Development of a NUV camera for Cherenkov telescopes...

Universita degli Studi di Bari “Aldo Moro”

Corso di laurea in Fisica

Tesi di laurea magistrale

Development of a NUV camera

for Cherenkov telescopes applications

Relatore:

Prof. Francesco Giordano

Correlatore:

Dott.ssa Elisabetta Bissaldi

Laureando:

Massimo Capasso

Anno Accademico 2013-2014

Contents

Contents ii

List of Figures v

Introduction ix

1 The Cherenkov Telescope Array 1

1.1 The IACT technique . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 CTA goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Radiation Interactions 15

2.1 Photon interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.1.1 Photoelectric absorption . . . . . . . . . . . . . . . . . . . . 16

2.1.2 Compton scattering . . . . . . . . . . . . . . . . . . . . . . . 17

2.1.3 Pair production . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Gamma-Ray attenuation . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3 Photon detection in Silicon . . . . . . . . . . . . . . . . . . . . . . . 21

3 Photodetectors 23

3.1 PMT: Photo Multiplier Tube . . . . . . . . . . . . . . . . . . . . . 23

3.1.1 The photocatode and the photoemission process . . . . . . . 24

3.1.2 Spontaneous electron emission . . . . . . . . . . . . . . . . . 25

3.1.3 Quantum Efficiency and spectral response . . . . . . . . . . 26

3.1.4 Secondary electron emission . . . . . . . . . . . . . . . . . . 26

3.1.5 Statistics of electron multiplication . . . . . . . . . . . . . . 29

3.2 Semiconductor detectors . . . . . . . . . . . . . . . . . . . . . . . . 30

3.2.1 The diode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Forward bias . . . . . . . . . . . . . . . . . . . . . . . 33

Reverse bias . . . . . . . . . . . . . . . . . . . . . . . 34

3.2.2 Solid state detectors: Photodiodes and APD . . . . . . . . . 35

Photodiodes . . . . . . . . . . . . . . . . . . . . . . . 36

APD: Avalanche PhotoDiodes . . . . . . . . . . . . . 38

Geiger Mode APDs . . . . . . . . . . . . . . . . . . . 39

4 SiPM Characterization 41

4.1 The work at FBK . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

iii

Contents iv

4.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.1.2 Experimental procedure . . . . . . . . . . . . . . . . . . . . 45

I-V and dark measurements . . . . . . . . . . . . . . 45

Pulsed LED Measurements . . . . . . . . . . . . . . . 50

4.1.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

I-V Measurements . . . . . . . . . . . . . . . . . . . . 54

Dark Measurements . . . . . . . . . . . . . . . . . . . 54

Pulsed LED Measurements . . . . . . . . . . . . . . . 56

4.2 The work at INFN Bari . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2.1 Experimental Procedure . . . . . . . . . . . . . . . . . . . . 69

4.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Conclusions 81

A Seminconductors Basics 83

A.1 Atomic and band structure . . . . . . . . . . . . . . . . . . . . . . . 83

A.2 Intrinsic and doped semiconductors . . . . . . . . . . . . . . . . . . 85

A.2.1 N-Type Semiconductor . . . . . . . . . . . . . . . . . . . . . 88

A.2.2 P-Type Semiconductor . . . . . . . . . . . . . . . . . . . . . 89

Bibliography 91

Acknowledgements 95

List of Figures

1.1 Cosmic rays spectrum . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Air Shower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Proton and gamma-ray initiated showers . . . . . . . . . . . . . . . 5

1.4 Cherenkov light images on a Cherenkov camera . . . . . . . . . . . 7

1.5 Event selection in a Cherenkov camera . . . . . . . . . . . . . . . . 8

1.6 World’s largest IACTs . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.7 The FACT telescope . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.8 CTA sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.9 CTA layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1 Schematic representation of photoelectric absorption . . . . . . . . 16

2.2 Photon elastic scattering on a free electron . . . . . . . . . . . . . . 18

2.3 Photon total cross sections as a function of energy in carbon and lead 19

2.4 The exponential curve for gamma rays measured in a transmissionexperiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.5 Optical absorption coefficients for various photodetector materials . 21

3.1 Basic elements of a PMT . . . . . . . . . . . . . . . . . . . . . . . . 24

3.2 Quantum efficiency dependence on wavelength . . . . . . . . . . . . 27

3.3 Variation of the secondary emission yield with primary electronenergy for different dynode materials . . . . . . . . . . . . . . . . . 28

3.4 Statistical broadening of the secondary electron yield from the firstdynode of a PM tube . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.5 Basic structure of a diode . . . . . . . . . . . . . . . . . . . . . . . 31

3.6 Abrupt p-n junction at thermal equilibrium . . . . . . . . . . . . . 32

3.7 Forward biased p-n junction . . . . . . . . . . . . . . . . . . . . . . 33

3.8 Flow of carriers in a forward biased p-n junction . . . . . . . . . . . 34

3.9 Effect of forward biasing a diode on the depletion layer . . . . . . . 34

3.10 Reverse biased diode . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.11 Volt-ampere characteristic of a diode . . . . . . . . . . . . . . . . . 36

3.12 Silicon photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.13 Effect of a photon impinging on a photodiode . . . . . . . . . . . . 37

3.14 P-I-N Photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.15 Avalanche PhotoDiode . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.1 NUV structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

v

List of Figures vi

4.2 Basic Structure of a Silicon Photomultiplier . . . . . . . . . . . . . 42

4.3 GM-APD Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . 42

4.4 Correlated noise in a SiPM . . . . . . . . . . . . . . . . . . . . . . . 44

4.5 I-V measurements: schematic . . . . . . . . . . . . . . . . . . . . . 45

4.6 Dark measurements: schematic . . . . . . . . . . . . . . . . . . . . 46

4.7 Schematic representation of the DLED method . . . . . . . . . . . . 47

4.8 Pulse amplitude as a function of the time distance in dark . . . . . 48

4.9 Time distance distribution in dark . . . . . . . . . . . . . . . . . . . 49

4.10 Amplitude distribution in dark . . . . . . . . . . . . . . . . . . . . 49

4.11 Pulsed LED measurements: schematic . . . . . . . . . . . . . . . . 50

4.14 1x1mm2 - 40µm cell, reverse I-V . . . . . . . . . . . . . . . . . . . 55

4.15 1x1mm2 - 40µm cell, forward I-V . . . . . . . . . . . . . . . . . . . 55

4.16 1x1mm2 - 40µm cell, quenching resistor . . . . . . . . . . . . . . . 56

4.17 1x1mm2 - 40µm cell, Dark Count Rate . . . . . . . . . . . . . . . . 57

4.18 1x1mm2 - 40µm cell, Dark Count Rate VS Temperature . . . . . . 57

4.19 Correlated noise in a NUV 1x1mm2 SiPM with 40µm cell . . . . . 58

4.20 Primary and correlated noise in a NUV 1x1mm2 SiPM with 40µmcell and a resin layer . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.21 Primary and correlated noise in a NUV 1x1mm2 SiPM with 40µmcell and 50µm cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.22 Photon Detection Efficiency comparison between 40µm and 50µmNUV SPAD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

4.24 Light absorption in different materials . . . . . . . . . . . . . . . . 64

4.25 Schematic representation of a p/n junction . . . . . . . . . . . . . . 65

4.26 Triggering probabilities Pe and Ph of an n+/p diode. . . . . . . . . . 66

4.27 1x1mm2 with 40µm cell charge and Poisson distributions . . . . . . 68

4.28 Block diagram of the setup for measurements at INFN - Bari . . . . 69

4.30 Measurements apparatus - Bari . . . . . . . . . . . . . . . . . . . . 71

4.31 Data acquisition software - Bari . . . . . . . . . . . . . . . . . . . . 71

4.33 Single and multiple photoelectrons signals . . . . . . . . . . . . . . 73

4.34 Amplitude distributions 1x1mm2 with 50µm cell. . . . . . . . . . . 74

4.35 Amplitude distributions 1x1mm2 with 40µm cell. . . . . . . . . . . 76

4.36 Gain 1x1mm2 with 50µm and 40µm cell. . . . . . . . . . . . . . . . 77

4.37 SNR 1x1mm2 with 50µm and 40µm cell. . . . . . . . . . . . . . . . 78

4.38 SNR 1x1mm2 with 50µm and 40µm cell. . . . . . . . . . . . . . . . 79

4.39 Poisson distributions 1x1mm2 with 50µm cell. . . . . . . . . . . . . 80

A.1 Energy diagrams for different type of materials . . . . . . . . . . . . 84

A.2 Diagrams of the silicon and germanium atoms . . . . . . . . . . . . 84

A.3 Illustration of covalent bonds in silicon . . . . . . . . . . . . . . . . 85

A.5 Hole-electron pair in silicon . . . . . . . . . . . . . . . . . . . . . . 86

A.6 Hole-electron pair generation and recombination . . . . . . . . . . . 86

A.7 Electron current in intrinsic silicon . . . . . . . . . . . . . . . . . . 87

A.8 Hole current in intrinsic silicon . . . . . . . . . . . . . . . . . . . . . 87

List of Figures vii

A.9 N-type semiconductor . . . . . . . . . . . . . . . . . . . . . . . . . 88

A.10 P-type semiconductor . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Introduction

In 1905 Albert Einstein called into question the classical theory of light, proposing

a particle-like point of view of the electromagnetic radiation. This “vision” turned

out to be one of the most important breakthroughs in the field of Physics, whose

inheritors still live today.

This thesis’ aim is to propose an overview of one of them: the Silicon Photo-

Multilplier (SiPM).

