent-bonded electron missing. The

dopant is thus called an acceptor, which is

ionized with a net positive charge. The resultant

hole impurity concentration is denoted by NA

(acceptor concentration).

Figure 2.8- Doping of silicon [2-7]


28

2.4.5 – Generation and recombination of charge carriers

In thermal equilibrium the concentration of positive (p) and negative (n) charge carriers is constant in time

and obeys the mass action law due to the balance of generation and recombination of charge carriers:

𝑛𝑝 = 𝑛𝑖2

Electrons in n-type and holes in p-type silicon are called majority carriers, while holes in n-type and

electrons in p-type silicon are called minority carriers. Noticeable is the fact that the product of electron

and holes densities (n and p) is always equal to the square of the intrinsic electron density, regardless of

doping levels, as expressed by the mass action law. The carrier concentration equilibrium can be

significantly changed by the application of an electric field, by heat or by irradiation with particles. Such

carrier injection mechanisms create excess carriers.

The thermal generation rate, Gth, of charge carriers is:

𝐺𝑡𝑕 = 𝑛𝑖

𝜏𝑔

with τg being the generation lifetime. The recombination rate is proportional to the product of the charge

carrier concentrations, np. When the majority carrier concentration is practically unchanged, the

recombination is in fact limited by the concentration of the minority carriers, leading to:

𝑅 = 𝑝

𝜏𝑟 ,𝑛 𝑓𝑜𝑟 𝑛 − 𝑡𝑦𝑝𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙

𝑅 = 𝑛

𝜏𝑟 ,𝑝 𝑓𝑜𝑟 𝑝 − 𝑡𝑦𝑝𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙

with τr,n/p the recombination lifetime in n- and p-type semiconductors, respectively. The numerical values of

τg and τr can differ significantly. In the presence of excess carriers the product of the electron and hole

concentration exceeds the value given in the mass action law. These excess carriers might be introduced by

injection or radiation, as explained in Chapter 5 of this thesis. After injection or radiation has stopped, a

thermal equilibrium is reached again by enhanced recombination proportional to the concentration of the

minority excess carriers. This leads to an exponential decay with the characteristic time τr. In case of

removal of the carriers the product of the carrier concentrations will fall below 𝑛𝑖2 and the generation,

which is unaffected by this change, dominates as the recombination rate will be very low. Generation

increases the carrier concentration and therefore also the recombination rate. This also leads to an

exponential return to the equilibrium condition but with time constant τg. If the generated carriers are

continuously removed, like in a reversely biased diode, the carrier concentration product will stay

permanently below 𝑛𝑖2 and the equilibrium state is never reached. The result is a steady generation current

of the drained carriers.


29

2.4.6 - Charge transportation

A first mechanism of charge transportation in semiconductors is identified under the name of drift

mechanism: it simply consists in the application of an electric field at the extremity of the semiconductor,

so that charge particles will move at velocities (vh, ve) proportional to the electric field E:

𝑣𝑕 = µ𝑃𝐸

𝑣𝑒 = −µ𝑛𝐸

where µP, µn are constants of proportionality called mobility. In silicon, at room temperature, typical values

of mobility are µn = 1450 cm2/(V∙s) for the electrons and µP = 450 cm2/(V∙s) for the holes. The total current

is the sum of the currents given by holes and electrons:

𝐽𝑇𝑂𝑇 = µ𝑛 𝐸 𝑛 𝑞 + µ𝑝 𝐸 𝑝 𝑞 = µ𝑛 𝑛 + µ𝑝 𝑝 𝐸 𝑞

It is important to note that the velocity does not increase linearly with the electric field, but saturates at a

critical value.

A second charge transportation mechanism is diffusion, that is due to the fact that charged particles move

from a region of high concentration to a region of low concentration.

The diffusion current is proportional to the gradient of charge along the direction of flow, as shown in the

following equation:

𝐽𝑛 = 𝑞 𝐷𝑛 𝑑𝑛

𝑑𝑥

𝐽𝑝 = −𝑞 𝐷𝑝 𝑑𝑝

𝑑𝑥

𝐽𝑇𝑂𝑇 = 𝑞 (𝐷𝑛 𝑑𝑛

𝑑𝑥− 𝐷𝑝

𝑑𝑝

𝑑𝑥)

It is important to say that a linear charge density profile means constant diffusion current, whereas a

nonlinear charge density profile means varying diffusion current.

𝐿𝑖𝑛𝑒𝑎𝑟: 𝐽𝑛 = 𝑞 𝐷𝑛 𝑑𝑛

𝑑𝑥= −𝑞𝐷𝑛

𝑁

𝐿

𝑁𝑜𝑛 − 𝐿𝑖𝑛𝑒𝑎𝑟: 𝐽𝑛 = 𝑞 𝐷𝑛 𝑑𝑛

𝑑𝑥=

−𝑞𝐷𝑛 𝑁

𝐿𝑑 𝑒

−𝑥𝐿𝑑

Figure 2.9 - Diffusion in a semiconductor [2-7]


30

There exists a relation between the drift and diffusion currents, although they are totally different. It is

Einstein’s relation, which connects diffusion constant and mobility constant to the absolute temperature:

𝐷

µ=

𝑘𝑇

𝑞

2.4.7 - PN junctions

Electrons and holes are discrete charge carriers, and the current generated by their drift and diffusion is

affected by a noise proportional to the current itself. The amplitude of this intrinsic noise depends on the

resistance of the semiconductor used (230 kΩ∙cm for silicon), and it can unfortunately be of the same order

of the signal generated by a particle passing through the semiconductor material. It follows that

semiconductors as they are cannot be suitable for particle detection. A PN junction (shown in Figure 2.10)

can instead solve this problem.

A PN junction is the location in a doped semiconductor where the impurity changes from p to n while the

monocrystalline lattice continues undisturbed. A bipolar diode is thus created, which forms the basis of any

bipolar semiconductor device. In order to understand how a diode works, it is necessary to study its three

operation regions: equilibrium, with the depletion zone and the built-in potential, forward bias, with the I-V

characteristic curve, and reverse bias, with the junction capacitance.

2.4.8 - Diffusion across the junction

Each side of the junction contains an excess of holes or electrons compared to the other side, and this

situation induces large concentration gradients. Therefore, a diffusion current flows across the junction

from each side, as shown in Figure 2.11.

As free electrons and holes diffuse across the junction, a region of fixed ions is left behind. This region is

known as the depletion region, and is particularly attractive for particle detection purposes, because

Figure 2.11 - Diffusion in a PN junction, with nn concentration of electrons on n side, pn concentration of holes on n side, pp concentration of holes on p side, np concentration of electrons on p side [2-7]

Figure 2.10 - PN junction and electrical schematic [2-7]


31

charges created by a passing-through particle are going to be swept out by the electric field generated in

this zone (see Figure 2.12), and can be detected by electronics connected to the junction.

The fixed ions in the depletion region create a build-in potential and an electric field that results in a drift

current; at equilibrium, the drift current flowing in one direction cancels out the diffusion current flowing in

the opposite direction, creating a net current of zero. The built-in potential depends on the dopant

concentration:

𝑉0 = 𝑘𝐵𝑇

𝑞ln

𝑁𝐴𝑁𝐷

𝑛𝑖2

This has to be added to the contact potential VC, that is the potential difference across the junction (for

silicon is about 0.7 V).

2.4.9 – Biasing the junction with forward bias

There are two ways for biasing the junction: one is the direct, the other is the reverse way. When the n-

type region of a diode is at a potential lower than the p-type region, the diode is in forward bias, as shown

in Figure 2.13. This situation shortens the depletion width and decrease the built-in potential. Under this

condition minority carriers in each region increase, and diffusion currents also increase to supply them.

Recombination of the minority carriers with the majority carriers accounts for the dropping of minority

carriers as they go deep into the p or n region.

Figure 2.12 – Creation of the depletion zone [2-7]

Figure 2.13 - Forward biasing [2-7]


32

2.4.10 – Biasing the junction with reverse biasing

Opposite to the previous situation, when the n-type region of a diode is connected to a potential higher

than the p-type region, the diode is under reverse bias, which results in a wider depletion region and a

larger built-in potential across the junction, as shown in Figure

2.14. This is important for creating a depleted zone as wide as

possible in order to increase the sensitive zone useful for particles

detection. Varying the value of the applied bias VR it is possible to

vary the width of the depletion zone W, according to the

formula[2-1]:

𝑊 = 𝑥𝑛 + 𝑥𝑝 = 2휀0휀𝑆𝑖

𝑒

1

𝑁𝐴+

1

𝑁𝐷 𝑉0 + 𝑉𝑅

where xn and xp are the widths of the depletion zone on the n and

p side, respectively, and ε0 and εSi are the absolute and relative

dielectric constants (εr = 12 for Silicon). In silicon sensors the

junction is usually realized by a shallow and highly doped p+ (NA>

1018 cm-3) implant in a low-doped n (ND≈1012 cm-3) bulk material;

therefore the term 1/NA can be neglected, meaning that the depleted zone extends much deeper into the

lower doped side of the junction. Moreover, also the built-in voltage can be neglected because it is small

compared to typical operation voltages (0.5 V compared to 50 V). This leads to:

𝑊 ≈ 𝑥𝑛 ≈ 2휀0휀𝑆𝑖𝑒𝑁𝐷

𝑉𝑅 = 2휀0휀𝑆𝑖 𝑉𝑅µ𝜌

where the second part of the equation is obtained introducing the resistivity ρ. This is an important

parameter to characterize doped silicon:

𝜌 =1

𝑒𝑁𝐷µ

and it depends on the dopant density ND and on the majority carrier mobility µ (e elementary charge of the

electron).

The width of the depletion zone increases with the applied voltage, and reaches a maximum at which the

junction breaks down and becomes conductive (breakdown zone). This is also the point at which the

electric field reaches its maximum value:

𝐸𝑚𝑎𝑥 =2𝑉𝑅

𝑊≈

2𝑒𝑁𝐷

휀0휀𝑆𝑖𝑉𝑅

A PN junction can also be thought as a voltage dependent capacitor with its capacitance described by the

following equation:

𝐶𝑗 = 𝐶𝑗0

1 +𝑉𝑅

𝑉0

Figure 2.14 - Reverse biasing [2-7]


33

with 𝐶𝑗0 = 휀𝑆𝑖 𝑞 𝑁𝐴𝑁𝐷

2 𝑁𝐴 + 𝑁𝐷 𝑉0 .

2.4.11 – I-V characteristic curve of a PN junction

The current vs voltage relationship of a PN junction is exponential in the forward bias region, and relatively

constant in the reverse bias region:

𝐼𝐷 = 𝐼𝑆 (𝑒𝑉𝐷𝑉𝑇 − 1)

Junction currents are proportional to the junction’s cross-section area; so two PN junctions put in parallel

are effectively one PN junction with twice the cross-section area, and hence twice the current. When a

large reverse bias voltage is applied, breakdown occurs and a huge current flows through the junction (see

Figure 2.15).

There exist two kinds of reverse breakdown: Zener and Avalanche breakdown.

Figure 2.15 – I-V characteristic curve [2-7]


34

2.5 – Semiconductor silicon detectors

In principle a semiconductor detector behaves like a ionization chamber, with a simple configuration made

by an absorbing medium, the semiconductor in PN junction configuration, with two highly doped p+ and n+

electrodes on the opposite side (see Figure 2.16). The electrodes are themselves connected to an external

reverse bias supply, which creates the electric field in the PN junction and the depleted zone empty of free

charges. When a particle passes through the material and generates charged carriers this electric field

makes the charges drift to the respective electrodes, holes to p+ and electrons to n+ , producing the signal.

Electron-hole pair production energy for silicon is 3.6 eV [2-8], and is much lower than the one for ionizing a

gas, ~30 eV, with the advantage of producing bigger signals, directly proportional to the released energy.

The full depletion voltage Vdepl is the voltage needed to extend the depletion zone W (defined in 2.4.10)

over the whole thickness d of the substrate:

𝑉𝑑𝑒𝑝𝑙 =𝑒𝑁𝐷𝑑2

2휀0휀𝑆𝑖

and depends on the substrate thickness and the substrate doping concentration ND. There exist different

doping configurations and electrode geometries of silicon detectors, which will be discussed in the next

chapter, focusing on the new architecture of 3D pixel sensors.

2.5.1 - Capacitance

By applying a reverse bias charges are built up on both sides of the detector and therefore the depletion

zone can be seen as a charged capacitor of value C per unit area:

𝐶 𝑉𝑅 =

𝑒휀0휀𝑆𝑖𝑁𝐷

𝑉𝑅 𝑓𝑜𝑟 𝑉𝑅 < 𝑉𝑑𝑒𝑝𝑙

휀0휀𝑆𝑖𝑑

𝑓𝑜𝑟 𝑉𝑅 > 𝑉𝑑𝑒𝑝𝑙

which implies that the increase of the reverse bias voltage increases the thickness of the depletion zone

and reduces the capacitance of the sensing element, and both these effects increase the signal-to-noise

Figure 2.16 - Example of silicon detector geometry


35

ratio (S/N), as will be shown in Chapter 4 of this thesis. Fully depleted detectors (with depletion zone

extending to the whole thickness of the silicon layer) gives the best S/N.

2.5.2 – Substrate and electrodes type

There are various ways to obtain a functional silicon detector. Table 2.2 is a summary of all the possible

configurations of substrate and electrode types:

Readout electrode Substrate

p-type n-type

p+ Double-sided process

(expensive). No advantage over p+-in-n

Typical single-sided processed sensor for

most applications

n+ Single-sided process.

May be a replacement of n+-in-n in future

Double-sided process necessary. Present

"standard-device" if radiation hardness is

required

2.5.3 – Signal development

Silicon detectors act as independent diodes: if reversely polarized they allow very little current passing

through them. There remains a small current generated by temperature, called “thermal background

current”. If a particle passes through the detector it creates charged carriers, which, if generated in the

depletion zone lead to a detectable current signal since higher than the thermal background current. Under

conditions of thermodynamic equilibrium at a temperature T, the uncertainty in the stored charge (the

charge fluctuation at fixed voltage) is given by:

< 𝜍𝑄 >2= 𝑘𝐵𝑇𝐶

This is known as kBTC noise.

Relativistic particles lose energy through collisions with the electrons of the crystal and generate ~110 e--h

pairs per micrometer of path in a few micrometer wide cylinder around its main trajectory. These charges

drift under the action of the external electric field at a speed which depends on the electric field. During the

drift the charges do not exactly follow the electric field lines, but also diffuse as a consequence of the

random thermal motion in the crystal lattice. Spread of the arrival position of the charge due to this effect

can be described as a Gaussian distribution with standard deviation

σ = 2Dt

which results in a spread of a few micrometers at the collecting electrode. The diffusion constant is higher

for electrons than for holes, as it scales with the mobility.

A magnetic field can be used to measure the momenta of the charged particles through the deflection of

their trajectories according to the Lorentz force. The magnetic field acts on all charged particles and

Table 2.2 - All possible combinations of substrate and electrode types [2-1]


36

therefore also on the electrons and holes drifting inside the silicon, which deviate from the electric field

lines by the Lorentz angle θL:

𝑡𝑎𝑛𝜃𝐿 = µ𝐻𝐵⊥ ≈ µ𝐵⊥

where B⊥ is the magnetic field component perpendicular to the electric field, μH is the Hall mobility, and μ is

the carrier mobility. Typical Lorentz angles range from a few to 20°.

2.5.4 - Photon detection

A photon interacts with a semiconductor and creates charge when its energy is higher than the silicon

energy gap of (1.11 eV), which corresponds to a λ of 1.12 μm (infrared region). If a photon has a

wavelength longer than 1.12 μm, it will cross the silicon sensor without being absorbed. For indirect band

gap semiconductor, such as germanium and silicon, the absorption of a photon is possible only involving a

phonon, which gives the additional momentum necessary to the electron to jump to the conduction band.

Indirect band gap semiconductors are characterized by an absorption coefficient growing gradually with the

photon energy; when the photon energy is high enough to allow the direct transition from the valence to

the conduction band, phonons are no longer required for the excitation, and the absorption coefficient

saturates. For direct band gap semiconductors, such as GaAs, the coefficient grows for energies close to the

energy gap value, and the transition does not require an extra particle like the phonon in order to conserve

momentum.

In a silicon detector, photons can be absorbed within the depletion region, electron-hole pairs are

produced, and the electrostatic field within the depletion region drifts the electrons to the n+ side and the

holes to the p+ side, decreasing the amount of stored charge.

2.5.5 – Charged Particle detection

The mean energy transferred per unit path length by charged particle passing through matter follows the

Bethe-Bloch formula. For high energy particles, the mean energy transferred to matter reaches a minimum,

which is nearly the same for protons, electrons and pions and grows slowly for higher energies; particles

having energies high enough to reach this minimum are knows as Minimum Ionizing Particle (MIP). The

typical energy spectrum of a MIP crossing a semiconductor material follows a Landau distribution,

characterized by an evident asymmetric shape given by the long tail for high energy losses which is due to

high energy recoil electrons (δ rays). Due to the asymmetry, the Most Probable Value (MPV) of the energy

loss, corresponding to the peak, differs from the mean energy loss, which is shifted at higher energies.