SiPMs are radiation detectors with extremely high sensitivity and efficiency: they

can be used in a wide range of applications where a very low intensity radiation

must be measured with high precision. The advantages brought by SiPMs in

radiation detection (such as their high detection efficiency, low operating voltages,

ruggedness, response rapidity and insensitivity to magnetic fields) have rapidly

made these devices competitive with respect to common Photomultiplier tubes

(PMTs).

The first chapter of this work will contain an overview of the Cherenkov Tele-

scope Array experiment, currently under development. The ultimate goal of this

experiment is the investigation of the Universe through indirect observations of

very high energy gamma-rays produced by Galactic and extra-Galactic sources.

Gamma-rays can interact with the atmosphere, producing “showers” of secondary

charged particles (electrons and positrons) that may travel with speed greater than

the speed of light in the atmosphere itself, emitting Cherenkov radiation mainly

concentrated in the near ultra-violet - blue region of the electromagnetic spectrum.

This light can be collected by means of telescopes and focused on a camera to be

detected. SiPMs are one of the candidate detectors to build this camera.

In simple terms, the working principle of SiPMs (as well as the other radiation

detectors) consists in the conversion of the electromagnetic radiation impinging on

ix

Introduction x

the device in an electric signal that can be subsequently analysed. Depending on

the energy of this radiation, different processes of interaction can take place: the

second chapter will then contain an overview of the basics about radiation-matter

interactions.

In order to frame the operation of SiPMs in the more general context of radiation

detection, an overview of the main photodetectors will be presented in the third

chapter.

Finally, the fourth chapter will contain the characterization measurements of the

SiPMs produced at the Fondazione Bruno Kessler (FBK) in Trento, Italy. The

performances of these detectors will be outlined both in terms of dark performances

and response under pulsed illumination.

Chapter 1

The Cherenkov Telescope Array

In high energy astrophysics, gamma-rays play a key role for probing new physics

and investigate non-thermal phenomena where cosmic rays (CRs) are accelerated

to extremely high energies. Cosmic rays consist of charged particles travelling

across the Universe, that may interact with the atmosphere and produce showers

of secondary particles that eventually reach the surface of the Earth.

As observed on the top of the atmosphere, about 98% of the particles are protons

and heavier nuclei, while about 2% are electrons. Of the protons and nuclei, about

87% are protons, 12% are helium nuclei and the remaining 1% are heavier nuclei

[1].

CRs cover a vast range of energies, from 109 to 1021 eV, as shown in figure 1.1.

Their flux dependence follows a power law with spectral index about -2.7.

CRs acceleration can occur either directly at the place of origin, for example at

the surface of a neutron star or a super-massive black hole (SMBH), or through

the interaction with irregular cosmic magnetic fields or shock wave fronts.

In any case, gamma-rays can provide a powerful tool to trace back CRs origin, as

they are produced in hadronic cascades and they can travel long distances without

being absorbed or even deflected by interstellar magnetic fields. Experimentally,

gamma-rays can be classified in terms of their energy:

• High energy (HE) gamma rays have energies in the MeV-GeV range.

• Very high energy (VHE) gamma rays have energies in the GeV-Tev range.

1

2 Chapter 1. The Cherenkov Telescope Array

Figure 1.1: The overall differential spectra of cosmic rays from various experi-ments [1].

For many sources, the power emitted at these energies overcomes the total power

emitted at other wavelengths: for this reason gamma-ray astrophysics has attained

large attention during the last years.

The scientific community committed in the study of VHE gamma-rays is cur-

rently developing the next generation ground-based Cherenkov experiment, under

a project named Cherenkov Telescope Array (CTA).

CTA will consist of two arrays of Cherenkov telescopes, one for each hemisphere,

in order to achieve a complete coverage of the sky. The main technical goals of

CTA are:

• Increase the sensitivity by an order of magnitude with respect to current

experiments, aiming for deep observations around 1 TeV.

Chapter 1. The Cherenkov Telescope Array 3

• Increase the detection area and hence the detection rates, particularly im-

portant for transient phenomena and at the highest energies.

• Increase the angular resolution, in order to improve the ability to resolve the

morphology of extended sources.

• Provide uniform energy coverage for photons from few tens of GeV to beyond

100 TeV.

One single size telescope can hardly cover more than 1.5 decades in energy, because

of the rapid falling CRs flux with energy: for this reason, in the CTA experiment,

an array of telescopes of different sizes will be employed [2].

The scientific goals of CTA (and more generally of gamma-ray astrophysics) range

from the study of galactic (pulsar and pulsar-wind nebulae, supernova remnants)

and extragalactic (active galactic nuclei and gamma-ray bursts) targets, to the

observations about fundamental physics (for example the study of dark matter

annihilation or decays with gamma signature).

1.1 The IACT technique

When impinging on Earth, gamma-rays interact with atmospheric nuclei, thus

generating electromagnetic showers. If the gamma-ray enters the atmosphere, it

disappears by pair production 1, the electron and the positron deviating very little

from the original trajectory, and an electron-photon cascade develops [3]. These

showers have a longitudinal extension of several kilometers and a width of hun-

dreds of meters, while their maximum is located at 8-12 km of altitude in case of

vertical incidence. Depending on the energy of the original gamma, the particles

produced in the shower can penetrate deeper in the atmosphere. In the case of

gamma energies below 100 GeV, the shower quenches early and the secondary par-

ticles cannot be directly detected. However, a fraction of these products (mostly

electrons and positrons) travel with superluminal speed and emit Cherenkov light

mainly concentrated in the near UV and optical region of the electromagnetic spec-

trum (this process is schematically depicted in figure 1.2). Cherenkov light reaches

the ground practically unattenuated: Imaging Atmospheric Cherenkov Telescopes

1See Chapter 2


Figure 1.2: A sketch of the IACT technique showing the formation of an elec-tromagnetic cascade for a 300 GeV photon primary, the production of Cherenkovlight, and the formation of an image in the camera of a Cherenkov telescope.Cherenkov light production for a proton initiated cascade is shown for com-parison. The colors are proportional to the signal amplitude detected (red forthe highest, blue-violet for the lowest). Shower images produced by Konrad

Bernlohr [4].

(IACTs) reflect this light to a focal plane where a multi-pixel camera records the

shower image. At about 10km above sea level (a.s.l.), the Cherenkov threshold

for electrons is around 40 MeV, and the Cherenkov light emission angle is 0.7◦ or

less. Light emitted at the Cherenkov angle reaches the ground within a circle of

100 to 150m depending on the height a.s.l. above the detection system.

The IACT technique is particularly suited for gamma-ray astronomy for several

reasons [5]:

• the forward momentum of the shower is so great, and the Cherenkov angle of

emission is so small, that the Cherenkov light retains the original direction

of the primary photon

• at the same time, the light does spread out appreciably so that the light pool

that reaches ground level has dimensions of several hundreds of meters;

• the amount of light radiated is proportional to the total number of particles

in the shower and is not strongly absorbed in the atmosphere; hence, the


Figure 1.3: Development of proton and gamma-ray initiated air showers inthe atmosphere [5].

Cherenkov light is a calorimetric component of the shower and can be used

as a good estimator of the primary energy.

The atmospheric Cherenkov telescopes use the atmosphere as detection medium:

this has the advantage that the gas does not need to be replenished and the

detector need never be lifted into orbit. The main drawbacks come from the

environmental fluctuations in temperature, pressure and transimissivity, as well

as from the background light sources, such as the sun, the moon and the stars.

Moreover, meteors and distant lightning are annoying sources of pulsed radiation,

even if the most troublesome background is the charged hadronic component of

the cosmic radiation, which may be more than thousand times more numerous

than the expected flux of gamma-rays at these energies.

Satellite experiments (such as the currently operating Fermi mission [6]) can over-

come this difficulty by means of an anticoincidence shield. Instead, the rejection of

Cherenkov photons originating from hadronic showers can be based on the shower

features. Figure 1.3 shows the simulation of two showers, respectively initiated by

a 250GeV proton and by a 250GeV gamma-ray.


Because of the smaller transverse momentum in electromagnetic interactions, the

electromagnetic cascade is much more compact and closer to the direction of the

primary than the hadronic one. Moreover, the electromagnetic cascade does not

have penetrating particles (mostly muons), which tend to dominate the Cherenkov

light image of the shower.

As already mentioned, the Cherenkov light produced in the showers is focused on

a multi-pixel camera by means of a telescope. The shape of the showers recorded

by the camera is approximately elliptical, and its orientation depends on the angle

it makes with the optical axis of the telescope. If the latter and the shower axis

coincide, the observed image will be a circle centered on the axis; showers which

are parallel to the axis but fall up to 120m away have elliptical images whose major

axis intersects the optic axis (see figure 1.4).

One method to select gamma-initiated events is the Alpha method, described in

[5] and briefly reported hereafter.

The first selection is based on the Length and Width parameters, which have to fall

in a domain predicted by proper simulations. The orientation of these candidates

within the field of view is then analysed; those coming from the direction of the

source (center of the field of view) should have their major axis aligned so that it

passes close to the center. This pointing is characterized by the angle Alpha, as

shown in figure 1.5; if Alpha is less than 15◦, the event has the characteristics of

a gamma-ray event from the source direction.

The world largest and currently operating ground-based IACTs are H.E.S.S.,

MAGIC and VERITAS, whose pictures are shown in figure 1.6.