2.5.6 - Functionality of silicon detectors

Holes and electrons created by the passage of a MIP through the depleted zone move respectively towards

p+ and n+ sides, driven by the electric field. The depth reached by a charge carrier as function of time is

calculated as:

𝑥𝑒,𝑕 =𝑑 (𝑉 + 𝑉𝑑𝑒𝑝𝑙 )

2𝑉𝑑𝑒𝑝𝑙+ 𝑥0 −

𝑑(𝑉 + 𝑉𝑑𝑒𝑝𝑙 )

2𝑉𝑑𝑒𝑝𝑙 𝑒

∓2𝜇𝑛 ,𝑝𝑉𝑑𝑒𝑝𝑙 𝑡

𝑑2

with x0 the position at t=0. The corresponding velocities can be calculated with:

𝑑𝑥𝑒,𝑕

𝑑𝑡= ±𝜇𝑛 ,𝑝

2𝑉𝑑𝑒𝑝𝑙 𝑥0

𝑑2−

𝑉 + 𝑉𝑑𝑒𝑝𝑙

𝑑 𝑒

∓2𝜇𝑛 ,𝑝𝑉𝑑𝑒𝑝𝑙 𝑡

𝑑2


37

The electron is stopped at xe(te)=d, and the hole at xh(th)=0, having drift times of:

𝑡𝑒 =𝑑2

2𝜇𝑛𝑉𝑑𝑒𝑝𝑙𝑙𝑛

𝑉 + 𝑉𝑑𝑒𝑝𝑙

𝑉 − 𝑉𝑑𝑒𝑝𝑙(1 −

𝑥0

𝑑

2𝑉𝑑𝑒𝑝𝑙

𝑉 + 𝑉𝑑𝑒𝑝𝑙)

𝑡𝑕 =𝑑2

2𝜇𝑝𝑉𝑑𝑒𝑝𝑙𝑙𝑛(1 −

𝑥0

𝑑

2𝑉𝑑𝑒𝑝𝑙

𝑉 + 𝑉𝑑𝑒𝑝𝑙)

The current induced by a moving charge q, which can be measured by a charge sensitive preamplifier, is:

𝑖 𝑡 =𝑞

𝑑

𝑑𝑥

𝑑𝑡=

𝑞

𝑑 −

𝑑𝑥𝑒

𝑑𝑡+

𝑑𝑥𝑕

𝑑𝑡 =

=𝑞

𝑑2 2𝑉𝑑𝑒𝑝 𝑙

𝑥0

𝑑− (𝑉 + 𝑉𝑑𝑒𝑝𝑙 ) 𝜇𝑛𝑒

−2𝜇𝑛𝑉𝑑𝑒𝑝𝑙 𝑡0(𝑡𝑒−𝑡)

𝑑2 + 𝜇𝑝𝑒−2𝜇𝑝 𝑉𝑑𝑒𝑝𝑙 𝑡0(𝑡𝑕−𝑡)

𝑑2

2.5.7 - Signal readout

In order to collect and read the signals produced by the charges created inside the depletion zone of a

silicon sensor, an appropriate readout system has to be designed and connected to the sensor. There are

many ways to create this kind of system, but the most used is to connect via wire or bump bonds the

sensors to a Front-End (FE) electronics chip able to read out the currents coming from the electrodes of the

connected sensor. A silicon sensor cannot be useful without a readout, so the two parts together form the

silicon detector concept. Various sensor geometries and detector concepts together with the ATLAS Front-

End electronics are going to be fully explained in the next chapter.

38

39

CHAPTER 3 SILICON PIXEL DETECTORS

Chapter 3 – Silicon Pixel Detectors

40


41

he aim of this chapter is to describe the silicon sensors in use or under investigation for tracking

detectors in High Energy Physics (HEP) Experiments; principally they are characterized by pixel

layouts with planar or 3D structures, built to be radiation hard and to cope with the forthcoming

higher fluences of particles. Present detectors, mainly for vertex reconstruction, use planar pixel sensors

but the 3D architecture looks very promising.

The 3D silicon detector concept has been first proposed in 1997 by S. Parker, as a promising new solid state

radiation detector architecture, consisting in an array of columnar electrodes of both doping types,

oriented perpendicularly to the wafer surface and penetrating through the entire substrate thickness [3-1].

The innovation and main advantage of this geometry is the decoupling of the substrate thickness from the

electrode distance, resulting in short inter-electrode distances in the sensor that allow to have low

depletion voltages, short collection distances, charge sharing reduction and the possibility of operating

active edge solutions, terminating the sensor with heavily doped trenches. With this last solution the

insensitive edge region can be reduced to a few μm, in order to facilitate the overall detector layout and to

reduce the material budget, since no sensor overlap is needed within the same layer [3-2]. Moreover, all

these properties make 3D sensors very high radiation tolerant, and can effectively reduce charge trapping

effects due to high levels of radiation, but at the expense of a more complicated fabrication process. As a

consequence, the fabrication time, the complexity and the costs of a 3D structure are significantly higher if

compared to the traditional planar technology. Electrodes possible configurations can form pads, strips or

pixels, depending on the application.

3.1 – Strip detectors

Silicon detectors can be obtained with different electrode shapes or different doping configurations,

according to the performance, efficiency and resolution wanted. A strip detector, commonly used in

various tracking devices, is obtained by creating one electrode segmented in thin parallel strips, and this is

usually called a “single-sided microstrip detector” *2-1]. Ion implantation and photolithographic techniques

are used to selectively dope the surfaces of the semiconductor wafer, of typically 300 μm thickness, and to

deposit the metallization patterns necessary to extract the signals, as shown in Figure 3.1:

A more complex pattern can be obtained by making rear contacts with thin strips tilted with respect to the

strips implanted on the front side; this configuration is useful to detect two coordinates. The inconvenient

of this pattern is the presence of “ghost hits”, in case of more than one hit, as shown in Figure 3.2:

T

Figure 3.1 - Strip detector typical pattern [3-3]


42

The ambiguity problem of multiple hit events is frequent with high particle fluxes. With reference to Figure

3.2, if n = 2 or more particles hit the same sensor without the possibility to separate the strip signals in time

and strips of each strip direction show a hit, p = n! hit allocations (represented by different colors in Figure

3.2) are possible. So it is not possible to distinguish between the n real and the p-n ghost hits. If pulse

height information is provided by the readout electronics systems, with equal amplification for each strip,

the ambiguity for small hit numbers n can be resolved by comparing the pulse heights. The crossings of

equal pulse heights represent the realized hit allocation (black circles for n = 2 case in Figure 3.2) [2-1].

3.2 – Pixel detectors

Away to obtain two dimensional information for high particle fluxes is to segment one of the electrodes in

both directions: it’s the pixel detector concept. In fact, to obtain both coordinates from the same microstrip

detector, both sides have to be segmented; pixel detectors, in contrast, measure both spatial coordinates

on the same side of the sensor, and segmentation is therefore necessary only on one side of the sensor.

The differences between the two configurations are shown in Figure 3.3. With these detectors the number

of electronic channels does not increases with only one of the detector dimensions, like for strip detectors,

but with the area of the detector. Moreover, the pixels have to be connected to the front-end chip at the

segmented electrode side of the sensor, by means of the bump-bonding technique. This layout is called

hybrid pixel detector, and is going to be explained in Section 3.4.2. Another possibility is to integrate parts

or the entire front-end electronics in the sensor, obtaining the so-called monolithic pixel detector.

The main differences between microstrip and pixel detectors are the following:

Implants with higher segmentation

Connection of the front-end electronics directly to each pixel and not on the sensor periphery

Low capacitance, that allows fast signal shaping with very low noise

Figure 3.2 – Ambiguity problem of strip detectors [3-3]

Figure 3.3 - Comparison between strip and pixel detector layouts [3-3]


43

3.2.1 – Pixel capacitance

The total capacitance of each pixel determines the noise of the preamplifier of the front-end electronics [2-

1], which is discussed in detail from Section 3.4.5. In addition, the capacitance between a pixel and its next

neighbour cell determines the cross talk between pixels. The total capacitance is made of [2-1]:

Capacitance to the backside, that can be calculated with the classical formula 𝐶 = 휀0휀𝑆𝑖𝐴

𝑑, with A

area of the pixel and d thickness of the sensor (~8.5 fF for cells of 50 x 400 µm2 and 250 µm thick)

Sum of the capacitances to the neighbour pixels, that is the largest contribution to the total

capacitance, and is approximately proportional to the perimeter of the pixel (this is why square-

shaped pixel are advantageous)

Capacitance to the ground plane of the (closely spaced) readout chip

Other (small) contributions, like the capacitance of the bumps

A total pixel capacitance of ≤100 fF for square pixels of about 125 × 125 μm2 (close to the choice of the CMS

experiment) and ≤200 fF for long and narrow pixels of 50 × 400 μm2 (choice of the ATLAS experiment) is

expected.

3.2.2 – Cross talk, spatial resolution and charge sharing in pixel detectors

A signal charge deposited in one pixel can, via capacitive coupling, induce a signal on its neighbours: it is the

so-called cross talk, that has to be kept as low as possible.

Spatial resolution of a pixel detector can immediately be established knowing the pitch p of the detector:

𝜍𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 =𝑝

12

Another characteristic of a pixel detector is the charge sharing: two (or more) pixels can be triggered by the

same particle if the signal charge is shared between the pixels (a group of pixels showing a signal from the

same particle is called cluster). Charge sharing is mostly determined by the position and angle of the track

with respect to the sensor surface, as shown in Figure 3.4a–c, and can be also produced by a magnetic field

surrounding the sensor, as shown in Figure 3.4d-e. Experiments try to get advantage from charge sharing

mounting the detectors with a tilted angle, since charge sharing allows a better reconstruction of the hit

position by weighting the various pixels of a cluster with the charge (basically by taking in account the

centroid of the cluster).

Figure 3.4 - Charge sharing effect [3-3]


44

A possibility of improving the spatial resolution in one of the directions without changing the pixel size is to

arrange the pixels in a bricked pattern as shown in Figure 3.5b. This is especially useful when the pixel

shape is not squared but rectangular with a high aspect ratio. If two pixels from different rows are triggered

in the same cluster, the effective pitch along the horizontal axis is halved. At the pixel corners only three

pixel cells join, reducing the probability for four-pixel clusters. Further advantage of such a pattern is that

the capacitance to the next neighbour responsible for cross talk is halved in one direction, which is, in the

case sketched, the more critical direction. However, the bricked pattern is not easily compatible with a

mirrored bump pad geometry favored by most readout chips.

3.3 –Planar and 3D pixel detectors

Silicon pixel sensors built using planar technology have the electrode structures parallel to the surface and

restricted to be within a few microns of the wafer’s top and bottom surfaces. In contrast, the three-

dimensional (3D) architecture have electrodes perpendicular to the wafer’s surface, extend partially or

completely through the volume of the wafer5. A schematic view of a full 3D sensor is shown in Figure 3.6,

with the front surface in the drawing cut through the middle of three n-type electrodes that penetrate all

the way from the top surface to the bottom. Both planar and 3D silicon sensors are reversely biased, with

the difference that in the planar sensors the electric field is largely perpendicular to the surfaces, while in

3D sensors it is parallel.

The 3D architecture has several advantages with respect to the planar one; among them are the following

[3-4]:

1) In a planar sensor the depleted region proceeds vertically and the full depletion voltage depends on the

substrate thickness, while in a 3D detector the depletion region proceeds laterally in between columnar

electrodes of different type. Charged carriers created by passing-through particles move to the electrodes

following parallel directions, and reach them nearly at the same time; combined with the short inter-

electrode distance, this charge produces a large pulse with a fast rise-time. Full depletion depends only on

the electrode distance, that for 3D sensors can be one order of magnitude smaller than the detector

thickness. Since it decreases with the square of the electrode distance, a 3D detector with, for example, an

5 Details on how these devices were first proposed as well as simulations can be found in [3-1]

Figure 3.6 – 3D detector showing electrode layout [3-2]

Figure 3.5 - Pixel patterns [3-3]


45

inter-electrode distance of 30 μm has a full depletion voltage 100 times lower than a 300 μm thick planar

silicon detector.

2) 3D structures have very small collecting distance and short collection time. In a planar sensor a ionizing

particle generates charges at different electrode distances determining different collection times for

carriers; in a 3D detector the carriers have all the same electrode distance and the arrival time spread is

extremely reduced (see Figure 3.7).

3) The use of a 3D architecture reduces the drift path of the signal carriers and hence produce higher signal-

to-noise ratio for materials with significant charge trapping and hence poor charge collection efficiency

(such as GaAs [3-5] and diamond).

4) 3D detectors show superior radiation hardness than planar sensors, since the small collection distance

reduces the trapping probability at high fluences6. Irradiation of the silicon with high fluences of interacting

particles produces damage centers that, in depleted silicon, are charged, increasing the voltage required to

fully deplete a silicon detector [3-6]. With respect to standard planar sensors, 3D sensors can be still fully

depleted after irradiation with higher fluences because the distance between electrodes of opposite sign is

smaller [3-7]. Radiation hardness of silicon detectors will be discussed in Chapter 5 of this thesis.

5) The possibility to add active edges [3-8] in 3D sensors allows to have detectors with negligible dead

volume at the edges, as it is not usually the case with guard rings in planar sensors.

6) 3D sensors have lower charge sharing thanks to an electrode configuration that provides high shielding

effect7.

Figure 3.7 compares the way in which charges are collected by a 3D and a standard planar device. For a 3D

detector, the distance between electrodes is limited only by the electrode dimensions (or “aspect ratio”),

and can be made as little as few tens of microns, allowing for very fast charge collection and low bias

voltages [3-9]. The new generation of Deep Reaction Ion Etchers [3-8], used to fabricate deep column

electrodes and active edges, allows to reach aspect ratios of ~25:1, that means an electrode diameter of

~10 microns [3-10].

6 as those expected at sHLC 7 appealing for X-ray imaging

Figure 3.7 - Differences between 3D and planar segmented sensors in geometry and charge collection


46

The advantages come at the expense of a more complicated fabrication technology, with more steps, that

requires Micro-machining steps such as Deep Reaction Ion Etching (DRIE) for the hole drilling, Chemical

Mechanical Polishing (CMP) for the removal of the poly-silicon in excess on the surface after the hole filling,

and the need of the support wafer because holes pass from side to side.

Column electrodes can be considered as low efficiency detector regions, so the response uniformity to

particles becomes a critical issue. For tracking purposing a simple tilt of a few degrees can be a valid

solution, as test beams on detectors have shown, as will be explained in Chapter 4 of this thesis.

The induced noise on the readout chip is higher in 3D than in a planar silicon structure, due to the small

electrode distance that increases the capacitance of the single sensitive element (pixel or microstrip)8.

3.3.1 - Active edges

3D technology is very interesting for the possibility of obtaining the so-called Active Edges. Exploiting the

DRIE process, “wall” electrodes can be realized at the sensor borders to reduce the dead area to a few

microns while closing the electric field lines [3-11]. Planar detectors need multiple guard ring structures at

the cutting edge of the silicon in order to prevent high leakage currents coming from the edge of the sensor

flowing into the active area, to smooth electric field from the active region to the edge and for the

confinement of the depleted region (sensitive area). Guard ring structures should be at least as wide as the

detector thickness to be effective,

so the dead zone is on average a few

hundred microns9. 3D sensors can

be diced by etching trenches with

the DRIE process. The trenches are

doped and filled with poly-silicon to

act as p+ or n+ electrodes. This

technique produces 3D detectors

with only a thin dead zone, as

represented in Fig. 3.8. Active edges

allow new designs for large area and

low mass devices, and the full

sensitivity of such detectors can be

of great advantage for applications

where several detectors have to be

stacked together to cover large

area. Large amount of material can

be saved since there is no need of

an overlapping region between one detector and the other [3-11]. Active edges can be also realized on

planar segmented detectors if the 3D architecture is not necessary, but saving material is a concern.

8 Nevertheless, in case of a thinned planar silicon sensor, the total capacitance can be comparable to that of a 3D detector 9 The present pixel sensors of ATLAS, for example, have an active region which is only 85% of the total area.

Figure 3.8 - Comparison between no active edge and active edge detectors


47

3.3.2 - 3D detector concepts

The first 3D sensor concept has been the Full-3D detector with active edges fabricated at the Stanford Nano

Fabrication Facility, California, U.S.A [3-12]. It is referred to as the standard 3D detector and is considered

as the state-of-the-art in this field. Detectors with this sensor concept have been fully tested in the past

years, confirming their radiation tolerance [3-13] and hit efficiency, measured in a 100 GeV pion beam at

CERN SPS [3-14]. The concept of Stanford 3D active-edge silicon sensors is shown in Figure 3.9; they are

built with different electrode configurations (the smallest inter-electrode spacing is 56 µm) and substrate

thickness of about 200 µm. Figure 3.9 presents a 3E detector, characterized by three junction electrodes

per pixel, with an inter-electrode distance of 71 µm and active edges.

Signal development in these sensors can be calculated by Ramo’s theorem, that includes the effect of

charge trapping caused by irradiation damages in the sensor [3-10]. Because of the radiation hardness, full-

3D sensors are within the promising candidates for applications at the LHC, such as the very forward

detectors at ATLAS and CMS, the ATLAS IBL10 and the general pixel upgrade. Moreover they could play a

role in applications where high speed and high resolution detectors are required, such as the vertex

locators at the proposed Compact Linear Collider (CLIC) at CERN, responding to the requirements of

present and future trackers at colliding beam experiments. Full-3D sensors are being now produced also by

SINTEF, Oslo [3-16], and development of passing-through column detectors is ongoing at FBK-irst.

Besides standard 3D detectors, other modified 3D detectors have so far been proposed by other research

groups in the world. The proposed 3D architectures are shown in Fig. 3.10 [3-17].

10 Insertable B-Layer, 4th low-mass pixel layer, planned to be inserted in the present ATLAS Inner Tracker

Figure 3.9 – (a) Full 3D silicon detectors layout, (b) 3E electrodes configuration [3-15]


48

Besides the already mentioned Stanford Full-3D sensors (a) and the FBK-3D DDTC sensors (b), that will be

described in the next section, the other main types are:

• Semi-3D detector approach (c), featuring columns of only one doping type, penetrating not all the

way through the wafer with a blank implantation on the back for the ohmic contact. These

detectors have been proposed by FBK-Trento [3-18], and VTT-Finland [3-19], in 2004 and

independently developed. The sensors fabricated at VTT have been electrically tested, before and

after 6×1015 cm−2 proton irradiation [3-20]. Semi-3D pixel detectors were also characterized with

the MEDIPIX2 readout chip, showing a higher energy resolution with respect to planar sensors [3-

21]. The development of semi-3D sensors ended in 2005. At the moment VTT has kept on

developing 3D technologies with the aim of fabricating and testing edgeless microstrip detectors on

six inch silicon wafers [3-22]. More results about the same approach can be found in [3-23],

concerning the developments at FBK-Trento

• Semi-3D detectors with columnar electrodes of only one type, etched from the top, with the other

electrode type also implanted from the top (f) have been proposed by BrookHaven National

Laboratory BNL at the end of 2005 [3-24]. 3D detectors with both p+ and n+ columnar electrodes,

etched on the same side and not penetrating all the way through the substrate (d) have also been

proposed by BNL. 3D-TCAD simulations have been performed to simulate the full depletion voltage

and the charge collection after irradiation.

• Double-sided 3D detectors have been proposed by CNM (e) [3-25] and FBK [3-23] (b)

independently, with few differences in the fabrication process. The columns are etched from

opposite sides of the wafer for each electrode type and do not pass through the entire thickness so

that no support wafer is needed. CNM has initially fabricated detectors on four inch in n-type

wafers (with p+ readout). The columns are 250 μm deep on a 300 μm thick substrate. The first

layout included MEDIPIX2 pixel detectors and microstrip sensors suitable to be read out with the

LHCb chip; capacitance measurements have shown a lateral depletion on only 2 V and a total

depletion of 9 V [3-26]. Functional characterization with the MEDIPIX2 chip has shown a reduced

charge sharing with respect to planar sensors, thanks to the 3D electrode configuration [3-27]. A

microstrip detector has been irradiated up to 5×1015cm−2 neutron equivalent and at a bias of 200

V the chip have recorded a most probable charge of 12800 electrons from a MIP particle,

comparable with the results obtained by the Stanford group [3-28]. CNM have also finished the

Figure 3.10 - 3D detector proposed until nowadays


49

fabrication of new 3D double side sensors, including ATLAS pixel and long strips, on p-type

substrate with n+ readout.

3.4 – Devices under test

Here follows a description of the sensors tested for this thesis.

3.4.1 –FBK-3D sensors

A particular 3D detector concept is the so-called 3D-DDTC (Double-Side Double-Type Column), where the

electrodes are etched perpendicularly to the surface but without penetrating for the entire substrate

thickness, stopping at a few tens of micrometers from the opposite surface, that makes the support wafer

(wafer bonging) not necessary. The etching is made in sequence on both surfaces and the number of

process steps is highly reduced if compared to a standard 3D process. Columns are not filled with poly-

silicon, so that the related deposition and final chemical mechanical polishing steps are not required.

Sensors using this technology [3-29] have been fabricated at FBK-irst11 MT-Lab, in Trento (Italy), in

collaboration with INFN12. They are built on Float Zone, p-type substrate, high resistivity silicon wafers.

Columnar electrodes of different doping types are etched from opposite wafer sides, using the non-

passing-through columns technique with junction columns from the front side and ohmic columns from the

back side, stopping at a short distance13 from the opposite surface. The key process for the realization of a

3D detector is the Deep Reaction Ion Etching (DRIE), a strong anisotropic process that allows holes to be

made with a width/depth ratio of 20-25. The process is an iteration of a two step sequence: a plasma

etching based on SF6 (fluorine) is used to etch in a vertical direction rather than laterally; then fluorine is

pumped out and a chemical inert passivation C4F8 covers the corners. The sequence starts again, with the

plasma etching digging the bottom of the hole, and so on.

The read-out columns are the junction columns, n+ doped, and they are connected by a surface n+ diffusion

and a metal strip that arranges them in the pixel configuration, while ohmic columns, p+ doped, are all

connected together by a uniform surface p+ diffusion and metallization on the back side of the sensor (see

Figure 3.11). All columns have a nominal diameter of 10 μm and are not filled with poly-silicon [3-30].

11 Fondazione Bruno Kessler (FBK-irst), Via Sommarive 18, 38100 Povo di Trento, Italy 12 Istituto Nazionale di Fisica Nucleare 13 ideally not exceeding a few tens of micrometers

Figure 3.11 – (a) layout of two adjacent pixels , (b) schematic cross-section of the sensor [3-30]


50

Surface insulation in-between n+ electrodes is achieved by combined p-spray/p-stop implants [3-31]. The

fabrication technology is similar to that described in [3-29] for 3D-DDTC detectors made on n-type

substrates, except for: (i) the substrate type, (ii) the inverted doping of the columns and related surfaces,

and (iii) the additional steps for p-spray/p-stop implantation on the front side. In the high-field region of the

sensor where the columns overlap, the charge collection is fast, while only in regions with low electric field,

like at the bottom of the wafer close to the ohmic columns where full depletion is not easy to achieve,

there is a slower tail due to diffusion. This explains the fast charge collection (just a few ns), in spite of the

non-optimized junction column depth, so that good charge collection efficiency is expected using fast read-

out electronics (like that used for ATLAS pixels). The peculiar shape of the present ATLAS pixels (50 μm ×

400 μm) can lead to different choices in terms of number of columns per pixel, and consequently of pitch

between the columns (schematically represented in Figure 3.12). Three different inter-electrode distances

have been implemented, with 2, 3 or 4 electrodes per pixel. The high number of columns per pixel shortens

the collection distance, making the detector fast and more robust to radiation; on the other hand, this is

obtained at the expense of an increased capacitance, and thus an increased noise. The inter-electrode

distances for the three configurations are summarized in Table 3.1:

Two batches have been fabricated by FBK-irst using the non-passing-through column technique. Table 3.2

summarizes the main parameters of detectors from the two batches (the first one called DTC2 and the

second one DTC2b). The wafer thickness values are the nominal ones. The column thickness values have

been extracted from the C-V curves of test structures.

Parameter Value

3D-DTC2 3D-DTC2b

Substrate (p-type) thickness 200 µm 200 µm

Junction column (n+) thickness 100 - 110 µm 140 - 170 µm

Ohmic column (p+) thickness 180 – 190 µm 180 - 190 µm

Column overlap 90 - 100 µm 110 - 150 µm

Dopant concentration in the substrate 1 X 1012 cm-3 7 X 1011 cm-3

Table 3.2 - Main parameters of FBK-3D DDTC detectors tested in this thesis [3-30]

Sensor type Distance (µm)

2E 103.0

3E 71.2

4E 56.0

Table 3.1 – Inter-electrode distances

Figure 3.12 - Inter-electrode distances for 2E, 3E, 4E configuration


51

3.4.2 – Hybrid Pixel Detectors

The two-dimensional high-density connectivity is the key characteristic of a hybrid pixel detector (see

Figure 3.13), and it determines the need of a vertical connection between sensor and electronics, with

matching between the size of the pixel and the size of the front-end electronics channel. Moreover, the

readout chip must be very close (10-20 µm) to the sensor. To deplete the sensor a sufficiently high bias

voltage must be applied on the backside plane while all the pixels are grounded. A pixel sensor can hardly

be tested before being connected to the electronics with the bump bonding technique [3-32]. The readout

chip has the logic functions needed to extract, organize and transmit the signal out. Each pixel covers a very

small area (≈10-4 cm2) over a thin layer (≈300 µm) of silicon, so another aspect to be considered is the very

low capacitance (≈0.2-0.4 pF), dominated by the coupling to the neighboring pixels rather than to the

backside plane which has to be kept to a minimum with a proper sensor design to avoid cross talk between

pixels. This low capacitance allows to obtain fast signals with low noise. It is common to have noise figures

of ≈200 e− for electronics operating at 40MHz and therefore a S/N ratio exceeding 100 for fully depleted

300-μm-thick sensors. This is a very comfortable situation as it allows operation in absence of spurious

noise hits [2-1]. A detection threshold set at, e.g., 10ςnoise gives, in fact, full efficiency and very low

probability that a noise fluctuation exceeds the threshold. Another way of taking advantage of the excellent

S/N ratio is to consider that the detector is robust enough to tolerate even a considerable signal loss. So

also sensors that have poor charge collection or limited active thickness can be used, such as diamonds and

GaAs, or sensors damaged by high radiation flux. In summary, a hybrid pixel detector is the ideal detector

to work close to the interaction region of a particle accelerator because:

• It provides non-ambiguous three-dimensional measurements with good time resolution (i.e. it can

operate in high instantaneous particle flux).

• It provides the space resolution which is needed to measure short-lived particles.

Figure 3.13 - Hybrid pixel detector schematic [3-3]


52

3.4.3 – Single Chip Assembly (SCA)

Pixel sensors studied in this thesis are bump-bonded on the current ATLAS Pixel read-out chip, called FE-I3

[3-33]. The bump-bonding process is based on Indium and it has been carried out at SELEX SI [3-34]. Figure

3.14 shows a snapshot of a single detector board, that is called Single-Chip Assembly (SCA).

The FE-I3 chip consists of 2880 cells of 50 × 400 μm2 size, arranged in a matrix of 160 × 18, matching the

geometrical characteristics of the sensor pixels. In each cell, the corresponding pixel charge signal is

amplified and compared to a programmable threshold by a discriminator. The digital readout provides

information on the hit pixel address, the hit time stamp and the digitized amplitude, expressed in terms of

Time over Threshold (ToT), which is the time measurement of the signal length above the discriminator

threshold. The ToT of a hit is determined by the width of the injected pulse and depends on the deposited

charge, on the discriminator threshold and on the feedback current. To measure the charge of a hit, the

discriminator output pulse is recorded in units of the LHC 40 MHz crossing clock [3-33]. FBK-irst has been

developing 3D detector technologies mainly oriented to the upgrade of the ATLAS Pixel Detector, and the

3D-DDTC approach is currently considered a possible alternative to standard 3D design for ATLAS-3D

Collaboration [3-15]. SCA characterized in this thesis are the ones produced at FBK-irst, with the 3D-DDTC

architecture which has been presented in the previous section. For this thesis extensive functional

characterization has been made on 3D FBK detectors compatible with the ATLAS readout chip, featuring a

pixel size of 50 μm x 400 μm with three types of columnar electrodes per pixel (2E, 3E, 4E configuration).

The detector characterizations and the results of β and γ source tests are the subject of the next chapter.

3.4.4 - Current ATLAS Silicon Pixel detectors

ATLAS pixel sensors were developed to meet geometrical constraints concerning thickness and granularity

and to have a high charge collection efficiency, while sustaining a massive amount of ionizing and non-

ionizing particle radiation damage [3-35]. This is reflected in the selection of a high resistivity n-type bulk

material and on pixel structure design. The sensor is made by implanting high positive (p+) and negative (n+)

doped regions on each side of a wafer. An asymmetric depletion region at the p+/n junction operates in

reverse bias and extends over the whole sensor bulk volume (see Figure 3.15). The sensor design

guarantees single pixel isolation, minimizes leakage current and makes the sensor tolerant to a radiation

damage up to ≤ 1015 neq/cm2.

Figure 3.14 - (a) Schematic of a SCA, (b) front view of a 3D FBK SCA, (c) back view of a 3D FBK SCA


53

The substrate has n+ implants on the read-out side and the p+-n junction on the back side. The ATLAS-like

planar sensors tested for this thesis have the same pitch (corresponding to 50 × 400 µm2) of 3D detectors,

but the bulk is thicker, (256 ± 3) µm. The main problem of this kind of sensor is that, aside from increased

leakage current, radiation damage will invert the sensor bulk and then gradually increase the depletion

voltage after some year of irradiation. For unirradiated sensors, the depletion starts at the back p-side,

where the pixels are not isolated from each other until full depletion of the bulk. Irradiation of the bulk

leads to a change in the effective doping concentration Neff (see Chapter 5). At type inversion, the junction

moves to the front n-side, isolating the pixels and enabling operation even if the bulk cannot be fully

depleted. Maximum achievable depletion is desirable to maximize the signal. Oxygen impurities have been

introduced in the bulk to increase tolerance of the silicon against bulk damage caused by charged hadrons

[3-40, 3-41]. In addition to the continuous irradiation of the sensors affecting the induced doping

concentration, Neff also evolves due to thermal effects. By choosing an appropriate temperature profile (i.e.

operation at 0 °C, short periods of +20 °C during ATLAS detector access, and cooling down to −20 °C during

longer operational breaks in the experiment), one tries to keep sensors near the lowest possible Neff and

avoid reverse annealing, so as to derive benefit from the lowest possible depletion voltage. The building

processes for this kind of sensor allow for a segmented n+ implantation used for the definition of pixel cells

and a guard ring structure on the p+ implanted wafer side, locating the main voltage drop on the sensor

surface opposite to the bump connections [3-38, 3-39]. The sensors can be fully depleted before type

inversion with bias voltages below 100 V. After type inversion the depletion zone grows primarily from the

segmented n+ implant when the region of highest electric field in the bulk now converts to p-type. On the

sensor front side, pixel structures are arranged and isolated by moderated p-spray [3-39, 3-40] implants,

which have proven to be radiation tolerant with respect to surface damages induced by ionizing charged

particles for doses up to 500 kGy in silicon. The sensor allows for a connection to each channel using a

bump-bond technique to front-end electronics FE-I3. In this thesis, current ATLAS planar detectors are used

as comparison for the characterization of new 3D detectors.

Figure 3.15 - Layout and depletion zone in n+-in-n pixel sensor [3-35]


54

3.4.5 – Front-End Electronics Description

After the discussion of the various kind of sensors, it is useful to describe the front-end electronics used for

ATLAS oriented pixel detectors, in order to have a complete portrait of the 3D devices under test. The

present front-end chip is the FE-I3 chip, and a new version of it, the FE-I4 chip, is currently being developed

and tested. Front-end chips have a few million transistors per square centimeter and a typical chip size

cannot, today, sensibly exceed 1 cm2 if a high enough yield (>50%) is desired [2-1].

The FE-I3 chip is implemented in a 0.25 µm CMOS technology using radiation tolerant layout rules, in order

to resist up to a total dose of 50 Mrad. The chip has an active dimension of 7.2 x 10.8 mm2, and contains

about 3.5M transistors. The chip has 2880 channels of charge sensitive amplifiers attached to a fast

digital readout, and it is designed for use in a pixilated tracker detector [3-41]. To reduce the multiple

scattering, the chip is thinned to a thickness of 180 µm. It digitalizes and buffers the pixel hit information

responding to the global ATLAS trigger system: the digital part operates synchronously to the 40 MHz beam

clock. The active area of the chip consists of 2880 readout cells of size 50 x 400 µm2 (matching the sensor

pixels), arranged in a matrix of 160 rows x 18 columns. Each cell contains an analogue block, where the

sensor charge signal is amplified and compared to a programmable threshold by a discriminator, and a

digital readout part, which transfers the hit pixel address, a hit time stamp and the digitalized amplitude

information, the Time over Threshold (ToT), to buffers at the chip periphery. Figure 3.16 shows the FE-I3

chip layout.

Figure 3.16 - FE-I3 layout with zoom on a single channel and on a hit buffer cell [3-41]


55

The connection pads are located on the lower edge of the chip. The homogeneously coloured region above

contains the end-of-column logic, which takes care of the hit buffering and read-out driving. The upper

region shows the pixel electronics, organized in 160 rows and 9 double columns. Taking a closer look, the

blue lines can be identified as the individual pixel connection pads. The FE-I3 uses two power supplies: an

analogue supply VDDA, grounded to AGND, with a nominal value of 1.6 V, and a digital supply VDD,

grounded to DGND, with a range from about 1.4 V to 2.5 V and a nominal value of 2.0 V. Moreover, a

VDDREF is used to provide power only to the preamplifiers, and it works as reference for the preamplifier

inputs. It is connected to VDDA outside the FE. Current is roughly 75 mA on VDDA and 35 mA on VDD.

AGND and DGND are connected together outside the module. The logic for the pixel readout, located at the

bottom of the chip, consists of two stages. The first stage continuously scans the pixel cells for hits, and the

identified hits are copied to the end of column (EOC) buffers. Two columns (320 pixels) share a common

buffer with a depth of 64 hits. While a pixel is waiting for the transfer of its hit information it is insensitive.

If no buffer space is left, a hit is lost. Consequently the number of hits detectable in parallel, but also in

sequence, is limited. The second stage consists in empting the EOC buffers. In ATLAS the trigger to readout

a specific event arrives with a fixed delay (latency). At the arrival of the trigger the current bunch crossing

ID is taken, the latency is subtracted and the hits corresponding to the resulting bunch crossing ID are

marked for readout. The marked hits are serialized and clocked out in turn at the 40MHz speed of the

system clock. If the latency time has passed, hits for which no trigger has arrived are discarded. One

consequence of this two staged readout is that a hit is only visible if its ToT is smaller than the trigger

latency, as otherwise the hit has not yet been transferred to the buffers by the first stage [3-42].

While the trigger is usually supplied from outside, the chip is also equipped with a self trigger for testing

purposes. The self trigger uses the signal of all discriminator outputs linked by an OR and additional logic.