H.E.S.S. (High Energy Stereoscopic System) consists of an array of 4 telescopes

arranged in a form of a square with 120m of side length, each having a 12m

diameter [7]. It is located in the Gamsberg mountain in Namibia and it is operating

since 2003. A fifth telescope with 28m diameter was added in July 2012 at the

center of the array, thus extending the energy coverage towards lower energies and

improving the array sensitivity.

MAGIC (Major Atmospheric Gamma-ray Imaging Cherenkov) consists of a system

of two clone telescopes with 17m diameter and it is located in the Canary Island

La Palma in Spain [8]. It was the first telescope among those implementing the


Figure 1.4: The contours of typical Cherenkov light images as seen in thefocal plane of the Whipple Observatorya camera (diameter 3.5◦). Images ofgamma-ray showers coming from a source along the optic axis (cross) are shownby full lines; they are narrow and point towards the center. The images frombackground cosmic rays are broader and have no preferred pointing direction [5].

aThe Fred Lawrence Whipple Observatory is an astronomical observatory owned and operatedby the Smithsonian Astrophysical Observatory (SAO) and is their largest field installation outsideof their main site in Cambridge, Massachusetts. It is located near Amado, Arizona on the slopesof Mount Hopkins. The observatory is known for its pioneering work in ground-based gamma rayastronomy through the development of the IACT technique with the Whipple 10-meter telescopein the early 1980s. It now hosts the VERITAS experiment.

IACT technique to reach energies below 100 GeV and it has detected the first ever

observed gamma-ray pulses at 25 GeV from the Crab pulsar.

VERITAS (Very Energetic Radiation Imaging Telescope Array System) is an array

of four 12m optical reflectors, having the highest sensitivity in the VHE band (50

GeV - 50 TeV). It is operating at the Fred Lawrence Whipple Observatory (FWLO)

in southern Arizona, USA [9].

H.E.S.S., MAGIC and VERITAS have a focal-plane instrumentation composed

of a multi-pixel camera of photomultiplier tubes. PMTs are an optimal solution

due to their high gain and fast read-out. Their drawbacks are their sensitivity

to magnetic fields, the relatively high operating voltages (hundreds to thousands


Figure 1.5: (a) The parameters definitions used to characterize images; (b)Observations on and off -source (the excess events are taken to be the gammarays from the test object). After selection using the Width and Length parame-ters (Shape) the surviving events are sorted according to their Alpha parameter(Orientation). The values of the parameters used in the selection are derivedfrom simulations and optimized on the Crab Nebula, which is regarded as a

standard source [5].

of volts) and their limited photon conversion efficiency for Cherenkov photons,

currently about 25-30%. For this reason more performing devices (i.e. Silicon

Photomultipliers) are under research.

The use of SiPMs for a Cherenkov camera has already been implemented by FACT

[11]. A picture of the telescope is proposed in figure 1.7. It is built on the mount of

the HEGRA CT3 telescope, located at the Observatorio del Roque de los Mucha-

chos on the Canary Island of La Palma, and it is operating since 2011. The

telescope’s camera is the first focal plane installation using SiPMs as photodetec-

tors; it is composed of 1440 channels individually read out, each pixel has a FOV

of 0.11◦ yielding a total field of view (FOV) of 4.5◦. The telescope is dedicated to

the long-term monitoring of the brightest known TeV blazars 2.

2Blazars are extragalactic objects belonging to the more general class of Active Galactic Nuclei(AGN). AGNs are compact regions at the center of a galaxy, having much higher luminosity thanthe galaxy itself over at least one portion of the electromagnetic spectrum.


(a) H.E.S.S.

(b) MAGIC

(c) VERITAS

Figure 1.6: Figures 1.6a, 1.6b and 1.6c respectively show the H.E.S.S., MAGICand VERITAS telescopes.


1.2 CTA goals

The future generation of IACTs aims at overcoming a number of limitations of

the current experiments:

• current generation IACTs are sensitive in a limited energy range, from 100

GeV (MAGIC can reach 30 GeV with a special trigger) to 50 TeV. The lower

limit is due to the background caused by hadronic showers, while the upper

limit is posed by insufficient statistics;

• they have a limited field of view, of the order of 3-5◦ and a limited angular

resolution (around few arcmin);

• they have limited collection area.

On the other hand, CTA’s expected performances are [10]:

• Improved sensitivity. As shown in figure 1.8, CTA will be about a factor

10 more sensitive than any existing instrument in its energy range. In the

core range, from about 100 GeV to several TeV, CTA will have milli-Crab

(mCrab) sensitivity.

Figure 1.7: A view of the FACT telescope [11].


• Broadened energy range. By employing telescopes of different sizes and

covering an area of several km2, CTA’s aim is to cover four orders of mag-

nitude in energy, from a few tens of GeV to a few hundred TeV.

• Improved angular resolution. CTA is expected to reach angular resolu-

tions of better than 2 arc minutes for energies above 1 TeV, 5 times better

than the typical values for current instruments.

• Improved temporal resolution. With its large detection area, CTA can

resolve flaring and time-variable emission on sub-minute time scales.

Figure 1.8: Integral sensitivity for a Crab-like spectrum for several currentIACTs and Fermi (5 sigma, 1 year) and expected for CTA (5 sigma, 50h) [2].

In order to achieve the goals previously listed, the CTA experiment will employ

an array of about 100 telescopes of different sizes distributed over a large area

(1-10 km2). An artistic view of the array is proposed in figure 1.9. The array will

include:

• Large Size Telescopes (LST). These telescopes (about 4) will have a

28m diameter and their aim is to catch low energy photons (below 100 GeV),

thanks to the large reflective area.

• Medium Size Telescopes (MST). Several tens of MSTs (about 25) with

12m diameter will perform the bulk TeV search.


• Small Size Telescopes (SST). These telescopes of 4m diameter will com-

plete the array (with about 70 elements) to perform the super-TeV search.

The number of telescopes, their size and the final configuration will be studied by

means of Monte Carlo simulations.

The INFN3 CTA consortium is presently following different lines of research;

among them are the focal-plane photo-detectors, the read-out electronics and trig-

ger, the mirrors and the Monte Carlo studies. The aim is the development of a

camera for SST based on signal sampling, using SiPMs instead of conventional

PMTs.

For what concerns the detectors, the most commonly used in IACTs (and con-

sequently the baseline detector type for CTA) are photomultipliers with alkali

photo catodes and electron multipliers based on a chain of dynodes. However, the

requirements for higher sensitivity push the research efforts towards the improve-

ment of both the collection and the detection efficiency of Cherenkov photons.

In this work, Silicon Photomultipliers will be presented as possible detectors for the

Cherenkov camera. These detectors can provide higher photon detection efficiency

than current photomultipliers at lower cost, do not require high voltage supply and

do not suffer from the influence of magnetic fields. On the other hand, these devices

typically require cooling to reduce their dark count rate, are not as well matched

to the Cherenkov light spectrum as PMTs and suffer from optical cross-talk. This

noise source is related to the structure of a SiPM, which consists of a matrix

of photosensitive cells. Each of these cells can produce a signal if illuminated;

however, during the process of formation of this signal, light can be generated

3Istituto Nazionale di Fisica Nucleare

Figure 1.9: The compound of the CTA telescopes [2].


too4. From the detector’s point of view, this “new” light is not different from the

one emitted by the physical source under study. As a consequence, the detector will

“see” more light than really emitted, because of a non-perfect insulation between

cells (in this sense, cells “talk” to each other).

Chapter 4 will present a characterization study of Fondazione Bruno Kessler’s

(FBK) Near Ultra-Violet (NUV) SiPMs as suitable candidates for the realization

of the focal-plane camera. As it will be shown later, these devices already reach

a photon detection efficiency of about 30% for 380nm photons and suffer from a

relatively low cross-talk noise, while efforts are currently done to further enhance

their performances.

4See Chapter 4 for more details.

Chapter 2

Radiation Interactions

2.1 Photon interactions

In Physics the term radiation refers to both charged (e.g. electrons, protons) and

neutral particles (e.g. neutrons, photons). The operation of any radiation detector

basically depends on the manner in which the investigated radiation interacts with

the detector’s material [12].

When passing through a medium, charged particles interact with its electrons

through the Coulomb force. Depending on the energy transfer, the electrons may

be raised to a higher-lying shell within the absorber atom (excitation process) or

may be completely removed, causing the ionization of the atom itself.

Instead, uncharged radiations are not subject to Coulomb force and must first

undergo an interaction producing at least one charged particle in the final stage.

If the interaction does not occur within the detector, neutral radiation can pass

through the detector without being revealed. In this section we will focus on the

interactions of electromagnetic (e.m.) radiation with matter.

As many experiments conducted beetween the end of the 19th and the beginning

of the 20th century pointed out, e.m. radiation has a dual nature.

In fact, depending on the circumstances it can behave wavelike or particlelike. In

the latter case, e.m. radiation can be described as composed by particles called

photons (from the Greek Φως, “phos” = light). Each photon carries a well defined

amount of energy Eph and momentum pph, which are respectively given by the

following equations:

15

16 Chapter 2. Radiation Interactions

Eγ = hν =hc

λ

pγ =h

λ

(2.1)

where h is the Planck’s constant (h = 6.626× 10−34Js), c = 2.99× 108ms−1 is the

speed of light in vacuum and λ is the wavelength of the examined radiation.

In atomic and nuclear physics, as well as in high-energy physics, energies are

usually expressed in electronvolts, where 1 electronvolt is defined as the kinetic

energy gained by an electron accelerated through a potential difference of 1 volt

(1eV = 1.602× 10−19J).

From (2.1) one can easily obtain the relation between the energy of a photon

expressed in eV and its wavelength expressed in nanometers:

Eγ =1240

λ[nm](2.2)

In radiation detection there are three major types of mechanisms through which

photons and matter can interact: photoelectric absorption, Compton scattering

and pair production. All of these processes lead to the partial or complete transfer

of the photon energy to one or more electrons. As a consequence, the photon can

“disappear” or be scattered through a certain angle.

2.1.1 Photoelectric absorption

In photoelectric absorption a photon transfers all of its energy to an electron of one

of the shells of the absorber atom, thus “disappearing”. A sketch of this process

is shown in figure 2.1.

Figure 2.1: Schematic representation of photoelectric absorption [12]

The extracted electron or photoelectron has a kinetic energy given by:

Chapter 2. Radiation Interactions 17

Ee− = hν − Eb (2.3)

where Eb is the binding energy of the extracted electron. From (2.3) one can

easily observe that photoelectric absorption is a threshold process: Eb can also be

interpreted as the minimum amount of energy a photon must carry to extract the

electron.

As the electron is extracted, the absorber atom is left with a vacancy in one of

its bound shells. This vacancy is then filled through the capture of a free electron

in the medium or the rearrangement of electrons from other shells in the atom.

Therefore, one or more characteristic X-rays may also be generated.

Photoelectric absorption is the dominant process for photons with energies up to

several tens of keV. Moreover, it is enhanced for absorber materials with high

atomic number Z. Though there is not an analytic expression which is valid over

all the ranges of Eγ and Z, an approximation of the photoelectric effect probability

may be given by the following equation:

τ ≈ constant× Zn

E3.5γ

(2.4)

The exponent n can vary between 4 and 5, depending on the energy of the radia-

tion. As one can notice, (2.4) highlights a severe dependence of the photoelectric

absorption probability on the atomic number of the absorber: this is why high-Z

materials are preferred when building gamma-ray shields.

2.1.2 Compton scattering

Compton scattering takes place between an incident photon and an electron in

the absorbing material and it is the dominant process for photons with energies

of several MeV. It can be described as an elastic scattering, in which the photon

is deflected through an angle θ with respect to its original direction and transfers

part of its energy to the electron, assumed to be initially at rest.

Writing the equations for the conservation of energy and momentum for the system

illustrated in figure 2.2, one can obtain the expression that relates the energy of

the photon before and after the interaction:


Figure 2.2: Photon elastic scattering on a free electron [12]

hν ′ =hν

1 +hν

m0c2(1− cosθ)

(2.5)

m0c2 is the rest-mass energy of the electron (0.511 MeV). The probability of Comp-

ton scattering per atom of the absorber depends on the number of electrons avail-

able as scattering targets and therefore increases linearly with Z.

2.1.3 Pair production

As photoelectric absorption, pair production is a threshold process: it becomes

energetically possible if the gamma-ray energy exceeds twice the rest-mass of the

electron (1.02 MeV). In practice, the probability of this process becomes signif-

icant only above photon energies of several MeV. In this interaction the photon

“disappears” and it is replaced by an electron-positron (e− − e+) pair; the ex-

cess energy above the 1.02 MeV threshold goes into kinetic energy shared by the

electron and the positron.

Figure 2.3 shows the probability of the three processes as a function of the incident

photon energy. For energies below 100 keV the dominant process is photoelectric

absorption.

2.2 Gamma-Ray attenuation

Let us consider the prototype of a transmission experiment, whose main compo-

nents are sketched in figure 2.4.

Monoenergetic gamma rays are collimated into a narrow beam and then sent to a

detector placed after an absorber of variable thickness. The intensity of the beam


Figure 2.3: Photon total cross sections as a function of energy in carbon andlead, showing the contribution of different processes[13].

σp.e. = Atomic photoelectric effectσRayleigh = Rayleigh (coherent) scattering - atom neither ionized nor excited

σCompton = Compton scatteringknuc = Pair production, nuclear fieldke = Pair production, electron field

σg.d.r = Photonuclear interactions, most notably the Giant Dipole Resonance

Figure 2.4: The exponential curve for gamma rays measured in a transmissionexperiment[12]


is then measured and plotted against the thickness of the absorber itself. The

result should be simple exponential attenuation of the gamma rays, as also shown

in figure 2.4.

Each of the interaction processes previously described removes photons from the

beam and can be characterized by a fixed probability of occurence per unit path

length in the absorber. The sum of these probabilities gives the probability per

unit path length that the photon is removed from the beam:

µ = τ(photoelectric) + σ(Compton) + k(pair) (2.6)

and it is called linear attenuation (or absorption) coefficient. The number of

photons transmitted is then I = I0e−µt, where I0 is the beam intensity without

the absorber.

To characterize the photon one can also introduce the mean free path λ, defined

as the average distance traveled in the absorber before an interaction takes place.

It can be evaluated as follows:

µ =

∫∞0xe−µx dx∫∞

0e−µx dx

=1

µ(2.7)

Since µ varies with the density of the absorber, the mass attenuation coefficient

is more widely used:

mass attenuation coefficient =µ

ρ(2.8)

where ρ is the density of the material.

Figure 2.5 shows the absorption coefficients for different materials employed in

photodetectors. The higher the absorption coefficient, the shorter the distance

traveled by the photon; as the value of the coefficient decreases the examined

radiation can penetrate deeper into the material. In the extreme, the radiation

can pass without undergoing any interaction.


Figure 2.5: Optical absorption coefficients for various photodetectormaterials[14]

2.3 Photon detection in Silicon

As already observed, the dominant process for photon energies up to 100 keV

is photoelectric absorption. A photon excites a carrier within the material and,

under proper conditions, can produce a detectable signal. Rewriting equation (2.1)

one can obtain the minum wavelength limit for detection in a given material:

λ[nm] =1240

∆E(2.9)

where ∆E is the transition energy between the absorber atom’s levels [14]. In

semiconductors ∆E is the energy gap between the valence and the conduction

band. In Silicon (Si, Z = 14) ∆E = 1.12eV : photons with lower energies can

pass through the material without interacting. As one can observe from figure


2.5 and easily obtain from equation (2.9), Silicon is transparent for photons with

wavelength greater than about 1100 nm.

Chapter 3

Photodetectors

3.1 PMT: Photo Multiplier Tube

In science there exist different applications having in common the need for devices

able to convert a weak light pulse into a corresponding electrical signal. The

photomultiplier (PM) belongs to this class of instruments and can convert light

signals that tipically consist of no more than a few hundred photons into a usable

current pulse [12].

PM tubes are employed in many applications, including optical spectroscopy, as-

tronomy and diagnostics. Commercially available PMs are sensitive to radiations

covering the ultraviolet, visible and near-infrared regions of the electromagnetic

spectrum.

Figure 3.1 illustrates the simplified structure of a typical PMT.

The two major components of a PMT are a photosensitive layer, called the photo-

catode, and an electron multiplier structure to which the photocatode is coupled.

To allow low-energy electrons’ efficient acceleration by internal electric fields, the

apparatus inside the PM works in vacuum: the outer envelope (usually glass)

serves as a pressure boundary to sustain this condition.

When the radiation under study hits the photocatode, low-energy electrons are

extracted. Because these photoelectrons are usually a few hundred, their charge

is too small to produce a convienent electrical signal. The multiplier section of a

PM serves as amplification stage and provides a number of electrons ranging from

23

24 Chapter 3. Photodetectors

Figure 3.1: Basic elements of a PMT [12]

107 to 1010, which carry a sufficient charge to be properly detected. This charge

is collected at the anode or output stage of the multiplier structure. Most photo-

multipliers provide a linear amplification, so that the output pulse is proportional

to the original number of photoelectrons over a wide range of amplitudes.

3.1.1 The photocatode and the photoemission process

The photoemission process consists of the conversion of an incident photon into

an electron and can be thought of as occuring in three sequential stages:

1) the absorption of an incident photon and the energy transfer to an electron

within the photosensitive material;

2) the migration of that electron to the surface of the photocatode;

3) the escape of the electron from the surface.

Chapter 3. Photodetectors 25

In the first step, the energy that can be transferred to the electron is hν. Any-

way, during the migration process, some of the initial energy can be lost through

collisions with other electrons of the material. Finally, if the remaining energy is

enough, the electron can overcome the potential barrier existing at the interface

between the material and the vacuum. This potential barrier (often called the

work function) is normally greater than 3 or 4 eV for most metals.

From these energy considerations, one can easily understand that the existence of

a potential barrier imposes a minimum energy on the incoming photon, even if all

other energy losses are zero. Below this cutoff value (usually in the red or near-

infrared region of the spectrum) no emission will occur. Even for higher-energy

photons the barrier should be as low as possible, in order to maximize the number

of escaping electrons. Moreover, the rate of energy loss during electron migration

should be kept small in order to enhance the depth in the material (called the

escape depth) at which electrons may originate with sufficient energy to overcome

the potential barrier. The rate of energy loss in metals is relatively high: the

typical distance an electron can travel before its energy drops below the potential

barrier is no more than a few nanometers. Therefore, only a very thin layer of the

material will be involved in the photoemission process.

In semiconductors, the rate of energy loss is much lower and the escape depth can

extend to about 25 nm. However, this is still a very small thickness compared

to visible light penetration depth. Photocatodes of this thickness are semitrans-

parent and will cause less than half the light to effectively interact within the

photosensitive layer. Semitransparent photocatodes generally are deposited on a

transparent backing (often the glass end window of the PM tube). Light first

passes through the transparent backing and subsequently into the photocathode

layer, and photoelectrons are collected from the opposite surface.