The functionality of the FE-chip can further be checked at several stages of the readout chain. First of all the

basic communication with the FE-chip can be verified by reading back the values written to the different

chip and pixel registers. The digital part of the hit detection and the readout stage can be tested with the

help of an externally applied strobe signal. The strobe signal can be used to overwrite the discriminator

output of selected pixel cells and thus for simulating hit detections. To check the pixel amplifier and

discriminator, each pixel cell contains a charge injection circuit. If enabled, the strobe signal is used to vary

the voltage applied to a capacity connected to the amplifier input. The voltage is switched between the

analog supply voltage (VDDA) and a calibration voltage VCAL. The resulting voltage step injects a charge

pulse into the amplifier input. Each chopper has two selectable capacitors with nominal values of C low = 7.5

fF and Chigh = 43 fF. The amount of injected charge is equal to:

𝑄𝑖𝑛𝑗 = 𝐶𝑙𝑜𝑤 /𝑕𝑖𝑔𝑕 ∙ ∆𝑉

The charge is usually measured in units of the elementary charge e. The voltage VCAL can be generated

inside the chip with the help of a 10-bit digital-to-analogue converter (VCAL-DAC). Typically, the resulting

slope for ΔV is 0.9 mV/DAC. This corresponds to an injected charge of about 42 e- per VCAL-DAC step in the

case of Clow and of 240 e- for Chigh. The exact capacitor values of the individual FE-chips are measured during

the tests following the wafer production. The dispersion of the capacitor values between the different pixel

cells of a chip has been found to be in the order of 1.5% for C low and 2.3% for Chigh [3-43]. In addition, the

characteristics of the VCAL-DAC are measured during the test. The linearity of the DAC is measured to be

within one DAC value. The injection of a known amount of charge is used for the adjustment of the

threshold settings, the feedback currents and for the calibration of the ToT values . More details on the chip

electronics and further test possibilities are given in [3-33], [3-41], and more detailed figures and

schematics can be found in Appendix 1 of this thesis.


56

3.4.6 – Single channel

Single cells are also called channels, or simply pixels, and they fit the size of a single sensor pixel (50 x 400

µm2) of the SCA. A schematic view of a single channel is shown in Figure 3.17:

The analogue part copes with signal amplification and discrimination, with its behaviour controlled with

DACs, while the digital part collects the time stamps, measures consequently the ToT and transports the

measurements to the EOC logic.

As it is shown in Figure 3.17, the analogue part is mainly composed by:

an injector circuit, which injects charge from the outside using a Vcal and two capacitors, Clow (8 fF) and Chigh (32 fF), usable for testing or calibration purposes;

the bump pad to sensor, which connects the sensor to the read out circuit;

a preamplifier, with a feedback capacitor of 5 fF, which incorporates a DC feedback scheme able to compensate DC leakage currents at the amplifier input of more than 100 µA;

a Feedback DAC (FDAC), a Trim IF and an IF DAC, which set the feedback current value;

a second stage amplifier followed by a discriminator, which set the threshold of a detectable signal over the electronics noise;

a Global DAC (GDAC), which set the threshold level of the preamplifier globally over the whole chip;

a Trim DAC (TDAC), which set the threshold level of the preamplifier channel per channel. The charge signal enters the FE from the sensor (or the injector circuit) and encounters the preamplifier,

which collects the charge in the 5 fF capacitor, which in turn is discharged by an adjustable constant current

source [3-42]. The preamplifier is designed for a silicon sensor of 250 µm thickness. A typical input signal of

about 20 ke-, equal to 3.5 fC, returns to baseline within about a micro second. Each amplifier can be

disabled to prevent noisy sensor pixels from continuously generating hit detections in the subsequent

stages, otherwise buffer overflows would result in losses of real hits. Then the signal passes through a DC-

paird second amplifier and a differential discriminator. The threshold of the discriminator can be adjusted

in the range from 2000 e- to 5000 e- and even wider, if higher noise levels and/or higher pixel to pixel

Figure 3.17 - Single channel schematic [3-33]


57

deviations of the thresholds are acceptable. By design, the output signal of the amplifier peaks always after

the same time, independently of the amount of injected charge. The time constant of the exponential rise

function depends on the sensor capacitance and the transconductance of the preamplifier. The limit is thus

set by the tolerated chip power consumption. The finite rise time implies that a hit with a small charge

deposition crosses the threshold later than one with a larger charge deposition. Hits with small charge

deposition thus might show up in the next event as the discriminator output is sampled every 25 ns,

corresponding to the 40 MHz bunch crossing frequency of the LHC. This effect is usually referred to as time

walk. Due to the constant discharge current, the time between the leading and the trailing edge of the

discriminator signal, the Time over Threshold (ToT), is a direct measure of the deposited charge in a sensor

pixel.

3.4.7 – FE-I3 calibration

The FE-I3 chip has to be calibrated be correctly match the behaviour of the bump bonded sensor and the

tracking requirements: a wanted discriminator threshold can be obtained varying the GDAC and the TDAC,

a correct ToT can be tuned varying the IF, TRIMIF and the FDAC values. In this way every single channel of

the chip will have a similar response to detection of signals. In Figure 3.18 the relation between the

threshold and GDAC is shown.

It is clear that growing the GDAC value increases the discriminator threshold value. By applying a TDAC

calibration to the wanted threshold value, and so choosing the correspondent GDAC values, one can then

decrease the threshold sigma value.

Figure 3.18 - Discriminator threshold vs GDAC


58

In Figure 3.19 the relation between ToT and IF is shown, from which it is also clear that in order to decrease

the ToT value it is necessary to increase the IF value:

Figure 3.19 - ToT vs IF

59

CHAPTER 4 CHARACTERIZATION AND TEST OF FBK-3D

PIXEL SILICON SENSORS

Chapter 4 – Characterization and Test of FBK-3D Pixel Silicon Sensors s

60


61

he purpose of this chapter is to provide a detailed description of the electrical tests performed on

FBK-irst Double side Double Type Column (DDTC) silicon pixel detectors, in the configuration with 2,

3 and 4 electrodes per pixel developed for the ATLAS upgrade, in comparison with an ATLAS planar

n-in-n detector. The modules are usually called Single Chip Assembly (SCA) and consist of the PCB board

with one single sensor mounted onto it, matched to one ATLAS FE-I3 read-out chip and a LVDS chip for

digital communication [4-1]. The fabrication technology for DDTC sensors is simpler than that required for

full 3D detectors with active edge, but the detector efficiency and radiation hardness critically depend on

the columnar electrode overlap and should be carefully evaluated. Selected results from the electrical and

functional characterization with radioactive sources are also discussed.

4.1 - Sensor properties and performance tests

The following tests are aimed at analysing the specific sensor properties:

Leakage current distribution

Noise as a function of the bias voltage

The remaining tests are aimed at analysing the performance of the detectors:

Threshold and noise tuning (at 3200 e- threshold)

Time over Threshold (ToT) tuning (for one MIP at 60 ToT)

Source tests with gamma and beta sources (109Cd, 241Am, 90Sr)

Tests have been performed at room temperature (23-24 ̊C), and also using a climate chamber (Vötsch

Industrietechnik VC 2020) in order to make measurements with temperature and humidity control.

4.2 – TurboDAQ setup

The experimental setup used for the characterization of the detectors is the so-called TurboDAQ setup,

developed at the LBNL14. It has also been used to perform automated electrical test of ATLAS Pixel Detector

Modules during the production phase. It runs under Windows and is based on National Instruments

LabWindows development suite [4-2].

For completeness a layout of the system is given in order to easily refer to specific equipment in the test

description:

Hardware components:

PC equipped with Pentium 4 processor or higher with at least 512 MB RAM

National Instruments GPIB control card [4-3]

National Instrument PCI-MXI2-VME kit [4-4]

VME (Versa Modular Eurocard) crate [4-5]

ATLAS Turbo Pixel Low Level card (TPLL) [4-6]

ATLAS Turbo Pixel Control Card (TPCC) [4-6]

Up to 4 Flex Read Out Card per TPCC for flex module characterization and/or custom made probe

card for bare module testing

14 Lawrence Berkeley National Lab, California, USA

T


62

Two LV power supplies with two channel each for TPCC and flex module front-end bias with at least

±5V and 2A rating (Agilent E3631A GPIB controlled)

Keithley 2410 Source Meter for I-V characterization and sensor bias voltage [4-7]

Software components:

Windows 2000 or Windows XP operating system

Visual Studio 6.0 or above

National Instruments Measurement Studio 6.0 or above

ATLAS Pixel TurboDAQ software [4-8]

Cern Root software vrs. 5.20.00 [4-9] to be used together with the Pixel Module Analysis framework

in order to analyze data from the TurboDAQ more easily [4-10]

The 3D TurboDAQ standard measurement system is built as shown in Figure 4.1, and can be either mobile

or fixed:

The measurements are performed by TurboDAQ software parametric scans. The scans are standardized

and their parameters are stored in configuration files (.cfg). For each kind of measurement a specific scan is

selectable from the software [Appendix 2]. Data for each modules are stored in a directory tree with the

top level identified by the module specific serial number (S.N.) for the specific detector module,

automatically generated the first time a new module is connected to the TurboDAQ by writing the S.N. in

the Configuration Console of the software [Appendix 2]. For data integrity it is essential that entering the

S.N. is the first operation which is done after connecting a module to the system. If a module has already

been tested (even in a different laboratory), a configuration file containing module information should be

available and must be loaded into the software. If not, a new configuration must be created. It should

Figure 4.1 - TurboDAQ setup


63

contain the measured values of the capacitances used for charge injection (Chigh and Clow) and the measured

slope of the VCAL DAC used for internal injection.

Within the above mentioned directory tree all measurement data files will have standard names, with a

test name for each test. The names are set from the TurboDAQ Data Control panel [Appendix 2], and for

our purposes they have been of the kind YEAR_MONTH_DAY_MEASUREMENT, to which the TurboDAQ

adds proper suffixes and extensions according to the measurement chosen (e.g. 2009-03-10-iv.iv for an I-V

scan measurement).

4.2.1 - Hardware description

The hardware setup allows the communication between the board under test and the test system. This is

routed by the VME controller board, while the TPLL board is used for clock generation and synchronization,

data FIFO, trigger FIFO, 16 Mbytes board SRAM support module level histogramming, and FPGA (see Figure

4.2).

A flat cable is used to connect the module board to the TPCC, and also this latter to the TPLL board: this

bridge transfers data coming from the detector under test to the TPLL, which converts them to be

transmitted on the VME bus to the PC. The TPCC card, shown in Figure 4.3, receives from two LV power

supplies four different values of voltage, to respectively supply itself (with +5 V for the analog part and -5 V

for the digital part) and the FE electronics on the module board (with +1.6 V for the analogical part and +2 V

for the digital part).

Figure 4.2 – On the left, hardware mobile setup at CERN Lab161; on the right the TPCC and module board


64

The leds on the left of the board serve as a control of the correct communication start between the TPCC

and the TurboDAQ software: if green, the communication has been set correctly, while if red initialization

problems have occurred. Moreover, an orange led lights in correspondence of the initialized channel, right

to the connector for the module board in use. Figure 4.4 shows in detail a SCA (or Detector Under Test,

DUT): it is, as an example, the module 2EM2, i.e. an FBK-3D pixel silicon sensor with two electrodes per

pixel bump bonded to the FE-I3 read-out electronics (in the centre of the card). The high voltage cable

supplies the bias voltage to deplete the sensor (negative voltage values).

4.2.2 - Software description

TurboDAQ runs under Windows, and is based on National Instruments's LabWindows developement suite.

TurboDAQ communicates to the SCAs via a combination of custom electronics (TPCC, TPLL) and a standard

PC-to-VME interface. This software allows to pilot the data acquisition and to display the data read out

from the pixel detector. It is written in CVI language, which is why the software LabWindows CVI from

National Instrument is needed. An introduction on how it works and on how it performs scans and

measurements is given in the Appendix 2 of this thesis.

Figure 4.4 - A SCA

Figure 4.3 - TPCC board


65

4.2.3 - Fixed setup at CERN Lab 161

Figure 4.5 shows a snapshot of CERN ATLAS Pixel Sensors R&D setup (Bld. 161-1-24) [4-11]. The main

feature with respect to the mobile setup is the climate chamber, operative in a range between -25°C and

100°C.

The experimental setup used for the characterizations and the source tests shown in Figure 4.6 was housed

inside the climate chamber:

Figure 4.5 - Fixed setup at CERN Lab 161

Figure 4.6 - Setup for beta source test


66

The fixed setup is composed of:

The climate chamber, in which a custom made plexiglas base has been mounted to fix the boards

during the measurements and to assure the reproducibility of tests. With this structure it has been

possible to put the sources straight onto the sensor, in correspondence with a scintillator placed

under the base, in order to give trigger signals out when recognizing a particle passing through, and

so passing also through the detector (see Figure 4.6). A brass collimator has been used to create a

straight fluence for the β particles coming out from the 90Sr source;

A three logic unit crate for the β source tests, composed of a discriminator, which receives from the

scintillator the trigger signals (in NIM15 logic) over threshold, a level adapter to convert NIM logic

signals into TTL16 (TTL is the standard used by the VME), and a counter, which shows the rate of

particles hitting the scintillator and so useful to set the discriminator threshold (see Figure 4.7);

The TurboDAQ software installed on a PC;

An oscilloscope used to check the signals coming out from the scintillator;

A voltmeter connected with the amplifier used for the amplification of the signals coming out from

the scintillator (as a check for the amplifier set).

15 Nuclear Instrumentation Module, with true logic signal of -2V 16 Transistor-Transistor Logic, with true logic signal of +5V

Figure 4.7 – On the left a picture of the logic modules for the scintillator; on the right the beta source setup scheme


67

4.3 – The SCAs and their characterization

For each test a detailed description is given in the next sections. Here follows a list of the main

measurements and tests done and a table with reference to the SCA on which they have been done (Table

4.1).

1. Leakage current

2. Threshold and noise

3. Noise vs bias voltage

4. ToT self-calibration

5. 109Cd source test

6. 241Am source test

7. 90Sr source test

Table 4.1 - Names of SCAs and tests performed on them


68

4.4 – I-V measurements

When a reverse bias is applied to a silicon sensor, a leakage (or dark) current of free recombining intrinsic

charges is created by the contribution of:

1. Volume generation current, generated by the charge flow due to the bias (current increases

proportional to the square root of the bias)

2. Surface generation, additional small contribution

3. Avalanche breakdown, at very high voltages

After full depletion the I-V curve displays a plateau region where the current increase is very small, before

the electrical breakdown occurs at very high voltages, as shown in Figure 4.8. The sensor has always to be

operated at voltages well below hard breakdown values, in order not to damage or even break it.

Considered as a very powerful tool for sensor testing, I-V curves are used to check for sensor damages after

dicing and chip flipping, and also give the information about the correct bias voltage to be applied for

working in fully depletion condition. This measurement is somehow uncorrelated to the other scans, and its

only requirement is to undergo thermal stability. Measurements of sensor characteristic I-V curves have

been performed from 0 to -70 V (-80 V being the value where breakdown starts) with 1.5 V steps for the 3D

sensors, and from 0 to -600 V at 10 V steps for the planar sensor. After each voltage step a 10 s settling

time is needed before starting the measurement of the current, and the measurement is repeated until

two consecutive readings differ by less than 1%. The source meter (Keithley 2410) is set with a current

limitation of 100 (200) μA. The measurement can be done over the entire sensor also for the 3D pixel

configuration because all the p+ columns on the back side are connected with a metallization to which the

voltage values are applied. A leakage current in the 0.1-0.2 μA range at -35 V depletion voltage and an

avalanche breakdown over -70 V for FBK-3D sensors are acceptable. For planar sensors, these values are in

the 1 μA range at -150 V depletion voltage with an avalanche breakdown over -400 V. Problems may be

expected if the leakage current is one order of magnitude higher. Earlier breakdown or not monotonic

pattern of the leakage current could determine a rejection of the SCA. Concerning the leakage current of a

single pixel, it has been found to be quite large as compared to predictions based on measurements

performed on test diodes, but it still remains at an acceptable level (~100 pA/pixel) [3-30].

Figure 4.8 - Typical shape of a silicon sensor’s I-V curve with indication of the origin of different current contributions [2-1]


69

4.4.1 - Measurement results on FBK-3D and planar sensors

Figure 4.9 provides an overview of the I-V curves of all FBK-3D DTC2 sensors available in the laboratory.

Leakage currents and breakdown voltages, which are technology-dependent parameters, show very similar

behaviours, evidence of the good reproducibility of the DDTC process. Possible problems in the sensor

production process lead to a deviation of the curve from the expected shape. The breakdown voltage is

normally over -70 V, a value that is determined by the n+/p-spray junction at the top surface. Two samples

show breakdown before than expected, probably due to some damage during the assembly of the sensors

with the readout chips, and they have not been considered for further tests. The plateau zones go from -10

V to -40 ÷ -50 V, and a good compromise for having all the SCAs tested under the same condition is to bias

the sensors at -35 V, with a leakage current in the 0.1-0.4 µA range.

Figure 4.10 focuses on a comparison between FBK-3D DTC2 2E, 3E and 4E sensors. The leakage current is

characteristic of how the sensor has been built, and globally does not “really” depend on the distance

between electrodes. To study temperature and humidity effects during measurements, comparison plots of

I-V measurements with a scan performed inside the climate chamber (21 °C and 20% of humidity) and

outside it (24 °C, no humidity check) are shown. It is important to stress that the changes in the leakage

current are mainly due to humidity, while temperature does not have a noticeable impact given the small

difference between the two values.