3.1.2 Spontaneous electron emission

Impinging photons are not the only cause of the electron emission process. Con-

duction electrons within the photocatode will always have some thermal kinetic

energy that, at room temperature, will average about 25 meV. However, some

electrons may exceed this average value and have enough energy to overcome the

potential barrier, giving rise to a thermally induced signal. In metals, the thermal

emission rate is low (≈ 100/m2s) because of the relatively high barrier. Instead,


in semiconductors thermal emission rates can approach values of 106 − 108/m2s,

because of the lower barrier. The rate of thermoionic emission increases with

temperature, as more and more electrons will have the energy to escape the pho-

tocatode.

3.1.3 Quantum Efficiency and spectral response

The sensitivity of photocatodes can be estimated in terms of their quantum effi-

ciency (QE). The quantum efficiency is simply defined as

QE =number of photoelectrons emitted

number of incident photons(3.1)

Common photocatodes show values of QE that typically do not exceed 20-30%.

Figure 3.2 shows the wavelength dependence of QE for different photocatode ma-

terials. As previously mentioned, the long-wavelength cutoff is related to the fact

that the photoelectron produced has not sufficient energy to escape the surface of

the photocatode. Instead, the response at shorter wavelengths depends on the ma-

terial of the PM’s window: for normal glass, the cutoff will be at about 350 nm.

However, there are some applications which require radiation to be detected in

the ultraviolet region of the electromagnetic spectrum: in this case fused silica or

quartz windows can be used. These windows allow the extension of the sensitivity

to wavelengths as short as about 160 nm.

3.1.4 Secondary electron emission

The multiplier section of a PM, whose aim is to amplify the primary extracted

charge, is based on the phenomenon of secondary electron emission. Electrons from

the photocatode are accelerated and focused towards the surface of an electrode,

called a dynode. If the dynode material is properly chosen, the energy released by

the incident electron can cause the subsequent emission of one or more secondary

electrons from the same surface. This process is similar to the photoemission

process: in this case, however, electrons within the dynode are excited by the

passage of an electron rather than by a photon.


Figure 3.2: Quantum efficiency dependence on the wavelength of the imping-ing radiation, for different photocatode materials [15].

Electrons emitted from the photocatode have a kinetic energy on the order of 1

eV. Therefore, the kinetic energy of the electrons at their arrival on the dynode

is mostly determined by the magnitude of the accelerating voltage of the dynode

itself. Depending on the bandgap of the dynode material and on the magnitude

of the voltage a certain number of secondary electrons may be extracted. For a

bandgap of 2-3 eV and an applied voltage of 100 V, one incident electron could

theoretically excite about 30 secondary electrons. In practice, only a small fraction

of the excited electrons ultimately reach the surface of the dynode and escape. This

happens because the motion of excited electrons follows random directions, so that

many of them will not reach the surface before their de-excitation or will not have

enough energy to overcome the potential barrier.

The secondary electron yield is a sensitive function of incident electron energy.

Figure 3.3 shows the dependence of the number of secondary electrons per primary

electron (secondary emission ratio or δ) on the accelerating voltage.

Low-energy primary electrons will cause only a few electrons of the dynode mate-

rial to be excited, thus resulting in a low δ. At the same time, because the distance

of penetration is not large, most of these excited electrons will be formed near the

surface. Increasing the accelerating voltage will raise the number of dynode elec-

trons excited, but this will not necessarily lead to a higher value of δ. In fact,

the higher the energy of the primary electron, the deeper the average distance

from the surface at which dynode electrons are excited. Because the probability of


Figure 3.3: Variation of the secondary emission yield with primary electronenergy for different dynode materials [16]

escape will diminish with the increasing depth, the incident electron energy must

be properly optimized in order to maximize the observed electron yield .

The overall multiplication factor for a single dynode is given by

δ =number of secondary electrons emitted

primary incident electron(3.2)

and should be as large as possible to maximize the amplification per stage in the

photomultiplier tube.

To achieve electron gains on the order of 106, all PM tubes employ multiple stages.

Electrons leaving the photocatode are accelerated towards the first dynode and

produce δ electrons with relatively low energy for each incident photoelectron.

Similarly, these electrons are attracted to the following dynode and each of them

can generate δ new electrons. If the multiplier section of the PM consists of N

stages, the overall gain for the photomultiplier tube will be given by

G = αδN (3.3)


where α is the fraction of all photoelectrons collected by the multiplier structure.

Conventional dynode materials are characterized by values of δ = 5 and α is

approximately 1 for well-designed tubes. If N = 10 the tube gain will then be 510

or about 107.

3.1.5 Statistics of electron multiplication

The output signal of a PM is dominated by the statistical fluctuations in the

secondary electrons emission process. δ is not strictly a constant and its specific

value fluctuates from event to event about its mean value. Measuring the pulse

height spectrum of a single photoelectron would then give an indirect estimate of

the degree of fluctuation of δ.

In the most simple model, the number of secondary electrons produced at a dynode

can be assumed to follow a Poisson distribution about the average yield. There-

fore, if a single photoelectron hits the first dynode, δ secondary electrons will be

produced on average. The standard deviation of δ will then be σ =√δ and the

relative variance, defined as (σ/δ)2 will be equal to 1/δ.

A multiplier section of N stages will finally produce a mean value of electrons given

by δN . It can be demonstrated from the properties of Poisson statistics that the

relative variance in this number is

1

δ+

1

δ2+

1

δ3+ ...+

1

δN≈ 1

δ − 1(3.4)

From equation (3.4) it can be noticed that, if δ � 1, the relative variance or spread

in the output pulse amplitude is dominated by the fluctuations in the secondary

emission ratio of the first dynode.

The value of δ turns out to be crucial in applications where the signal generated

by a few photoelectrons has to be amplified. As previously mentioned, secondary

electron extraction may also occur in the absence of incident light, for example

because of thermal generation. These noise events generally produce output pulses

analogous to those associated with a single photoelectron. If the value of δ is

small, it can become impossible to separate cleanly the events caused by one

photoelectron from those in which more photoelectrons are involved. Figure 3.4

shows the expected distribution in the number of secondaries produced by the first


Figure 3.4: Statistical broadening of the secondary electron yield from thefirst dynode of a PM tube. Numbers identify the number of incident pho-

toelctrons[12]

dynode when struck by different number of photoelectrons. The larger the value

of δ the clearer the separation between the peaks.

Experimental measurements on single photoelectron pulse height spectra from

PM tubes generally show a distribution whose relative variance is larger than that

predicted by the Poisson model. This discrepancy has led to an alternate model

of the multiplication statistics in which a Polya distribution is substituted for the

simple Poisson description of electron multiplication.

3.2 Semiconductor detectors

In the last decades many efforts have been put in studying and optimizing solid

state detectors. These devices show several properties which make them more

suitable than traditional vacuum or gas-based detectors in a wide range of appli-

cations. They are more compact, lightweight, rugged and tolerant to magnetic

fields. They also allow fine pixelization, are easy to integrate into large systems,

and can operate at low electric potentials [17]. This section’s aim is to provide a

brief overview of semiconductors properties related to detectors’ physics.

3.2.1 The diode

The p/n junction or diode is the fundamental core of solid state detectors. It

is a device consisting of two joined pieces of a semiconductor (e.g. Silicon) with


different concentrations of doping atoms 1.

Figure 3.5 shows the basic structure of a diode.

The p-region of the diode is doped with donor atoms, represented with a plus sign.

In fact, after these impurity atoms “donate” an electron, they become positive

ions [19]. On the contrary, the n-region of the diode is doped with acceptor atoms,

represented with a minus sign for a similar reason.

When the junction is formed, positive ions (or holes) and electrons will diffuse

in opposite direction because of the carrier density gradient across the junction

itself. Holes drifting towards the right will neutralize the excess electrons in the

n-region and similarly will do the electrons entering the p-region of the junction.

The unneutralized ions in the neighbourhood of the junction are referred to as

uncovered charges. The general shape of the charge density ρ depends upon how

the diode is doped. Since the region of the junction is depleted of mobile charges,

it is called the depletion region. In the case we are considering, the p- and the n-

region are doped with uniform density of donors and acceptor atoms, respectively

ND and NA. This type of doping where the concentration changes abruptly from

p- to n-type is called step grading. In this simplified hypothesis the depleted charge

distribution is box-shaped, as showed in figure 3.6.

The electric field profile can be derived by solving Poisson’s equation:

1See Appendix A for more details

Figure 3.5: Basic structure of a diode[18]


Figure 3.6: Abrupt p-n junction in thermal equilibrium. Figure (a) and (b)respectively show the space charge and the electric field distribution. Dashed

lines in figure (a) indicate correction to the abrupt junction hypothesis [14].

d2V

dx2= −ρ

ε(3.5)

where ε is the permittivity. Between the two regions there exists a built-in potential

V0 called the contact difference of potential. Since at thermal equilibrium the

electric field in neutral regions (far from the junction at either side) must be zero,

the total negative charge in the p-side must be precisely equal to the total positive

charge per unit area in the n-side:

NAWDp = NDWDn (3.6)

where WDp and WDn are respectively the widths of the p- and n-depleted regions

[14].

It can also be demonstrated that the extension d of the depletion region is:


d =

√2εV0(NA +ND)

eNAND

(3.7)

where e is the elementary charge. Equation (3.6) states that the extension of the

depletion layer in each region depends inversely on the doping atom concentration:

in the case of a p+/n junction WDp will be narrower than WDn.

Because of the presence of immobile charges, a capacitance value C can be asso-

ciated to the depletion layer:

C = εA

d(3.8)

where A is the section of the depletion layer.

This formula is exactly the same expression obtained for a parallel-plate capacitor

of area A.

Forward bias To forward bias a diode, its p- and n-side must be respectively

connected to the positive and negative terminals of a voltage source, as shown in

figure 3.7.

In this configuration the majority carriers of each region have enough energy to

overcome the potential barrier at the junction and start flowing, as schematically

shown in figure 3.8.

As more electrons flow into the depletion region, the number of positive ions is

reduced; similarly, as more holes effectively flow into the depletion region on the

other side of the p/n junction, the number of negative ions is reduced. This

Figure 3.7: Forward biased p-n junction [18].


reduction in positive and negative ions during forward bias results in a reduction

of the depletion region width, as sketched in figure 3.9.

Reverse bias To reverse bias a diode, its p- and n-side must be respectively

connected to the negative and positive terminals of a voltage source, in a symmet-

rical way to that showed in figure 3.7. Figure 3.10 illustrates what happens when

a diode is reverse biased.

The positive side of the bias-voltage source “pulls” the free electrons, which are

the majority carriers in the n-region, away from the junction. As the electrons

flow toward the positive side of the voltage source, additional positive ions are

created. Similarly, in the p-region, electrons from the negative side of the voltage

source enter as a valence electrons and move from hole to hole toward the depletion

Figure 3.8: A forward biased p-n junction showing the flow of majority carriers[18].

Figure 3.9: On the left a p/n junction at equilibrium (without any bias). Onthe right, the application of a forward bias narrows the depletion region [18].

Figure 3.10: The diode during the short transition time immediately afterreverse-bias voltage is applied [18].


region where they create additional negative ions. This flow of valence electrons

can be viewed as holes being “pulled” toward the negative side. The net result is

a further depletion of majority carrier in each of the regions across the junction

and consequently a broadening of the depletion layer.

In this configuration the number of majority carriers available for conduction de-

creases with increasing width of the depletion region: no current flows into the

device, except for a very small reverse current I0, named leakage current.

Shockley’s equation describes the current dependence on the bias voltage VB ap-

plied to the junction:

I = I0

(eeVBηkT − 1

)(3.9)

where the k is the Boltzmann constant and η is a coefficient taking into account

generation and recombination processes near the junction (η ≈ 2 in silicon).

When the reverse applied voltage exceeds a value known as breakdown voltage VBD,

the current flowing in the device suddenly increases. The high reverse-bias voltage

imparts energy to the free minority electrons so that, when colliding with atoms

in the p-region, they are capable of extracting other valence electrons which are

“promoted” in conduction band. These extracted electrons have enough energy to

repeat the process, quickly multiplying the number of electrons travelling through

the p-region. As these high-energy electrons go through the depletion region, they

have enough energy to cross it without recombining with positive charges and thus

enter the n-region as conduction electrons. The multiplication process described

is known as avalanche: without a quenching resistor, once reached VBD, current

starts flowing indefinitely in the device. Figure 3.11 shows a typical volt-ampere

characteristic of a diode.

Avalanche multiplication is exploited in solid state detectors to amplify signals

otherwise too small to be measured.

3.2.2 Solid state detectors: Photodiodes and APD

The most common and widely employed radiation detectors are PMTs. However,

solid state detectors have proved to be effective substitutes when low intensity


Figure 3.11: The volt-ampere characteristic of a germanium diode redrawnto show the order of magnitude of currents [19].

radiation has to be detected with high precision. Generally, these detectors show

higher detection efficiency, require lower operating voltages, are more compact and

robust and are insensitive to magnetic fields.

As already mentioned, however, one of their main limitations is the high dark

count rate. For this reason their temperature of operation must be conveniently

monitored and stabilised.

In the following paragraph, a brief review of the main solid state detectors will be

presented. All of these devices are based on reverse-biased p − n junctions. The

main difference between photodiodes, APDs and SiPMs is the value of their oper-

ating voltage: the former two are biased below VBD, while SiPMs are conveniently

biased above VBD.

Photodiodes Photodiodes are photosensors that generate a current or voltage

when the p/n junction in the semiconductor is irradiated by light.

Figure 3.12 shows a cross section example of a Si photodiode [20]. The photoelectric

converter is formed by the P -layer and the N -layer at the substrate. By varying


Figure 3.12: Schematic of a Si photodiode cross section [20].

Figure 3.13: Effect of a photon impinging on a photodiode [20].

the thickness of the outer P -layer, N -layer and the bottom N+ layer, as well as the

dopant concentration, the spectral response of the device can be controlled. The

outer layer is generally covered with an Anti-Reflecting Coating (ACR), whose

aim is to maximize the light transmission at a given wavelength.

When a Si photodiode is illuminated by light having energy at least equal to

the band gap energy, the valence band electrons are excited to the conduction

band, leaving holes in their place in the valence band 3.13. This hole-electron

pair generation can occur at any point within the detector, depending on the

wavelength of the incident light. If a pair is created within the depletion layer,

the electric field within this region will make the electron and the hole drift in

opposite directions and eventually reach the electrodes, thus producing an output

current proportional to the number of pairs created (and therefore to the number

of impinging photons).


A layout further improving the simple photodiode performances is shown in figure

3.14.

An almost undoped (intrinsic) layer of semiconductor is inserted between the p-

and the n- layer. The advantage brought by this expedient is the enhancement

of the active area of the device, because the depletion layer practically spreads

throughout the intrinsic layer due to its low level doping.

Conventional and p-i-n photodiodes performances are mainly limited by the ab-

sence of a charge multiplication process: for this reason they are not suitable for

detecting single photoelectrons signals.

APD: Avalanche PhotoDiodes Avalanche Photodiodes aim at overcoming

this limit by increasing the device operating voltage, still biasing the junction

below the breakdown voltage. A schematic representation of an APD is proposed

in figure 3.15.

In these devices, the intense electric field within the junction allows avalanche

multiplication. This condition leads to the amplification of the initial signal, with

gain factors around 103. As sketched in figure 3.15, a photon enters the device

through the SiO2 window. It is then converted in a hole-electron pair and, because

of the intense electric field, triggers an avalanche process. The produced charges

pass across a drift region and are then collected.

It is worth noticing that an APD, while allowing avalanche multiplication, still

operates in linear regime: the amplitude of the output signal will be proportional

to the initially produced charge and, hence, to the number of impinging photons.

Figure 3.14: P-I-N photodiode, from http://www.rp-photonics.com/p_i_

n_photodiodes.html.

http://www.rp-photonics.com/p_i_n_photodiodes.html

http://www.rp-photonics.com/p_i_n_photodiodes.html


Figure 3.15: Simplified structure of a common APD. On the left is shown theelectric field profile along the device vertical section [21].

Geiger Mode APDs When a p/n junction is biased above the breakdown

voltage, a single hole-electron pair can trigger a self-sustaining avalanche. An

APD operating in these conditions is also called Geiger-Mode APD (GM-APD):

its gain factor ranges from 104-107, even with relatively low applied voltages (few

tens of volts).

In this case, any proportionality between the initially released charge and the out-

put signal is lost. Thanks to its high gain the device is able to amplify single-photon

induced signals, even if the produced pulse will have the same characteristics of a

multi-photon induced one.

As it will be shown in the next chapter, to overcome this difficulty silicon pho-

tomultipliers are arranged in a matrix structure, where each pixel consists of a

GM-APD.

Chapter 4

SiPM Characterization

4.1 The work at FBK

This section’s aim is to describe the work conducted at the Fondazione Bruno

Kessler, Trento - Italy (FBK) Silicon Radiation Sensors (SRS) laboratory. My in-

ternship work consisted in characterizing the Near Ultra-Violet (NUV) technology

of FBK Silicon Photomultipliers in terms of I-V, Dark Count Rate and Photon

Detection Efficiency (PDE) performances. A sketch of the structure of a NUV

SiPM is shown in figure 4.1. It basically consists in a p+/n structure, optimized

for the detection in the NUV-blue region of the electromagnetic spectrum through

proper doping and design.

Figure 4.1: Structure of a Near Ultra-Violet FBK SiPM. The active area isat the interface between the p+ and the n region.

41

42 Chapter 4. SiPM Characterization

Figure 4.2: Basic Structure of a Silicon Photomultiplier [22]

Figure 4.3: The equivalent circuit of a Geiger-Mode Avalanche Photodiode.RS is the silicon substrate series resistance [22]

4.1.1 Introduction

Silicon Photomultipliers (SiPMs) are radiation detectors with extremely high sen-

sitivity and efficiency.

They basically consist of a matrix of reverse biased p/n junctions connected in

parallel, as shown in figure 4.2. Each cell works beyond the breakdown voltage

(VBD) as a Geiger-Mode Avalanche Photo-Diode (GM-APD) and it is equipped

with a quenching resistor Rq. The equivalent circuit of a single GM-APD is shown

in figure 4.3

Chapter 4. SiPM Characterization 43

Each of the GM-APDs composing the SiPM is biased at VBias = VBD + VOV (VOV

is the excess voltage beyond VBD) and the switch in the equivalent circuit is open,

meaning that no current flows within the device (except leakage currents). Cd

is the capacitance associated to the junction when it is reverse biased. When a

photon hits one cell a hole-electron pair will be created. Because of the electric

field within the active area of the cell itself, these carriers can trigger an avalanche

multiplication process that eventually leads (after proper amplification) to a de-

tectable signal. In the equivalent model, this corresponds to the closing of the

switch and the subsequent Cd discharge from VBias to VBD through RS. Thanks

to Rq the avalanche process is quenched: the switch opens and Cd recharges to

VBias through Rq. The Cd discharge and recharge will produce an output pulse

with time constants τr = Cd ×Rs and τf = Cd ×Rq respectively.