Figure 4.9 – I-V measurements of FBK-3D DTC2 detectors


70

Figure 4.11 shows the different behaviour of the I-V curve of a sensor coming from the second batch of

FBK-3D DDTC (DTC2b), where a sharp increase of the current occurs already at low voltage. The four

sensors so far tested that were produced in this batch have all shown the same behaviour (only 3E sensors

have been initially considered in view of their use in a beam test at CERN). Such an early breakdown is

supposed to be related to the presence of local defects and indeed from maps of the pixel leakage current

at different voltages it has been noticed that a few pixels start exhibiting a high leakage current already at

low voltages [3-30]. Nevertheless, this sensor has been tested during the May Test Beam at CERN

(described at the end of this chapter), and shows correct working responses [4-12] when kept at -8 V bias

voltage.

Figure 4.10 – I-V measurements with temperature and humidity check for FBK-3D DTC2 sensors


71

For comparison with the new FBK-3D DDTC sensors, Figure 4.12 shows the I-V curve of an ATLAS n-in-n

planar single-chip module. The major difference is that the same small values of leakage current are

obtained with consistently higher values of bias voltage. Usually a good compromise for a satisfactory low

level of leakage current is to apply a Vbias of -150 V to these sensors.

Figure 4.12 - ATLAS n-in-n planar sensor I-V curve

Figure 4.11 - I-V for a FBK-3D DTC2b sensor (3E7)


72

4.4.2 - Leakage current from Monleak Scan

The TurboDAQ provides a useful extra feature: the Monleak Scan. It is a measurement of the combined

feedback and leakage current from the feedback circuit, as described by the following relation:

𝐼𝑚𝑜𝑛𝑙𝑒𝑎𝑘 = 𝐼𝑙𝑒𝑎𝑘 + 𝐼𝑓𝑒𝑒𝑑𝑏𝑎𝑐𝑘

where Ifeedback is defined by the IF and TDAC parameters (each of them divided by some correction factors

and then summed together) of the feedback current of the front-end preamplifier and Ileak is the sensor

leakage current per pixel [4-10+. This measurement is made possible by a “monleak” ADC: the pixel to be

measured is selected with the hitbus mask bit of the FE-I3 and its Imonleak is digitized to a precision of 0.125

nA in a range up to 128 nA [3-38]. This procedure is designed to read the leakage current pixel by pixel, and

because of the relation between leakage current and radiation damage, it provides a useful monitoring and

diagnostic tool, even if the FE is not able to obtain precise values. With this capability the defective pixels

can be clearly identified as they have a leakage current well outside the dynamic range of the inbuilt

measurement circuit.

Figure 4.13 shows the results of the monleak scan of an FBK-3D sensor (4EM9) taken as example. The sum

of the currents over all pixels is specified in the text above the plots. The plots on the top show the

behaviour over the entire chip, the plots in the middle show the mean value and the sigma of the

measurements over the single pixel, and the plots on the bottom show the values channel by channel, for

Monleak readings on the left and leakage current on the right, respectively. The TurboDAQ log file of the

Monleak scan is used to determine Ifeedback (if no logfile is found, a default of Ifeedback=2 nA is assumed). The

absolute accuracy of the measurement is very limited due to FE-I3 chip capabilities in performing them [3-

37]. Various measurements show a mean leakage current of ~1 nA for a good pixel in an FBK-3D detector.

Figure 4.13 – On the left, the map of the raw Monleak readings; on the right, the map of the leakage current values


73

4.5 - Threshold and noise

The purpose of this test is to measure the threshold and noise of each pixel, where only pixels with a charge

deposit above a set threshold are taken into account for readout by the front-end electronics. Signals are

induced in each pixel by means of on-chip charge injectors (an on-chip chopper generates a VCAL to be

injected into Clow or Chigh capacitors of each pixel, and the input of the preamplifier sees a charge signal

equivalent to VCAL x Clow/high), and the number of collected hits versus the injected charge is recorded. Ideally

a step function with an immediate transition of the detection efficiency from 0 to 100 % at the threshold

could be expected, but in practice, because of the pixel noise, some injected charges below the threshold

are detected while some others are not (as shown in Figure 4.14). The error function, which is a convolution

of the ideal step function with the Gaussian pixel noise distribution, is the best candidate to describe the

discriminator output:

This function, the so-called S-curve, is used to fit the threshold scan results of each pixel.

The exact procedure of the scan is:

1. 100 digital injections per pixel are made

2. A charge between 0 and 9000 e- in 45 e- steps is injected

3. The collected hit number for each pixel and each injected charge is recorded

The probability of detecting a charge is given by the following formula:

𝑃𝑕𝑖𝑡 𝑄 = 1

2 𝐸𝑟𝑓𝑐

𝑄𝑡𝑕𝑟𝑒𝑠𝑕 − 𝑄

2𝜍𝑛𝑜𝑖𝑠𝑒

=1

𝜋 exp

𝑄 − 𝑄𝑡𝑕𝑟𝑒𝑠𝑕

2𝜍𝑛𝑜𝑖𝑠𝑒

𝑑𝑄∞

0

t

x

error dxexf0

2

2

1)(

Figure 4.14 - Threshold curve [3-4]


74

The 50% hit efficiency on the S-curve defines the threshold value of a pixel, as shown in Figure 4.15. The

noise of a pixel is inversely proportional to the steepness of the transition from no detected hits to full

efficiency, and is calculated between the 70% and the 30% points:

𝜍 = 𝑄70% − 𝑄30%

𝑓𝑒𝑟𝑟𝑜𝑟−1 (70%) − 𝑓𝑒𝑟𝑟𝑜𝑟

−1 (30%)

The threshold calibration is obtained by first setting the correct value of GDAC (global setting - see section

3.4.6), then by applying the TDAC tuning (pixel setting) file, obtained from a TDAC tuning scan. Scans are

repeated to reduce the threshold dispersion by adjusting the TDAC parameter individually for each channel

[3-20, 4-1].

For the FE-I3 chip this test can be performed in the so-called “auto-tune” mode, where a fixed charge,

corresponding to the desired threshold, is continuously injected into each pixel and an internal counter

checks for which TDAC value its count rate is 50%. This tuning procedure is extremely fast, even if it may

show some systematic patterns. The threshold dependence of each pixel on the TDAC is fitted to these data

using the parameterization:

𝑇𝑕𝑟𝑒𝑠𝑕𝑜𝑙𝑑 𝑇𝐷𝐴𝐶 = 𝐴 + 𝐵log 𝑇𝐷𝐴𝐶

128 − 𝑇𝐷𝐴𝐶

This relationship is used to determine, for each pixel, the TDAC value closest to the target threshold, which

is set to 3200 e- [4-1,4-13].

4.5.1 – Measurements results on FBK-3D and planar sensors

Setting the correct threshold value is the first step to calibrate the front-end with a suitable configuration

to recognize particles, and it has been performed on all those sensors not affected by early breakdown

problems. The results of the threshold scan and the bias voltage for the sensors tested at CERN Lab 161 are

summarized in Table 4.2:

Table 4.2 - Threshold and noise results


75

As an example, Figure 4.15 shows a threshold measurement and a noise distribution for a FBK-3D DTC2

sensor with 2E configuration (2EM2), with the entire chip map and the mean value with correspondent

sigma over all channels for both measurements, and the threshold values channel per channel.

Concerning the noise values obtained, one can see from Table 4.2 that the noise increases with the number

of electrodes per pixel, as it will be better demonstrated by the next measurement (and that the noise of

the planar sensor is lower than those for 3D sensors) .

Figure 4.15 – On the left, threshold for FBK-3D DTC2 (2EM2); on the right, noise for FBK-3D DTC2 (2EM2)


76

4.5.2 - Noise versus bias voltage of the sensor

To measure how the noise depends on the bias voltage given to the sensor, a threshold scan over various

bias voltages, from 0 V to -80 V with 5 V steps, has been performed and the threshold and noise have been

determined, using the same configuration file for each bias voltage value (same TDAC/FDAC settings).

Figure 4.16 shows the noise vs voltage of FBK-3D DTC2 detectors with 2E, 3E and 4E configuration.

The measurements confirm that having more electrodes per pixel increases the noise (under the same

operating conditions). The reason is that this situation is equivalent to having more capacitors connected in

parallel, which increases the total capacitance and consequently the total noise because there is more

charge involved (C2E < C3E < C4E). The plot also shows that the noise is higher for low voltage values than for

high values. Since the noise is determined from threshold scans with the same TDAC settings, it is useful to

check the dependence of the threshold on the bias voltage. The threshold should be almost independent of

the bias voltage because the threshold scan is fitting an S-curve which is a convolution of a Gaussian and a

step function, as already explained. The value of the step function is the threshold and should thus not be

affected by changing the width of the Gaussian which is overlaid. This is verified with the measurements of

the threshold as a function of the bias voltage, as shown in Figure 4.17.

Figure 4.16 - Noise vs Bias voltage for FBK-DTC2


77

Also the width of the threshold and of the noise are plotted as a function of the bias voltage (Figure 4.18),

showing no evidence of any dependence:

Using the information given by the I-V curves and the noise versus bias voltage plots, and knowing the

theoretical full depletion value for this kind of sensors (-10 V), a depletion voltage of -35 V has been chosen

for these sensors during all the test, in order to have full depletion and to minimize the noise. The same

behaviour of the noise with respect to the bias voltage has been measured for the planar detector, with

one order of magnitude higher bias and lower noise values than FBK-3D SCAs; results of this measurement

are reported in Figure 4.19.

Figure 4.17 - Threshold vs bias voltage

Figure 4.18 - On the left, noise width as a function of the bias voltage; on the right, threshold width as a function of the bias voltage


78

4.6 – Time over Threshold (ToT) measurements and internal calibration of the

detector

In silicon, the mean energy loss of a MIP is 1.66 MeV g-1cm2, while the density is 2.33 g cm-3, so the mean

loss of energy is 390 eV/μm. Since to generate a hole-electron pair an energy of 3.6 eV is needed, this

means that an average MIP creates ~110 pairs per μm in the silicon. With a thickness sensor of 250 μm,

this results in a most probable value of the Landau curve for a MIP of about 20000 hole-electrons pairs [3-

35].

The ToT (Time over Threshold) is used to measure the deposited charge of a hit: it is the length of the

discriminator signal in units of the 40 MHz LHC bunch crossing clock (25 ns), and depends on the deposited

charge itself, on the discriminator threshold and on the preamplifier feedback current.

Figure 4.20 - ToT dependences [3-4]

Figure 4.19 - Noise vs bias voltage for the planar sensor


79

The on-chip injection circuit of the FE-I3 is used to calibrate the ToT response of a signal back into charge

(see Figure 4.20). The standard tuning aims to a ToT of 60 units for a charge of 20000 e-, so given a standard

threshold of 3200 e- this corresponds to a charge of about 250-350 e- per ToT unit. The ToT calibration

consists of injections of various charges above threshold and then subsequent measurement of the average

ToT. The feedback current, and thereby the ToT, is determined by a global DAC current per FE chip (IF) and

a DAC for each pixel (FDAC). The tuning fixes the feedback current to the desired response of 60 ToT for a

MIP of 20000 e-. The purpose of a ToT scan is to tune the ToT response to a MIP for each pixel in order to

have a uniform signal of the collected charge in a time acceptable for the operation of the detectors (such

as ATLAS or CMS), and to calibrate the relationship between the measured ToT and the collected charge.

The pixel detector gives an indirect pulse height information using the Time over Threshold (ToT)

technique: the pulse shape is approximately triangular and the time that the preamplifier output stays over

the threshold is approximately proportional to the pulse height (see section 3.4.6). Then the descending

slope to baseline of the triangular pulse is determined by the feedback current of the preamplifier, which

can be tuned at the chip level by changing the IF DAC register and at the pixel level by using the 3-bit FDAC

pixel register. The ToT tuning consists of two parts. At first, the ToT response of all pixels to the charge

deposited by a MIP is made uniform by proper setting of the IF and FDACs: this is done by injecting a fixed

charge of 20000 e-, corresponding to the most probable energy loss in a 250 μm thick silicon sensor, and

choosing the above mentioned DACs in order to have an average ToT response of 60 clock cycles. The 60

clock cycles allow to keep full efficiency up to deposited charges of 4 MIPs. The subsequent step is to inject

different charges, compute the average ToT observed for each pixel and each charge, and fit a calibration

function to these data:

𝑇𝑜𝑇 = 𝑃1 +𝑃2

𝑃3 + 𝑄𝑖𝑛𝑗

This is performed using both the Clow inject capacitance, which allows a fine granularity measurement of the

ToT-charge relationships in the region of charge up to 1 MIP, and the Chigh inject capacitance to cover the

region of higher charges. These calibrations will be used to translate ToT to charge when collecting data

with real particles. Since changing the feedback current also slightly affects the threshold, the threshold

tuning needs to be re-done after the IF and FDAC tuning.

The procedure of the tuning begins with setting to 20000 e- the ToT reference charge in the TurboDAQ, and

then going through an FDAC scan. Then the average ToT value of each chip can be moved toward the

desired average ToT response of 60 by changing the IF DACs. This scan is repeated until all chips have a

matching average ToT response. After this tuning is finished a full FDAC tuning scan has to be performed

(FDAC Tune Internal-Cal): the results of the FDAC determination are put in files ##_fdacs_#.out, which are

moved from the data folder in the module directory tree to the FDACs. Then these files are loaded in the

module configuration file and saved. Finally the ToT calibration has to be performed, which consists of two

scans (TOT Calibration Internal-Cal. CLow Concurrent, TOT Calibration Internal-Cal. CHigh Concurrent). The Clow

capacitance is best to fit low values of charge, while Chigh capacitance is used for high values, as shown in

Figure 4.21.


80

4.6.1 – Measurements results on FBK-3D and planar sensors

The aim is to obtain calibrated SCAs ready to be used to recognize MIPs passing through the sensor. Figure

4.22 shows the ToT value obtained for a FBK-3D DTC2 (4EM9), while Table 4.3 is a summary of the results

of all the calibrated SCAs. For the complete set of plots, see Appendix 3 of the thesis.

Figure 4.21 - ToT vs charge using the two injection capacitances

Figure 4.22 - ToT value obtained from calibrated FBK-3D DTC2 4EM9

ToT


81

4.7 – Gamma source measurements with 241Am and 109Cd

241Am and 109Cd gamma sources have been chosen to calibrate the detectors. The source tests have also

been used to identify dead or noisy pixels. The main point of this test is to obtain the characteristic

photoelectric peaks of 241Am and 109Cd, thereby having a proof of the correct working condition and

calibration of the detectors. 241Am (109Cd) gamma source emits 60 keV (22 keV) photons, which can

convert anywhere in the bulk to a 60 keV (22 keV) primary electron. If ionization takes place in the

substrate region where columns overlap, a signal of 16.5 ke- (6.1 ke-) is expected. On the other hand, if a

photon converts in a high doping region or close to the surfaces, a fraction of the charge could be lost.

Thus, in the charge distribution, a high end peak at 16.5 ke- (6.1 ke-) and a tail towards smaller values are

expected.

4.7.1 –Measurements results on FBK-3D and planar sensors

Figure 4.23 shows the spectra for 241Am and 109Cd, as reconstructed from the ToT values with the 60 ToT

calibration discussed in the previous section, and with a sensor bias voltage of -35 V. In both cases, the

position of the main peak agrees with expectation within the uncertainty due to the calibration process,

which has been estimated to be of the order of 10-15% [4-15]. To perform the measurement, the standard

TurboDAQ Source Test Self Trigger has been used, which collects data with the self capability of the FE-I3 to

send out signal only when a gamma particle has hit a pixel (one hit-one trigger mode) and with the

possibility to create mask files to cover noisy pixels. Figure 4.23 refers to a 2E detector; on the left the 241Am spectrum obtained is shown, while on the right the 109Cd spectrum is shown.

Table 4.3 - ToT values obtained after SCAs calibration


82

Similar plots have been obtained for SCAs with 4E configuration (all plots in Appendix 3). This is not

surprising, since no appreciable difference in the charge collection process is expected between the

different layouts. A more interesting point is to see that the measurement remains almost the same when

varying the bias voltage of the sensor: Figure 4.24 shows this result for the same 2E detector biased at -15 V

(on the left) and at -55 V (on the right).

At -15 V a peak around 3200 e- appears: it is the noise effect over the threshold, that causes an higher peak

because the sensor is biased at a voltage near the nominal depletion voltage value (-10 V). Table 4.4 is a

summary of the values obtained from the gamma photoelectric peak of 241Am with different set of bias

voltages (-15 V, -35 V, -55 V) for the FBK-3D DTC2 2EM2 module.

Figure 4.23 - On the left the 241

Am spectrum obtained with FBK-3D DTC2 2EM2; on the right the 109

Cd spectrum obtained with the same detector

Figure 4.24 - On the left the 241

Am spectrum obtained with FBK-3D DTC2 2EM2 biased at -15 V; on the right the 241

Am spectrum obtained with FBK-3D DTC2 2EM2 biased at -55 V


83

Vbias (V) Charge (e-)

-15 14440.0 ± 822.7

-35 14490.0 ± 784.3

-55 14590.0 ± 707.2

Table 4.4 - 241

Am photoelectric peak values in charge obtained at three different bias voltage values with FBK-3D DTC2 2EM2

Results obtained with 3D sensors agree with those from measurements on the planar reference detector

[see also 4-14,4-16] using the same setup and biasing it at -150 V, as shown in Figure 4.25 for 241Am and in

Figure 4.26 for 109Cd, for which also the behaviour of a single pixel is shown. It is important to notice that

not only the mean values of the peak but also the shapes of the spectra are very similar between the two

sensors, so plots are shown without the fit line. Table 4.5 summarizes the peak charge values obtained

from this comparison.