Thanks to its matrix structure, a SiPM can detect simultaneously more than one

photon. If N photons impinge on N different cells of the SiPM, a current pulse

proportional to the number of fired cells will be produced. The saturation value

of this pulse depends on the total number of cells the SiPM is composed of.

Carriers in silicon can also be generated by thermal agitation. When a thermally

produced hole-electron pair triggers an avalanche, an output pulse identical to

a single-photon one will be observed. This kind of event is called a dark event,

because it produces a signal that cannot be distinguished from a light-induced one

even if the device is not exposed to any light source. The number of dark events

per unit time is called Dark Count Rate (DCR).

Thermal generation represents the primary noise source in Silicon Photomultipli-

ers. Besides this one, two other noise sources must be taken into account when

estimating the DCR of a SiPM: aferpulsing (AP) and optical-cross talk (OC).

Both AP and OC counts follow a previous event, either a dark or a photon-induced

one: for this reason they are referred to as correlated noise [22].

Afterpulsing is caused by carriers trapped in silicon defects during the avalanche

process. These carriers are released at a later stage, during the recharge phase of

the GM-APD: as sketched in figure 4.4a, a new pulse will be observed on the tail

of the previous one.

During an avalanche multiplication process, there is a finite probability for a pho-

ton to be emitted and subsequently absorbed in the sensitive area of a neighbouring


(a) Afterpulsing in a SiPM (b) Cross-Talk in a SiPM

Figure 4.4: Figure 4.4a shows the typical output observed when an afterpuls-ing event takes place. Figure 4.4b shows a single-cell signal (on the left), a directcross-talk signal (in the middle) and a delayed cross-talk signal (on the right)

rising a few nanoseconds after the primary pulse [22].

cell, thus giving birth to a new avalanche. This kind of event is called a direct

optical cross-talk event. Considering the speed of light in silicon (vSi = c/nSi

where n ≈ 3.4 is the refractive index of crystalline silicon) and the rapid avalanche

ignition in GM-APDs, the time delay between the original event and the optical

cross-talk one is about 10−13s for distances between cells of about 10µm. In the

case of a single-photon primary event followed by OC, the resulting output will

be identical to a double pulse produced by two simultaneously fired cells, as il-

lustrated in figure 4.4b. Photons emitted during avalanche processes can also be

absorbed in the inactive regions of the SiPM. The generated carrier would then

have to diffuse to the active region of a cell before triggering an avalanche, thus

giving origin to a delayed cross-talk event after a few nanoseconds.

The analysis method developed by FBK [23] allows to easily estimate the DCR of

a SiPM and distinguish the different components of correlated noise, as it will be

described later on.

The response of a SiPM can be quantified by means of its Photon Detection Effi-

ciency (PDE). Photon Detection Efficiency can be defined as the ratio of detected

photons over the number of incoming ones. PDE can also be described in terms

of the device’s characteristics as the product of three factors:

• Quantum Efficiency (Q.E.): it expresses the probability for a photon to

be converted in a hole-electron pair.


• Triggering Probability (Pt): it is the probability that the generated pair

triggers an avalanche.

• Geometry Efficiency or Fill Factor (FF): it specifies the active area of

the cell.

As it will be shown in the results section, PDE depends on both the wavelength

of the impinging radiation and the voltage at which the device is biased.

4.1.2 Experimental procedure

The analysed FBK devices are:

• 1x1mm2 NUV SiPM with 40µm cell

• 1x1mm2 NUV SiPM with 40µm cell, covered with a layer of resin

• 1x1mm2 NUV SiPM with 50µm cell

I-V and dark measurements The first step of the characterization process

consists in measuring the forward and reverse I-V curve of the device. The exper-

imental setup is very simple and it is shown in figure 4.5. The system is kept at

fixed temperature by means of a climatic chamber.

Figure 4.5: Schematic view of the apparatus for the I-V measurements.

As already mentioned, a SiPM needs to be reverse biased beyond the breakdown

voltage VBD when used as a radiation detector. VBD is the minimum bias that can

cause a self-sustaining avalanche process: this means that, without any quenching

resistor, current will flow indefinitely within the device. The breakdown voltage


can be determined from the reverse I-V characteristic of the SiPM and depends

on several structural features as well as on temperature [24].

As shown in figure 4.2, a SiPM consists of a parallel arrangement of p/n junctions,

each one equipped with a quenching resistor. The value of Rq can be determined

by fitting the ohmic portion of the forward I-V curve beyond the knee.

After the I-V characterization the dark measurements can begin. The setup is

shown in figure 4.6.

Figure 4.6: Schematic view of the apparatus for the measurements in dark.

The SiPM is placed in the climatic chamber and biased at a certain voltage beyond

VBD. The output signal is then amplified and sent to the oscilloscope. Finally,

the acquired data are processed and analysed by means of a Lab-View acquisition

software [25].

The process starts with the acquisition of 1ms-long waveforms. The simplest

method to give a first estimate of the total dark rate of the device would then

consist in counting the pulses that cross a chosen threshold Vth (this method is


Figure 4.7: The DLED method. The original signal is first delayed and thensubtracted to itself, in order to suppress the long tail [26].

known as the Leading Edge Discriminator - LED). Actually, since each pulse is

characterized by a long tail, the amplitude discrimination is not always straight-

forward because of the piling-up phenomenon. For this reason, the signal is filtered

by means of the Differential Leading Edge Discriminator (DLED) technique be-

fore being analysed [23]. Figure 4.7 schematically shows the DLED method. This

method exploits the difference between the time constants of the rising and the

falling edges of the pulse from a single cell, also called Single Cell Response (SCR).

A slightly delayed (∆t ≈ 1ns) replica of the acquired waveform is subtracted to

the original one, in order to preserve only the fast rising edge of each signal. The

DLED waveform is then analysed through a traditional LED discriminator in order

to characterize the DCR of the SiPM.

The software stores in two different arrays the amplitudes and the time distances

between the pulses that cross the threshold. The amplitude of each event as a

function of its time distance from the preceding one is then plotted. An example

of this scatter plot is shown in figure 4.8 for measurements performed on the

1x1mm2 with 50µm cell SiPM. All the different components that contribute to

the DCR of the device are visible:

• points with amplitude around 1 and placed between 2µs and 80µs are pri-

mary dark events; the density of these events follows a Poisson distribution.

• points with amplitude between 0.5 and 1 that lie between 20ns and 600ns

are afterpulsing events. The minimum amplitude does not fall below 0.5

because this is the value typically chosen as a threshold.

• points with amplitude exceeding 1 correspond to direct cross-talk events,

while those with amplitude 1 and time distance ranging from a few ns to

20ns are delayed cross-talk events.


Figure 4.8: Scatter plot of pulses amplitudes as a function of their time dis-tance from a previous event.

This classification has been tested by means of Montecarlo simulators, as explained

in [23].

In order to extract the primary DCR, an histogram of the time distances between

the dark events is built. As already mentioned, the density of primary dark events

follows a Poisson distribution: the part of the histogram corresponding to these

events is then fitted with an exponential law, whose decay constant represents the

DCR. The histogram corresponding to the scatter plot shown above is proposed

in figure 4.9.

The software also shows the amplitude and the cumulative amplitude histograms.

The DCR on the y scale is calculated as the average number of events divided by

the time length of the acquired waveform. The histograms shown in figures 4.9

and 4.10 refer to the same device of figure 4.81 1.

Finally, the acquisition software evaluates other parameters from the original sig-

nal (not filtered with the DLED), such as the device gain (expressed in carriers

11Graphs shown in figures 4.8, 4.9, 4.10 are realized with the data acquired by the acquisitionsoftware described


Figure 4.9: Time distance distribution of dark events. The continuous redline is the exponential fit, started from 10µs (dashed vertical line).

Figure 4.10: Amplitude (blue) and cumulative (red) amplitude histograms


Figure 4.11: Schematic of the apparatus for measurements under pulsed LEDillumination.

number) or the mean amplitude and time constant of a typical pulse, as described

in detail in [23].

Pulsed LED Measurements As previously mentioned, the response of a SiPM

can be expressed in terms of its PDE, defined as the ratio of the detected photons

over the incoming ones. It is then necessary to have a system that allows to know

the number of photons impinging on the device as well as a method to extract

informations about the revealed ones. A scheme of the apparatus employed for

measuring the SiPMs performances under pulsed LED illumination is shown in

figure 4.11.

The pulser is used to set the operating voltage of the LED, the duration of the light

pulse and the period of each pulsing cycle (the value typically chosen is T = 20µs).

The light emitted by the LED is guided to an integrating sphere by means of an

optical fiber. The sphere is mounted on a mechanical support along with the

amplifier and the SiPM, as illustrated in figure 4.12. A calibrated photodiode,


placed on top of the sphere, gives informations about the number of photons sent

on the device area. The acquisition is triggered by the pulser: the amplified signal

is then sent to the oscilloscope and finally fed to a LabView software.

Figure 4.12: Mechanical support for measurements under pulsed LEDillumination.

SPAD Measurements One method to extract a SiPM efficiency is to test one

of its cells, also called Single-Photon Avalanche Diode or SPAD. The advantage

brought by using a SPAD is to reduce the contribution of correlated noise to

the measure, for a SPAD does not suffer from optical cross-talk. Moreover, the

device behaves as a “digital” instrument: it can count at most a photon at a time,

producing an output pulse with an amplitude in the range of a value depending

only on the bias voltage. It is then easier to separate the pedestal events (in

which the acquisition is triggered by the pulser but no photon is revealed) from

the light ones (see figure 4.13). For the same reason, it is though reasonable to

avoid sending on the SPAD a high number of photons, as the output would be a

single-photon pulse in any case.