FBK-3D DTC2 2EM2

Planar n-in-n

FBK-3D DTC2 2EM2

FBK-3D DTC2 2EM2

Planar n-in-n

Planar n-in-n

Figure 4.25 – 241

Am spectrum obtained with an FBK-3D DTC2 2E (top) compared with the same spectrum from the reference planar detector (bottom)

Figure 4.26 – 109

Cd spectrum obtained with an FBK-3D DTC2 2E (top) compared with the same spectrum from the reference planar detector (bottom), over the entire sensor (left) and on a single pixel (right)


84

Table 4.5 - 241

Am and 109

Cd photoelectric peak values in charge obtained with the reference planar sensor

This is the first demonstration of the correct 3D detector calibration when used for the measurement of

real particles.

4.8 – Beta source measurements with 90Sr

A β source test consists of MIPs passing through the sensor and creating free charges by ionization.

Ionization is subject to statistical fluctuations and the value of energy loss returned by the Bethe-Bloch

formula (see Chapter 2) is only the average value of a Landau distribution. If a particle is not stopped in the

sensor, its response varies around the peak of the distribution with a significant probability of high signals,

and due to this tail of high signals the average value is higher than the most probable value (MPV) of the

distribution. The fluctuation around the maximum of this distribution becomes higher for thin sensors. The

main reason for the Landau fluctuation is the rare but measurable occurrence of the so-called δ-electrons

(or knock-on electrons), which obtain enough energy in the interaction to become ionizing particles

themselves, as explained in Chapter 2. They have typically a direction perpendicular to the direction of the

incoming particle which leads to irregular charge clouds and degrades the spatial resolution.

4.8.1 - Measurements results on FBK-3D and planar sensors

The single chip module on the PCB frame is mounted with a hole under the sensor, especially designed for

this kind of tests, which allows the β particles to pass through. The TurboDAQ, with the scintillator set up

described in section 4.2.3, uses the Source Test External Trigger capability of the FE-I3 to collect data from

the detector only when the incoming particle is also seen by the scintillator, giving the acquisition trigger.

Results have been found using a brass collimator which kept the distance between source and detector to

20 mm (the shape of the hole of the collimator can be seen in Figure 4.27). Before going through the

description of the β source test, the trigger delay of the setup has to be considered, which is given by the

latency of the FE to read out the event (stored locally and discarded after this time) and the external delay,

which is set to catch 16 consecutive “bunch crossings” around the one that contains the actual trigger

(since particles hit the scintillator and the sensor almost at the same time and we are only interested in the

"bunch crossings" associates with the trigger).

Source 3D-DTC2 2EM2 (e-) Planar (e-) 241Am 14490.0 ± 784.3 14400.0 ± 664.9 109Cd 5858.0 ± 484.7 5753.0 ± 551.8


85

Figure 4.28 shows the pulse height spectrum in response to a 90Sr β-source in a FBK-3D DTC2 3EM5 biased

at - 35 V. The distributions have been fitted with the expected Landau curve. The plots have been obtained

by applying a clusterization to the data: it contains an algorithm which recognizes and collects the charge

due to a single events hitting more than one pixel, making a better interpretation of the source test and so

producing Landau curves representing also the high energetic δ rays. This kind of clusterization is called

“Digital Clusterization”: it recognizes ToTs belonging to the same events with a specific algorithm, and

attributes the correct ToT to the event either by taking the highest ToT value between near hit pixels

(cluster size1), or the highest plus the second (cluster size2). For the FBK-3D DTC2 3EM5 the most probable

charge value is 13.580 ke- with a sigma of 1.150 ke- (cluster size1) and 14.880 ke- with a sigma of 1.345 ke-

(cluster size2), where the charge is obtained from the ToT using the calibration curve described in section

4.6. The front-end electronics have been tuned to 60 ToT at 20.000 ke-, suitable for ATLAS sensors of 250

µm, but in this case the sensor thickness is 200 µm, as measured at FBK with C-V measurements on planar

diodes coming from the same wafer of DTC2 sensors [4-12]. To evaluate the expected MPV one should then

consider the measured values for the planar sensor; the two curves corresponding to cluster size1 and 2

are shown in Figure 4.30. Rescaling the measured MPV for the 250 µm planar to 200 µm, the expected MPV

is 14.128 ke-, with the observed difference between expected and measured value attributed to the

uncertainty due to the calibration process (about 10-15%, propagated from the known value of the FE

capacitor Clow and Chigh, as already mentioned for γ source tests). For all sensors available the pulse height

spectrum has been measured in response to a 90Sr source. All the plots are shown in Appendix 3. The

various behaviours as function of the electrode configuration and the bias voltages are under investigation.

Preliminary results are summarized in Table 4.6.

Figure 4.27 - Map of hits from ToT measurement without (left) and with (right) collimation


86

2EM2

Vbias (V) MPV with Cluster Size1 (ke-) MPV with Cluster Size2 (ke-)

-15 12.94 ± 1.28 14.93 ± 1.57

-35 13.59 ± 1.35 15.02 ± 1.52

-55 13.52 ± 1.31 14.90 ± 1.53

3EM7


-15 13.12 ± 1.28 14.93 ± 1.50

-35 13.35 ± 1.28 14.89 ± 1.47

-55 13.40 ± 1.28 14.95 ± 1.46

4EM9


-15 12.73 ± 1.26 14.52 ± 1.55

-35 12.92 ± 1.33 14.49 ± 1.53

-55 12.97 ± 1.30 14.47 ± 1.52

Table 4.6 - 90

Sr MPV preliminary results for FBK-3D DTC2 2EM2, 3EM7, 4EM9 at -15, -35, -55 V of bias voltage and with cluster size1 and 2

The reference planar detector has been built with a golden layer on the bottom of its board, from which

beta particles can pass through re-creating the layer shape in the measurement results, as shown in Figure

4.29:

Figure 4.28 –On the left, measurement results for a FBK-3D DTC2 3E with cluster size1 (charge values in excess of 12 ke- have

been fitted with a Landau function); on the right, measurement results for the same FBK-3D DTC2 3E with cluster size2 and same fit


87

4.9 - Test Beam

3D detectors are still under investigation. They are usually tested in test beams together with some well

known planar devices, before and after irradiation. The first test beam analysis on full-3D detectors with

active edges fabricated at Stanford has been published in 2008 [3-17]: 3 different pixel configuration,

connected to the ATLAS readout FE-I3 chip, have been investigated in a 100 GeV pion beam at the CERN

SPS17. A similar test has been done at the CERN SPS on a FBK-3D DTC2 (3EM5) and a FBK-3D DTC2b (3E7),

together with a Full-3D Stanford sensor and a planar sensor, during the May 2009 Test Beam, to which I

contributed for the data taking. Its main goal has been to test the 3D sensors within a large magnetic field

17 Super Proton Synchrotron

Figure 4.29 – On the left, map of hits from ToT measurement with collimation; on the right, shape of the golden layer behind the planar detector

Figure 4.30 - On the left, measurement results for a planar sensor with cluster size 1 (charge values in excess of 15 ke- have been

fitted with a Landau function); on the right, measurement results for a planar sensor with cluster size 2 (charge values in excess of 15 ke

- have been fitted with a Landau function)


88

at different angles (0° and 15°), analyzing the signal response, hit efficiency, charge sharing and the in-time

efficiency of the detectors.

4.9.1 - The experimental setup

The test beam has been carried out at the CERN site of Prevessin (North Area), in H8 beam line, using the

180 GeV secondary π+ coming from CERN SPS. The experimental setup was mounted inside the bore (1.6 m

diameter) of the “Morpurgo”-magnet, a superconducting dipole magnet that was recommissioned for the

purpose of these measurements. The dipole provided a vertical magnetic field of about 1.6 T at the nominal

current of 5 kA. Two overlapping scintillators in front of the tracking system were used to provide a

coincidence trigger; in the rear a large 150 x 150 mm2 paddle scintillator with a 15 mm hole was used in

anti-coincidence mode, allowing efficient suppression of showers and multiple-scatter events. The veto was

implemented purely for data-taking efficiency reasons, and only successfully reconstructed tracks from

clean events have been used for the final analysis [4-16]. Figure 4.31 shows the experimental setup in the

beamline, while Figure 4.32 and 4.33 show the position of the SCAs in the cooling box (previewed but not

used) with a respective schematic.

Figure 4.31 - Experimental setup for the test beam


89

I have calibrated all the SCAs used in the test beam in Lab 161 before sending them to the test beam area.

In the test beam setup, each SCA was connected to its own read-out chain (Sensor-TPCC-TPLL-TurboDAQ).

Starting from the last one with respect to the direction of the incoming beam (see Figure 4.33), they were

four:

1. an FBK-3D DTC2 (3EM5), with bias voltage of -35 V

2. an FBK-3D DTC2b (3E7), with bias voltage of -8 V

3. a Full-3D Stanford (3E), with bias voltage of -35 V

4. an ATLAS planar n-in-n used as reference, ), with bias voltage of -150 V.

Figure 4.33 - Position of the SCAs inside the cooling box

Figure 4.32 - Cooling box for the SCAs


90

Track reconstruction was provided by three planes (BATs in Figure 4.33), the Bonn ATLAS Telescope [4-17].

The telescope consists of double-sided silicon micro-strip detectors with 50 μm pitch on both sides rotated

by 90° with respect to each other, each plane therefore providing X and Y measurements. The telescope

planes were mounted on a precision table together with the SCAs as illustrated in Figure 4.33, with a single

plane in front separated by about 900 mm from a pair of planes in the back, with BAT 2 and 3 mounted 60

mm apart. A Hall probe was positioned on the table in order to measure the intensity of the magnetic field.

The sensors were installed in such a way that the pixel long direction (400 µm) was in the vertical position.

Data were taken with beam at normal incidence and with a 15° degree angle. This angle simulates the tilt

angle in the ATLAS barrel detector. Tilt angle, beam and B field directions are sketched in Figure 4.34.

4.9.2 - Selected events

After masking noisy strips, events with exactly one hit in each telescope plane were selected for the

reconstruction. The resulting beam shape is a convolution of the trigger and tracking efficiencies [4-16].

Tracks were fitted to a constant curvature helix, essentially treating all particles as having identical

momenta, and the magnetic field as being uniform. Any model error arising from the actual field non-

uniformity was absorbed in the transverse alignment, which was done independently of runs with and

without magnetic field. Excess extrapolation errors arising from a finite spectral width are expected to give

a limited contribution to the tracking error. The spatial resolution of the telescope was estimated by

comparing hits in one of the doublet planes to tracks extrapolated from the two remaining planes. The

distribution of unbiased residuals is compatible with the results of a toy Monte-Carlo model which assumes

a spatial resolution of 5 μm. The same model predicts the error of the extrapolated track position in the

Device-under-Test planes to be of order 3 μm, which has been considered a lower bound on the total track

resolution [4-17]. For preliminary results of the test beam the reader can refer to [4-16],[4-12],[4-18],[4-

19].

Figure 4.34 - Tilt angle, beam and B field directions

91

CHAPTER 5 IRRADIATION

Chapter 5 - Irradiation s

92


93

his chapter is meant to describe the physics that stands behind the radiation damage of silicon, and

analyze the behaviour of FBK-3D detectors after irradiation. This has been done at the PS18 facility of

CERN in the period September-November 2009. One of the aims of this study is to demonstrate that

3D-DDTC pixels would be a feasible alternative to the planar pixel sensors now installed in the ATLAS

experiment, proving their radiation hardness.

5.1 – Radiation-induced effects on silicon

Radiation-induced damage is usually divided into bulk and surface damage. The former is caused by the

displacement of crystal atoms while the latter include all effects in the surrounding dielectric layers. The

most important surface effect is the charge density increase in the oxide passivation layer, which saturates

after some kGy to values of about 1012 cm−2 [2-1]. At higher hadron fluence, bulk damage becomes

important. The main effects are:

• Increase of the leakage current

• Change of the space charge in the depleted region and subsequent increase of the full-depletion

voltage

• Charge trapping

5.1.1 – Bulk damage

Properties of silicon change with radiation because of its crystal nature. High energy particles do not

interact exclusively with the electrons of the silicon sensor producing ionization, but also interact with the

nuclei, often displacing them out of the lattice position: this produces crystal imperfections which may be

electrically active and hence change the electric properties of the material, causing the so-called bulk

damage [2-1]. In contrast to ionization such interactions are not reversible in most cases. To remove a

silicon atom from its lattice position a minimum recoil energy of about 25 eV is required [5-1]. Electrons

need an energy of at least 260 keV in order to provide such a recoil energy in a collision, while protons and

neutrons, because of their higher mass, require 190 eV only. If the recoiling silicon atom gets enough

energy through the collision, it can cause further defects. In case this energy exceeds about 2 keV a cluster

of defects is created and most of the energy is released in a very localized area. According to simulations

these clusters are believed to have an inner diameter of about 10 nm surrounded by an about 200-nm wide

volume with a lower defect density [5-2].

In order to compare the damage caused by different types of particles with different energies, radiation

damage is scaled using the non-ionizing energy loss (NIEL) conversion [5-3],[5-4],[5-5]. This is based on the

hypothesis that the damage only depends on the energy deposited in the crystal which is not related to the

fully reversible process of ionization but only to non-ionizing interactions. Fluences are normalized to that

of neutrons of 1 MeV, used as reference, through the following relation:

𝜙𝑒𝑞 = 𝜅𝜙𝑝𝑕𝑦𝑠

The energy-dependent hardness factor κ of a certain type of particle, which converts the “physical” fluence

Φphys into the neutron equivalent fluence Φeq able to produce the same NIEL, can be calculated according to

[5-3]. The experimental determination of the hardness factors is done via the normalization of the leakage

current [5-6]. For the most frequently used irradiation facilities measured values are available, and in

18 Proton Synchrotron

T


94

particular the hardness factor κ of the 24 GeV protons provided by the CERN-PS is 0.62 [5-7]. In general

there exists a factor of ~2 between a flux of neutrons and protons.

Primary defects caused by irradiation, mainly silicon vacancies and interstitials, are not stable, i.e. they can

move through the crystal. This movement can lead to annealing if defects meet during their migration. But

secondary point defects, together with other defects already present in the crystal, might be stable and

display different electrical properties. Point defects can in general determine new energy levels in the gap

band whose positions can be measured by different spectroscopic methods. Depending on the energy, they

can have an impact on the space charge in the depletion zone [2-1].

5.1.2 – Leakage current and annealing

The energy levels in the band gap caused by crystal defects act as generation–recombination centers. They

lead to a decrease of the generation lifetime, τg, proportional to the fluence Φ [2-1]:

1

𝜏𝑔=

1

𝜏𝑔 ,𝜙=0+ 𝑘𝜏𝜙

with kτ being the lifetime-related damage rate, and to an increase of the volume generation current, Ivol:

𝐼𝑣𝑜𝑙𝑣𝑜𝑙

= 𝐼𝑣𝑜𝑙 ,𝜙=0

𝑣𝑜𝑙+ 𝛼𝜙

with vol being the depleted volume and α the current-related damage rate. Because of the relation

between generation lifetime and volume generation current expressed in :

𝐼𝑣𝑜𝑙 ≈ −𝑒 𝑛𝑖

𝜏𝑔 𝑊 ≈ −𝑒

𝑛𝑖

𝜏𝑔

2휀0휀𝑆𝑖𝑒𝑁𝐷

𝑉𝑅

the two damage constants are also related:

𝛼 = 𝑒𝑛𝑖𝑘𝜏

The lifetime-related damage rate kτ is more fundamental than the current-related damage rate α, as it does

not depend on the intrinsic charge carrier concentration, and therefore not on the temperature at which

the measurement is performed. However, α is usually quoted as the parameter directly determined from

the current–voltage measurements. The damage constant α is independent of the initial resistivity of the

silicon, the concentration of other dopants like oxygen or carbon, and the production process of the sensor

[5-8]. Figure 5.1 shows the dependence of the leakage current, normalized to the depleted volume V, for

several types of silicon semiconductor detectors [5-4]. From these data but also from many other

measurements made on p-type, n-type, FZ or CZ irradiated materials the current damage rate tends to α =

(3.99 ± 0.03) × 10−17A/cm. Due to the strong dependence of the leakage current on the temperature, the

data measurements have to be normalized to the same reference temperature (i.e. TR = 20 °C) for doing a

meaningful comparison between different data set.


95

After irradiation the leakage current anneals with time as shown in Figure 5.2, through the α dependence

on time. This strongly temperature-dependent annealing behaviour was fitted in the past to a sum of

exponential functions with different “decay” times and could be interpreted as several defects which

anneal with different time constants [5-9]. Such a parameterization describes the measured data for

annealing times at room temperature of less than one year. For longer annealing times or higher annealing

temperatures no saturation of the annealing has been observed and therefore the time evolution of the

current-related damage rate has been described using an additional logarithmic term [5-4]:

𝛼 𝑡 = 𝛼𝑖𝑒−

𝑡𝜏𝑖 + 𝛼0 − 𝛽 ln

𝑡

𝑡0

with t0 arbitrary set to 1 min. The dependence on the annealing temperature Ta is hidden in

1

𝜏𝑖= 𝑘0,𝑖𝑒

−𝐸𝑖

𝑘𝐵𝑇𝑎

and in α0. The fitted parameters were determined to be:

𝛼𝑖 = 1.26 ± 0.06 × 10−17 𝐴

𝑐𝑚

𝑘0,𝑖 = 1.2−1.0+5.3 × 1013𝑠−1

𝐸𝑖 = 1.11 ± 0.05 𝑒𝑉

𝛽 = (3.07 ± 0.18) × 10−18𝐴

𝑐𝑚

𝛼0 = − 8.9 ± 1.3 × 10−17 𝐴

𝑐𝑚+ 4.6 ± 0.4 × 10−14

𝐴𝐾

𝑐𝑚×

1

𝑇𝑎

Figure 5.1 - Induced leakage current increase for several detector materials as function of the fluence. Current has been measured after an annealing step at 60 °C for 80 min [5-4].


96

5.1.3 – Effective doping and fluence dependence

If several dopants and electrically active defects are present in a silicon sensor, the concentrations of

donors, ND, or acceptors, NA, have to be replaced by a quantity called net doping or effective doping, Neff ,

which is the difference between all donor-like states and all acceptor-like states, and can be determined

from the full-depletion voltage:

𝑁𝑒𝑓𝑓 = 2휀0휀𝑆𝑖𝑉𝑑𝑒𝑝𝑙

𝑒𝑑2

with d the depleted layer width. Since the effective doping concentration is, according to the definition,

positive for n-material and negative for p-material, all formulas contain only its absolute value |Neff |.

The effective doping concentration changes with irradiation. Figure 5.3 shows the dependence of the

effective doping and the full-depletion voltage on the equivalent fluence.

In n-type silicon, Neff decreases up to a fluence of (2÷5) × 1012 cm−2 at which the space charge almost

vanishes. With further irradiation the absolute effective doping concentration increases again, dominated

by acceptor-like defects with a negative space charge, and the material becomes a p-doped one. As a

Figure 5.2 - Current-related damage rate α as function of the cumulated annealing time [5-4]

Figure 5.3 - Change of the full-depletion voltage of a 300-µm-thick silicon n-type sensor and its absolute effective doping versus the normalized fluence,

immediately after irradiation [5-9]


97

consequence of this type inversion, or more correctly space charge sign inversion, the PN-junction moves

from the p+-side of the sensor to the n+-side, causing problems to the charge collection at the readout

electrodes. This behaviour has been proven using short-range α-particles [5-9]. Contrary to n-type, p-type

substrates do not undergo type-inversion for fluences up to the ones foreseen for sLHC [5-10] Due to the

mobility of the defects the net doping concentration changes after the end of the irradiation. The time

evolution of the effective space charge at temperature of 60 ˚C is shown in Figure 5.4. As the defects and

their behaviour are not yet understood in detail, a phenomenological parameterization is performed. The

most accepted description is the so-called Hamburg model [5-4]:

𝑁𝑒𝑓𝑓 = 𝑁𝑒𝑓𝑓 ,𝜙=0 − [𝑁𝑐 𝜙 + 𝑁𝑎 𝜙,𝑇𝑎 , 𝑡 + 𝑁𝑌 𝜙,𝑇𝑎 , 𝑡 ]

with 𝑁𝑐 𝜙 + 𝑁𝑎 𝜙,𝑇𝑎 , 𝑡 + 𝑁𝑌 𝜙,𝑇𝑎 , 𝑡 = Δ𝑁𝑒𝑓𝑓 𝜙,𝑇𝑎 , 𝑡 .

In the equation NC(Φ) describes the fluence dependence of the effective doping and contains only the

fluence Φ as parameter. The other two terms describe the change of the effective doping after the

irradiation and are therefore also dependent on the temperature Ta. In particular, the first term NC(Φ)

describes the stable damage, combining the deactivation of the initial donor states with the creation of

acceptor-like defects:

𝑁𝐶 𝜙 = 𝑁𝐶,0 1 − 𝑒−𝑐𝜙 + 𝑔𝑐𝜙

with c = (1-3) x 10-13 cm2, called removal constant [5-4]. The second term of the Hamburg Model, Na,

specifies the short-term or beneficial annealing, while the third, NY, is the so-called reverse annealing term,

which describes the increase of the full depletion voltage after some weeks at room temperature [see 5-4

for various parameterizations]. It is also important to mention that irradiation-induced space charge sign

inversion influences the electric field inside the sensor: it is the so-called double junction model, which

describes the presence of a new electric field in the undepleted region of the sensor [5-12,5-13].

Figure 5.4 - Typical annealing behaviour of the irradiation-induced changes of the effective doping concentration ∆Neff at a temperature of 60 °C after

irradiation with a fluence of 1.4 x 1013

cm-2

[5-11]


98

5.1.4 – Charge trapping

Radiation-induced defects act as generation–recombination centers, which increase leakage current and

charged defects (with dramatic influence on the full-depletion voltage), but also create trapping centers.

Traps in the depletion region are mostly unoccupied due to the lack of free charge carriers, and can hold or

trap part of the signal charge for a time longer than the charge collection time and consequently reduce the

signal height. A parameter to describe trapping is the trapping time τt, which is inversely proportional to the

concentration of traps and therefore inversely proportional to the fluence Φ *5-9]:

1

𝜏𝑡(𝜙)=

1

𝜏𝑡,𝜙=0+ 𝛾𝜙

The coefficient γ was measured to be 0.41 × 10−6 cm2/s for electrons and 0.60 × 10−6 cm2/s for holes after

neutron irradiation. After irradiation with charged hadrons (protons and pions) this coefficient was found

to be significantly larger: 0.56 × 10−6 cm2/s for electrons and 0.77 × 10−6 cm2/s for holes [5-14]. For most of

the tracking devices in use in particle physics this effect is less important than the other radiation-induced

effects previously discussed; after a fluence of 1014 neq/cm2 about 90% of the signal charge can be still

collected in a 300-μm-thick detector. However, this number decreases to about 50% for 1015 neq/cm2 and

trapping will eventually limit the use of silicon detectors for fluences beyond this number, as the sLHC ones

will be.

5.1.5 – Surface effects

In silicon also the surface region is sensitive to radiation. Surface damage summarizes all defects in the

overlaid dielectrics, like the silicon oxide passivation layer, and the interface between the silicon and the

dielectrics. Since the crystal structure of silicon oxide is highly irregular, displacements of single atoms due

to irradiation do not lead to macroscopic changes. Ionization in the oxide, however, is not fully reversible

and may cause steady changes of the interface properties. Electrons have high mobility in the oxide and if

created by radiation will be collected by any positively biased electrode close by. Holes have instead a very

low mobility in the oxide, because of the large number of shallow hole traps, and they move very slowly in

the direction of the electric field, hopping from one shallow trap into the next. If the holes arrive in the

transition region between silicon and oxide, where many deep hole traps exist, they may be kept there

permanently [5-15].

5.1.6 – Consequences of irradiation damage on sensor operation

The main consequence of the bulk damage on the operation of irradiated sensors consists basically in the

increase of leakage current and operation voltage; this leads to an increased power dissipation, which heats

the sensor, and higher temperature implies higher leakage current and therefore larger dissipated power.

The result is a feedback system that may quickly diverge (thermal runaway), unless prevented by proper

cooling. If a sensor (n-type) is irradiated above the fluence causing type inversion, the increase of the net

doping concentration leads to an increase of the full-depletion voltage, which can, in some applications,

exceed thousand volts after some years of operation. As it is unpractical to increase the operation voltage

up to this range, the alternative would be to work with partially depleted sensors. However, for a given

maximum operation voltage, the depth of the depletion zone and therefore the electrical signal will

decrease. The detector system has therefore to be designed in such a way that it can still work with

reduced signals, with a maximal operation voltage still high enough to provide sufficient signal.


99

3D detectors seem a good solution with respect to these problems since their architecture allows a starting

operation bias much smaller than for planar detectors, and at the same time provides higher radiation

hardness [5-16],[5-17]. Reverse annealing also turns out to be critical if the sensors are planned to be used

for several years. The full-depletion voltage increases significantly after some weeks at room temperature,

which means that a proper cooling should be foreseen without long interruptions.

5.2 – PS irradiation facility overview

The irradiation work presented in this thesis has been done at the CERN Proton Synchrotron (PS) facility

from September to November 2009, using the Irrad 1 shuttle and Irrad 3 table for irradiation located in the

East Hall Area of the PS [5-18]. Figure 5.5 shows the PS ring in the contest of CERN Accelerator complex [5-

19].

The East Area for irradiation includes two facilities, one for proton irradiation (Irrad 1, Irrad 3, Irrad 5 and

Irrad 7) and the other for neutron irradiation (Irrad 2), which make use of the 24 GeV/c proton primary

beam of the CERN-PS (shown in Figure 5.6). The proton and the neutron bursts are delivered during the

14.4 s supercycle of the PS in 1-3 spills of about 400 ms [5-20].

Figure 5.5 - CERN Accelerator Complex


100

Both proton and neutron irradiation zones are equipped with a remote controlled shuttle to move small

dimension samples (maximum with a 5 cm2 area) from the counting room into the irradiation area. For

bigger size samples or for irradiations requiring cooling, fixed mechanical tables are positioned along the

beam line, as shown in Figure 5.7:

To control the status of the beam during irradiation, a Secondary Emission Chamber (SEC) provides a

measurement of the proton beam intensity (at about 10 meters from the Irrads), and a Beam Profile

Monitor BPM electronics board allows to have online all the information and shape of the beam. The value

of fluence taken by the irradiated samples is measured by activation of aluminum foils positioned near

them. This technique provides fluence measurements with an accuracy of ~7%, and is performed with a Ge-

spectrometer for Na-22 (long irradiation) and Na-24 (short irradiation) decay analysis.

Figure 5.6 - PS East Hall Area with beam characteristics

Figure 5.7 - Irrad 1 and Irrad 3, 5, 7 (inside tables) places at the PS


101

5.3 – Irradiation of FBK-3D and planar sensors

3D detectors are being investigated to be possibly used for the ATLAS IBL-modules; so they need first to be

qualified for radiation doses of 300 Mrad or fluences of 5 × 1015 1MeV neutron equivalent per cm2, after

which they will be tested with beams to measure their performance as tracking detectors. The preliminary

results about the first step of such irradiation program are presented here. Irradiated sensors are bump-

bonded with FE-I3 chips, which cannot go over 2 × 1015 n/cm2, or 4 × 1015 p/cm2 [3-20].

5.3.1 – Irradiation of FE-I3

Before irradiating the SCAs, the FE-I3 has been investigated to confirm till which fluences it can be properly

operated. A board with only a FE-I3 chip mounted on it has been used (shown in Figure 5.8), which has

been irradiated at room temperature (~27 °C) without clock and power. Irradiation has been performed at

the CERN PS with the 24 GeV/c proton beam, using the shuttle Irrad1, in three steps:

1. 1.07 × 1015 ±7.0% 𝑝

𝑐𝑚2

2. 2.24 × 1015 ±7.3% 𝑝

𝑐𝑚 2

3. 3.78 × 1015 ±7.5% 𝑝

𝑐𝑚 2

After each step it has been re-calibrated in order to verify its functionality.

The FE-I3 has been confirmed working after each step (Figures 5.9, 5.10 and 5.11 show results of the 3 rd

step of irradiation, while in Table 5.1 there is a complete summary of the results).

Figure 5.8 - FE-I3 chip board


102

Before Irradiation

1.07x1015 p/cm2 ± 7.0%

2.24x1015 p/cm2 ± 7.3%

3.78x1015 p/cm2 ± 7.5%

Threshold (e) 3262.00 ± 37.33 3224.00 ± 47.07 3250.00 ± 42.53 3293.00 ± 57.03

Noise (e) 101.8 ± 8.3 103.3 ± 8.76 101.90 ± 8.12 105.50 ± 8.12

ToT (e) 61.67 ± 1.84 59.21 ± 2.32 58.80 ± 2.34 59.85 ± 2.42

Table 5.3 - Results of FE-I3 calibration before and after irradiation steps

Figure 5.10 - Noise of calibrated FE-I3 irradiated at 3.78 x 10

15 p/cm

2

Figure 5.9 – Threshold of calibrated FE-I3 irradiated at 3.78 x 10

15 p/cm

2

Figure 5.11 - ToT of calibrated FE-I3 irradiated at 3.78 x 1015

p/cm2


103

5.3.2 – Irradiation of SCAs – Setup

The SCAs which have been irradiated are:

an FBK-3D DTC2 (3EM5), with bias voltage of -35 V;

an FBK-3D DTC2b (3E7), with bias voltage of -8 V;

an ATLAS planar n-in-n, used as a reference, with bias voltage of -150 V.

They have been irradiated all together inside a cooling system, to avoid thermal runaway, keeping the FE-I3

chip not clocked and not powered. During the irradiation the temperature has been kept in the range -14 to

-7 °C. The cooling was obtained with a vortex tube (produced by Meech manufactory [5-21]), shown in

Figure 5.12 and 5.13.

The Vortex Tube (VT) cooler is a mechanical device to separate a compressed gas into hot and cold streams.

It has no moving parts, as can be seen from Figure 5.14.

The VT cooler is composed by one or more inlet nozzles, a vortex chamber, a cold-end orifice, a hot-end

control valve and a tube. Pressurized gas is injected tangentially into a swirl chamber via the inlet nozzles,

and accelerates to a high rate of rotation: a swirling flow is so created inside the vortex chamber. Due to

the conical nozzle at the end of the tube, only the outer shell of the compressed gas is allowed to escape at

that end. The remaining gas is forced to return into an inner vortex of reduced diameter within the outer

vortex, it swirls to the center of the chamber and is expanded and cooled. In the vortex chamber part of the

gas swirls to the hot end, and another part exits via the cold exhaust directly. Part of the gas in the vortex

tube reverses the axial component of the velocity and moves from the hot end to the cold end. At the hot

exhaust the gas escapes with a higher temperature, while at the cold exhaust the gas has a lower

temperature compared to the inlet temperature. There are different explanations for the effect and there

Figure 5.12 - Vortex Tube Meech schematic Figure 5.13 - Cooling box on Irrad 3 with Meech Vortex Tube

Figure 5.14 - Separation of a compressed gas into a hot stream and a cold stream in the VT


104

is debate on which explanation is best or correct. What is usually agreed is that the air in the tube

experiences mostly "solid body rotation", which means that the rotation rate (angular velocity) of the inner

gas is the same as that of the outer gas. This is different from what is considered a standard vortex

behaviour, where inner fluid spins at a higher rate than outer fluid. The (mostly) solid body rotation is

probably due to the long time each parcel of air remains in the vortex, allowing friction between the inner

parcels and outer parcels to have a notable effect. It is also usually agreed upon that there is a slight effect

of hot air wanting to "rise" toward the center, but this effect is negligible — especially if turbulence is kept

to a minimum. One possible explanation is that the outer air is under higher pressure than the inner air,

because of centrifugal force. Therefore the temperature of the outer air is higher than that of the inner air.

Another explanation is that as both vortices rotate with the same angular velocity and direction, the inner

vortex loses angular momentum. The decrease of angular momentum is transferred as kinetic energy to the

outer vortex, resulting in separated flows of hot and cold gas. This is somehow analogous to a Peltier

device, which uses electrical voltage to move heat to one side of a dissimilar metal junction, causing the

other side to become cold. This principle was first discovered by Ranque in 1933 [5-22], and by Hilsch in

1947 [5-23]. In memory of their contribution, the VT is also known as Ranque Vortex Tube (RVT), Hilsch

Vortex Tube (HVT), and Ranque-Hilsch Vortex Tube (RHVT). A RHVT has the following advantages compared

to the normal commercial refrigeration devices: simple, no moving parts, no electricity or chemicals, small

and lightweight, low cost, maintenance free, instant cold air, durable (because of the stainless steel and

clean working media), adjustable temperature [5-24,5-25]. The counterpart for these advantages is its low

thermal efficiency, which is the limiting factor for its application, together with the noise and availability of

compressed gas. The research on vortex tubes generally concerns aspects of the compressible fluid

dynamics of turbulent and unsteady flows, thermodynamics and heat transfer. These aspects make the

research complicated and challenging [5-26]. Irradiation with this cooling device has also been a test for its

functionality in radioactive environment, in order to be adopted as mean of cooling for PS cooling box

upgrades. It performed well during the entire period of irradiation, maintaining temperatures between -15

and -7 °C without any problems.


105

5.3.3 – Irradiation of SCAs – Results

The irradiation of the sensors has been performed in two fluence steps:

1. 2.00 × 1015 ±7.0% 𝑝

𝑐𝑚 2

2. 3.50 × 1015 ±7.0% 𝑝

𝑐𝑚 2

During each day of irradiation the leakage current has been monitored (sensors have been kept with bias

on), and after every step the I-V behaviour has been investigated. Figure 5.15 shows the Ileakage vs fluence:

it’s the global sensor leakage current (over 2880 pixels), and it has been measured with Keithley 2410, with

a precision of ±0.01 µA.

Figure 5.15 - Ileakage vs fluence for 3E7, 3EM5 and planar sensors

As predicted from the theory, there is a grow in the leakage current with the increasing of the fluence

received by the sensors, and the dependence is linear. From the fluence and the hardness factor κ = 0.62 of

the 24 GeV protons provided by the CERN-PS, which converts the “physical” fluence Φphys into the neutron

equivalent fluence Φeq, it is possible to calculate:

𝜙𝑒𝑞 = 𝜅𝜙𝑝𝑕𝑦𝑠 = 0.62𝜙𝑝𝑕𝑦𝑠 = 0.62 × 2 ∙ 1015 = 1.24 ∙ 1015

𝑛𝑒𝑞

𝑐𝑚2

0.62 × 3.5 ∙ 1015 = 2.17 ∙ 1015 𝑛𝑒𝑞

𝑐𝑚2

This allows to estimate the effective dopant concentration Neff:

𝑁𝑒𝑓𝑓 = 𝑁0 + 𝑔𝐶𝜙𝑒𝑞

with (for the considered 3D silicon FZ p-type):

𝑁0 = 1012 𝑐𝑚−3

y = 2E-15x - 2E-14

y = 7E-15x - 2E-14

y = 2E-14x - 3E-14

05

1015202530354045505560

0,00

E+0

0

5,00

E+1

4

1,00

E+1

5

1,50

E+15

2,00

E+1

5

2,50

E+1

5

3,00

E+1

5

3,50

E+1

5

4,00

E+15

I leak

age

(µA

)

Fluence (p/cm2)

Ileakage vs fluenceDTC2b (3E7) 200µm

DTC2 (3EM5) 200µm

Planar 250µm


106

𝑔𝐶 = 0.01 𝑐𝑚−1

obtaining

𝑁𝑒𝑓𝑓 2 ∙ 1015 = 1012 𝑐𝑚−3 + 0.01 𝑐𝑚−1 × 1.24 ∙ 1015 𝑐𝑚−2 = 1.34 ∙ 1013 𝑐𝑚−3

𝑁𝑒𝑓𝑓 3.5 ∙ 1015 = 1012 𝑐𝑚−3 + 0.01 𝑐𝑚−1 × 2.17 ∙ 1015 𝑐𝑚−2 = 2.27 ∙ 1013 𝑐𝑚−3

From these values it is possible to calculate the depletion voltage after irradiation:

𝑁𝑒𝑓𝑓 = 2휀0휀𝑆𝑖𝑉𝑑𝑒𝑝𝑙

𝑒𝑑2

With the previous values of Neff, knowing d = 71.2 µm for the distance between two electrodes in the 3E

configuration, the values obtained are:

𝑉𝑑𝑒𝑝𝑙 2 ∙ 1015 ≅ 51.2 𝑉

𝑉𝑑𝑒𝑝𝑙 3.5 ∙ 1015 ≅ 86.7 𝑉

Given these values, one should apply higher voltages to full deplete the sensor, in order to also deplete the

region under the n-columns.

The current-related damage rate α can be calculated as:

𝐼𝑣𝑜𝑙𝑣𝑜𝑙

= 𝐼𝑣𝑜𝑙 ,𝜙=0

𝑣𝑜𝑙+ 𝛼𝜙

With a volume of 15552 x 10-12 m3 for FBK-3D sensors and of 19440 x 10-12 m3 for the planar sensor, and

values of Vdepl chosen at -100 V and -150 V for both irradiations to 2 x 1015 and 3.5 x 1015 p/cm2 (using the

correspondent values of fluences in Φeq) for 3EM5, at -100 V and -150 V for irradiation to 3.5 x 1015 p/cm2

for 3E7, and at -300 V for irradiation to 2 x 1015 and for 3.5 x 1015 p/cm2 for the planar sensor, one obtains

the values of α summarized in Table 5.2:

3EM5

Vbias [V] Φeq [neq] α [A/cm]

-100 1.24 E 15 3.236 E-17

-150 1.24 E 15 5.876 E-17

-100 2.17 E 15 2.673 E-17

-150 2.17 E 15 3.816 E-17

3E7

-100 2.17 E 15 3.608 E-17

-150 2.17 E 15 5.500 E-17

Planar

-300 1.24 E 15 2.094 E-17

-300 2.17 E 15 3.200 E-17

Table 5.4 – Values of α for the irradiated sensors

To compare with values obtained for other silicon detectors in literature (see section 5.1.2), the α values

are scaled using the room temperature correction given in [5-27], that accounts for the strong dependence


107

of the leakage current on the temperature (roughly a factor 2 every 7.5 °C). The agreement between the α

values of Table 5.2 and the generally accepted value of ~4 x 10-17 A/cm is good enough considering the

uncertainties in the irradiation fluence and in the temperature.

The results of the I-V measurements after the two steps of irradiation are shown in Figure 5.16 for both the

FBK-3D from first and second batch irradiated at 2 x 1015 p/cm2 with all the data taken before restarting the

irradiation.

Figure 5.16 - Preliminary I-V curves for irradiated FBK-3D sensors at 2 x 1015

p/cm2

Data for the DTC2b at this first step were not fully taken due to the restarting of the irradiation. The

behaviour of the DTC2 sensor reflects the same shape of an unirradiated sensor, but with bias voltages and

currents much higher than before due to irradiation damages. From the plot one could derive that at about

-100 V the irradiated sensor is fully depleted. The same considerations can be done on Figure 5.17, where

the same comparison has been done after 3.5 x 1015 p/cm2 irradiation (second step of irradiation). This

time, the full depletion voltage is at about -150 V for both sensors.

0,00E+001,00E+012,00E+013,00E+014,00E+015,00E+016,00E+017,00E+018,00E+019,00E+011,00E+021,10E+021,20E+021,30E+021,40E+021,50E+021,60E+021,70E+02

01

02

03

04

05

06

07

08

09

01

00

11

01

20

13

01

40

15

01

60

17

01

80

19

02

00

21

02

20

23

02

40

25

02

60

27

0

reve

rse

Bia

s C

urr

en

t (u

A)

reverse Bias (V)

FBK-3D DDTC (@ 2 x 1015 p/cm2)3E - DTC2

3E - DTC2b


108

Figure 5.17 - Preliminary I-V curves for irradiated FBK-3D sensors at 3.5 x 1015

p/cm2

0,00E+002,00E+014,00E+016,00E+018,00E+011,00E+021,20E+021,40E+021,60E+021,80E+022,00E+022,20E+022,40E+022,60E+022,80E+023,00E+023,20E+023,40E+023,60E+023,80E+024,00E+024,20E+024,40E+024,60E+024,80E+025,00E+025,20E+025,40E+025,60E+02

02

04

06

08

01

00

12

01

40

16

01

80

20

02

20

24

02

60

28

03

00

32

03

40

36

03

80

40

04

20

44

04

60

48

05

00

52

05

40

56

05

80

60

06

20

64

06

60

68

07

00

reve

rse

Bia

s C

urr

en

t (u

A)

reverse Bias (V)

FBK-3D DDTC (@ 3.5 x 1015 p/cm2)3E - DTC23E - DTC2b


109

In Figure 5.18 the behavior of the 3D DTC2 at the two different fluences of irradiation is shown, while in

Figure 5.19 the same thing is plotted for the reference planar sensor. Results clearly show the increasing

current values with the irradiation.

Figure 5.18 – Comparison between preliminary I-V curves for irradiated FBK-3D DTC2 sensor (at 2 x 1015

p/cm2 and 3.5 x 10

15

p/cm2)

Figure 5.19 - Comparison between preliminary I-V curves for irradiated planar sensor (at 2 x 1015

p/cm2 and 3.5 x 10

15 p/cm

2)

0,00E+00

2,00E+01

4,00E+01

6,00E+01

8,00E+01

1,00E+02

1,20E+02

1,40E+02

1,60E+02

1,80E+02

0 50 100 150 200 250 300

reve

rse

Bia

s C

urr

en

t (u

A)

reverse Bias (V)

FBK-3D DTC2 - 3EM5 @ 3.5 E15 p/cm2

@ 2 E15 p/cm2

0,00E+002,00E+014,00E+016,00E+018,00E+011,00E+021,20E+021,40E+021,60E+021,80E+022,00E+022,20E+022,40E+022,60E+022,80E+02

02

55

07

51

00

12

51

50

17

52

00

22

52

50

27

53

00

32

53

50

37

54

00

42

54

50

47

55

00

52

55

50

57

56

00

62

56

50

67

57

00

72

57

50

reve

rse

Bia

s C

urr

en

t (u

A)

reverse Bias (V)

Planar n-in-n @ 3.5 E15 p/cm2@ 2 E15 p/cm2


110

111

CHAPTER 6 CONCLUSIONS

Chapter 6 - Conclusions s

112


113

rom the first proposal in 1997 by S. Parker, the 3D detector concept for particle tracking has been

developed and investigated, with considerable success. Columnar electrodes have undergone

continuous modifications, penetrating in different ways through the substrate thickness, following

the development of the Micro Machining techniques. Sensors with very short inter-electrode distances

have been designed, leading to very low depletion voltages and short collection distances, properties which

make 3D sensors very high radiation tolerant; other important properties are charge sharing reduction and

the possibility of active edge solutions, at the expense of a more complicated fabrication process with

respect to traditional planar technology.

This thesis focused on the characterization of a particular type of 3D detector called 3D-DDTC (Double Side

Double Type Column), where the electrodes are etched perpendicularly to the surface but do not penetrate

the entire substrate thickness. The etching is made alternatively on both the surfaces and the number of

process steps is highly reduced compared to a standard 3D process.

Detectors from two batches of 3D-DDTC (DTC2 and DTC2b, with different columnar overlap) have been

characterized and calibrated for this thesis, studying their performance in comparison with a planar sensor.

Important results have been obtained from 241Am, 109Cd and 90Sr source tests, showing for 3D detectors a

behaviour similar to the planar one in detecting gamma and beta particles. Moreover, preliminary

irradiation tests show that detectors are still working correctly after irradiation fluences up to 4×1015 p/cm2,

proving good radiation hardness as expected.

In conclusion, 3D detectors are indeed one of the most promising technology for the LHC upgrades, where

a very high radiation hardness will be required. At the same time, because of their peculiar characteristics,

they are also presently considered for other possible applications like imaging and dosimetry in Biomedical

Physics.

F


114

115

APPENDIXES

Appendixes

116

Appendixes

117

Appendix 1 – FE-I3

FE-I3 detailed photo

FE-I3 detailed schematic

Figure A1.1 - [3-4]

Figure A1.2 - [3-4]

Appendixes

118

Appendix 2 - TurboDAQ

A2.1 - Start-up

The program is launched with a double click on the icon “TurboDAQ.exe” wherever it has been put on the

PC (usually on the desktop). It appears the TurboDAQ main panel, as shown in Figure A2.1:

Figure A2.1: Main TurboDAQ panel

In this first panel all the functions of the software are present. It has to be noticed that always after

switching on the VME crate of the custom system the application “Resman.exe” needs to be launched in

order to configure the VME bus, and only after that it is possible to correctly start the TurboDAQ. For

testing purposes only the following parts of the software have been used and are going to be explained:

1. POWER CONSOLE

2. INITIALISATION

3. CONFIGURATION

4. DATA CONTROL (with DATA FITTING CONSOLE)

5. SCAN CONSOLE

This is the

.exe starter This is the

main panel

This is the status

of measurement

panel

Appendixes

119

A2.2 - POWER CONSOLE

One mouse click on POWER CONSOLE allows the operator to switch on the power supplies from the

software interface itself (thanks to GPIB connection to the power supplies) as shown in Figure A2.2:

Figure A2.2: POWER SUPPLY

The voltage generators are activated by clicking on the “POWER ON” buttons.

Appendixes

120

Figure A2.3: Power supply values

When active, it appears the name of the power supply, as shown in Figure A2.3 (one is for the TPCC, a

second is for the FE and a third is to deplete the sensor). The values of voltage and current have to be set

(and read) from the panel. Nominal values for the low voltage meters are stored in the power configuration

files (shown on the panel).

A2.3 - INITIALISATION

The first operation to be done when beginning every test is to let the TPLL communicate with the TPCC, and

this is done by opening the INITIALISATION panel

and pushing the button “Initialise PLL&PCC” on it

(see Figure A2.4). If it is all working, the leds on

the TPCC are going to remain green. If not, the

ones shown on the left in Figure A2.4 are going to

turn into red. So, if the TPCC is not communicating

with the TPLL, there is a problem to cope with. It

could happen that the TPCC board, because of the

large dimensions, may move or being dilated by

overheating when kept operative for long times.

When the problem seems to be solved, the board

has to be reinitialized.

Figure A2.4 - INITIALIZATION

Appendixes

121

A2.4 - CONFIGURATION

This panel allows the operator to define the configuration parameters for the measurement desired:

Figure A2.5: STATIC CONFIGURATION CONSOLE

From the panel all the Front-End DACs of FE-I3 chips are manageable: GDAC values, IF and TRIMF values,

TDACs and FDACs tuned files (see Figure A2.5). Moreover, on the top right of the panel there is the place in

which the name of the module under test has to be inserted (which is going to be recognized by the system

during the entire measurement time and every time the same module is reconnected to the system). When

all wanted values are set or uploaded, in order to send them to the system the three buttons on the

bottom of the panel have to be clicked on. On the bottom left it is shown the operative temperature kept

during the test.

A2.5 - DATA CONTROL

This panel is used to give the path where the software will save

the data files and to set the name for each of them (see Figure

A2.6). The “Fitting Console” button at the bottom of the panel

opens the DATA FITTING CONSOLE, which cannot be opened

from the main panel of TurboDAQ directly, but only from this

panel.

Figure A2.6 - DATA CONTROL PANEL

Appendixes

122

A2.6 - DATA FITTING CONSOLE

In this panel the target threshold for all pixels in units of electrons and the characteristic values of the FE

(the capacity Clow and Chigh) and the calibration voltage (VCAL) which are used to tune each pixel have to be

manually written. They are proper values given by the builder of the sensor, and are saved in the final

configuration file for the module. Here there is a need to be careful with the “Feedback TrimDAC” because

the value must stay at 20000 e- for the measurement, but sometimes, when tuning other parameters or

opening other panels, this value returns to the default value of 10 (see Figure A2.7).

Figure A2.7: DATA FITTING CONSOLE

A2.7 - SCAN CONSOLE

Last (but not at all least!) there is the SCAN CONSOLE, which allows to choose the measurement or scan to

be performed on the detector under test. The blue square button next to “SCAN CONFIG” allows to choose

the type of test wanted. The “main

scan” zone set the number of data

to be taken, as shown in Figure A2.8.

Figure A2.8 - SCAN CONSOLE

Appendixes

123

Figure A2.8 shows the default setting for an I-V scan, with 61 points taken starting from 0 to -80 V. Another

important scan is the “threshold scan internal cal” (with internal calibration). The goal for this scan is to

obtain the same threshold for each pixel. When selecting

the threshold scan, the Scan Console panel is configured by

itself (see Figure A2.10). On the bottom right, in order not

to waste time for measuring the voltage supply, one can

just change the scan option by selecting “No LV/HV Supply

Measurement” (see Figure A2.9). Then the measurement

can be launched with the “Start scan” button.

The I-V measurements, which involves only the sensor and not the electronics, can be immediately done

from SCAN CONSOLE after the power is on and data path and name are set.

Figure A2.9 - No LV/HV Supply Measurements

Figure A2.10 - Scan choosing

Appendixes

124

When a measurement is finished, by clicking on “Online plot” the results can immediately be seen.

Figure A2.11: On-line plot of a threshold scan

In Figure A2.11 it is shown an example of what comes out from a typical threshold scan.

Threshold

value

Noise

Appendixes

125

Appendix 3 – Complete plots collection

A3.1 - Threshold

FBK-3D DTC2: 2EM2/3EM5/4EM9

Appendixes

126

FBK-3D DTC2b: 3E7 ; ATLAS planar n-in-n

Appendixes

127

A3.2 - Noise

FBK-3D DTC2: 2EM2/3EM5/3EM7/4EM9 ; FBK-3D DTC2b: 3E7 ; ATLAS planar n-in-n

Appendixes

128

A3.3 - ToT

FBK-3D DTC2: 2EM2/3EM5/4EM9

Appendixes

129

FBK-3D DTC2b: 3E7 ; ATLAS planar n-in-n

A3.4 - 241 Am

FBK-3D DTC2: 2EM2/4EM9 @ -35 V

Appendixes

130

A3.5 - 109Cd

FBK-3D DTC2: 2EM2/4EM9

Appendixes

131

A3.6 - 90Sr with Cluster Size1 and Cluster Size 2, with collimator, at different bias

values (-15V, -35V, -55V) – PRELIMINARY ANALYSIS PLOTS

(2 cm distance from source to sensor surface, 1 cm of collimator included):

FBK-3D DTC2: 2EM2

Appendixes

132

FBK-3D DTC2: 3EM7

Appendixes

133

FBK-3D DTC2: 4EM9

Appendixes

134

135

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Acknowledgements

The work for this thesis has been done at CERN during almost a year. This has been a very important period

for myself and for my career. I had the opportunity to learn a lot of Physics in the most important center of

Physics in the world, surrounded by the excitement connected to the start of LHC, and I could learn how to

work applying my studies, being inserted in a competitive environment and being given responsibilities. I

have worked and cooperated with people coming at CERN from all over the world, and learn something

from each of them. I have spent an exciting period abroad, finding the CERN area really attractive and

pleasant to live in, and with all the mentioned above people could establish good friendships outside the

work time.

Coming to specific thanks, I would like to express my acknowledgement to Dr. Alessandro La Rosa (who has

been my CERN supervisor) for his guidance, support and continuous encouragement, and to Prof. Ada

Solano and Prof. Michele Arneodo (who have been my University advisors), who believed in me, giving me

the possibility to enter this project, and supporting me continuously from the very beginning. I would also

thank Prof. Gian-Franco Dalla Betta for his excellent suggestion during our brainstorming, and Jens

Weingarten for his hints in the TurboDAQ usage.

I also have to thank all the people involved in the ATLAS 3D Pixel project with which I collaborated, in

particular to Cinzia Da Vià, Håvard Gjersdal, Phillippe Grenier, Ole Rhøne, Per Ola Hansson, Sebastian

Grinstein, Dmitri Tsybychev, Jie Wen Tsung, Salvatore Fazio; it has been an excellent experience to work

and to learn from them.

I have also spent four months at CERN PS Irradiation Facility under the supervision of Maurice Glaser and I

would like to thank, first and foremost, Maurice and all the people I have worked with during my stage. In

particular, my thanks to Nicola Pacifico, Michael Moll, Gianluigi Casse and the RD50 Collaboration for

having involved me in their activity.

I want to also thank also my “brother in arms” Marcello, with whom I divided the first part of my

experience at CERN, and all the people I met during these months.

Finally, I want to thank my family and Sara, since they make leaving CERN not too sad!

I really enjoyed this experience. Thanks a lot to all who have been involved in!

…and good luck to the LHC!

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