For the reasons listed above, the response of a SPAD can be tested for relatively

high over-voltages, as it will be shown in the results section. Instead, when evalu-

ating a SiPM PDE, it becomes more difficult to test the device beyond 4V of OV,

as the correlated noise probability worsens the measurement.

Depending on the response of the employed LED, the time distribution of the light

pulses can vary from a few nanoseconds to a few hundreds of nanoseconds. Before

starting the measurement it is then necessary to properly choose the time length

of the acquisition window.


Figure 4.13: 40µm SPAD amplitude histogram under pulsed LED illumina-tion.

The software acquires a certain number of waveforms in the user-defined time win-

dow. For each of them, it allows the measurement of different quantities, as the

amplitude maximum or the integral of the signal. The chosen quantity is then

histogrammed and the histogram saved in a text file: for the SPAD measurements

the software was set to evaluate the maximum amplitude of the analysed wave-

forms. These operations can be repeated varying a series of parameters taken as

an input by the software, e.g. the bias voltages or the acquisition mode (light only,

dark only or alternate).

The PDE can be evaluated using the following expression:

PDE =N1,light −N1,dark

Npulses ×Nph/pulse

(4.1)

N1,light and N1,dark are respectively the single-photon counts in the presence or

absence of the light source; Npulses is the total number of acquisitions (defined by

the user) while the quantity Nph/pulse represents the number of photons sent on

the detector in a single pulse and varies depending on the chosen LED and the

device area.


As it can be inferred from (4.1), the acquisition procedure for a fixed LED wave-

length consists in a light-dark cycle repeated over a chosen range of over-voltages,

incremented by a fixed step (usually 0.5V) every new cycle. The analysis software

takes care of implementing equation (4.1).

SiPM Measurements The PDE for a SiPM can be evaluated following a pro-

cedure similar to the one described for the SPAD measurements. In this case:

PDE =λlight − λdark

λimp, (4.2)

where λlight and λdark are the mean values of the amplitude or charge distributions

of the acquired signals, while λimp is the number of photons impinging on the device

(as in the previous case, λimp = Npulses ×Nph/pulse).

The probability function for the above mentioned distributions should follow a

Poisson law:

fk(λ) =λk

k!e−λ (4.3)

Actually, when the correlated noise contribution becomes relevant, the distribu-

tions show deviations from (4.3) that can be taken into account using the expres-

sion derived by S. Vinogradov [27]:

fk(p, λ) =

e−λk∑i=0

Bi,k[λ(1− p)i]pk−i

k!

Bi,k =

1 if i = 0 and k = 0

0 if i = 0 and k > 0

k!(k−1)!i!(i−1)!(k−i)! otherwhise

(4.4)

where λ and p are respectively the mean value of the simple Poisson law and the

correlated noise probability. As reported in the article, it is assumed that each

pixel of the SiPM produces an identical pulse regardless of its origin (whether

primary or not). Moreover, it is assumed that:

• The number of primary pulses (produced by impinging photons or thermal

generation) is a random variable belonging to Poisson distribution.


• Every primary event may produce an infinite chain of secondary events (both

cross-talk or afterpulsing events) with the same probability p for each sec-

ondary event, that is one preceding event may produce 0 or 1 succeeding

event. The number of secondary pulses is then a random variable following

a geometric distribution.

• All produced events are measured including all events in the tails.

4.1.3 Results

In this section the results of the measurements on the previously listed devices

will be presented. The performances of the 40µm-cell SiPMs (with and without

resin) will be reported and compared to those of the SiPM with 50µm cell.

I-V Measurements Figure 4.14 and 4.15 show the reverse and forward I-V

measurements on the 1x1mm2 device with 40µm cell, repeated at different tem-

peratures (T = −20◦C, 0◦C, 20◦C, 24◦C). As it can be observed, the breakdown

voltage drops by 25mV every degree, while the quenching resistor dependence on

temperature is shown in figure 4.16. The breakdown voltage variation with tem-

perature is relatively low if compared to other existing technologies (Hamamatsu

multi-pixel photon counters show variations of about 60mV/◦C [28]): this will

allow slighter temperature corrections for the telescope cameras. Moreover, know-

ing the values of the quenching resistor gives informations about the signal decay

constant (τf = Cd ×Rq, as previously mentioned).

Similar measurements have been carried out for the other devices, showing break-

down voltages in the range of 25V.

Dark Measurements Figure 4.17 shows the primary DCR dependence on the

applied OV for the 1x1mm2 device with 50µm cell, repeated at different temper-

atures (T = −20◦C, 0◦C, 20◦C, 24◦C). DCR eventually saturates with increasing

OV, up to about 150kHz at 3V of OV for the 24◦C curve. As it can be observed in

figure 4.18, DCR halves about every 9.2◦C (data points have been fitted with an

exponential law [14]). Figure 4.19 shows the OV dependence of the correlated noise

probabilities for the same device. Afterpulsing and delayed cross-talk probabilities

are not always easily distinguishable from the time distance histogram shown in


Figure 4.14: Reverse I-V characteristics of a NUV 1x1mm2 SiPM with 40µmcell at different temperatures.

Figure 4.15: Forward I-V characteristics of a NUV 1x1mm2 SiPM with 40µmcell at different temperatures.


Figure 4.16: Quenching resistor of a NUV 1x1mm2 SiPM with 40µm cell asa function of the temperature.

figure 4.9: for this reason, their contribution is considered as a single one. It can

be noticed that correlated noise probabilities do not depend on temperature.

As it can be observed from figure 4.20 the presence of the resin does not signif-

icantly alter the SiPM performances, neither in terms of primary DCR nor for

what concerns correlated noise probabilities.

Figure 4.21 shows the comparison between the 50µm and the 40µm cell technolo-

gies. At a fixed over-voltage, the former shows lower correlated noise probabilities:

this difference is due to the lower fill factor.

Pulsed LED Measurements Figure 4.22 shows the OV dependence of the

PDE, measured for different LED wavelengths. As it can be observed, both tech-

nologies (with 50µm and 40µm cell) are optimized for light detection in the blue

region of the spectrum. For a given over-voltage in this region, the 40µm-cell

device shows PDEs equal to about twice those of the 50µm-cell device. It is worth

noticing that the detection efficiency for 380nm radiation already reaches about

30%, even if the device best performances are recorded beyond 400nm.


Figure 4.17: Dark Count Rate (DCR) of a NUV 1x1mm2 SiPM with 40µmcell as a function of the over-voltage, at different temperatures.

Figure 4.18: Dark Count Rate (DCR) of a NUV 1x1mm2 SiPM with 40µmcell as a function of temperature, at a fixed over-voltage.


(a) 1x1mm2 - 40µm cell, Direct Cross-Talk probability

(b) 1x1mm2 - 40µm cell, Delayed Cross-Talk and Afterpulsing probabilities

Figure 4.19: Figure 4.19a shows the direct CT over-voltage dependence of theSiPM at different temperatures. Figure 4.19b shows the contribution of delayed

CT and afterpulsing.


(a) 1x1mm2 - 40µm cell with resin, PrimaryDCR

(b) 1x1mm2 - 40µm cell with resin, DirectCross-Talk probability

(c) 1x1mm2 - 40µm cell with resin, DelayedCross-Talk and Afterpulsing probabilities

Figure 4.20: Primary and correlated noise comparison between a SiPM cov-ered with an resin layer and a “naked” SiPM. Figure 4.20a shows the primaryDCR of the SiPM at different temperatures. Figure 4.20b shows the direct CTover-voltage dependence of the SiPM at different temperatures. Figure 4.20c

shows the contribution of delayed CT and afterpulsing.


(a) 1x1mm2 - 50µm cell, Primary DCR

(b) 1x1mm2 - 50µm cell, Direct Cross-Talkprobability

(c) 1x1mm2 - 50µm cell, Delayed Cross-Talkand Afterpulsing probabilities

Figure 4.21: Primary and correlated noise comparison between SiPMs withdifferent cell size. Figure 4.21a shows the primary DCR of the SiPM at differenttemperatures. Figure 4.21b shows the direct CT over-voltage dependence of theSiPM at different temperatures. Figure 4.21c shows the contribution of delayed

CT and afterpulsing.


The experimental data are fitted with an exponential law [29]:

PDE(λ,OV ) = η(λ)Pt(OV ) = η(λ)(

1− e−OVV0

)(4.5)

η(λ) is the product between the photon absorption efficiency and the collection

efficiency of the generated carriers, while Pt is the triggering probability. V0 is a

normalizing coefficient: after about 3 V0 of OV, the PDE eventually saturates to

η(λ). The wavelength dependence of V0 for the 50µm SPAD is shown in figure

4.23


(a) 50µm SPAD, Photon Detection Efficiency

(b) 40µm SPAD, Photon Detection Efficiency

(c) 40µm SPAD with resin, Photon Detection Efficiency

Figure 4.22: Comparison between PDE in SPADs with different size. Figure4.22b shows the PDE dependence on the over-voltage for a 40µm SPAD. Figures4.22c and 4.22a respectively refer to a 40µm SPAD with resin and to a 50µm

SPAD.


Figure 4.23: V0 dependence on the LED wavelength for the 50µm SPAD.

The difference between short and long wavelengths depends on the type of carrier

(electron or hole) triggering the avalanche. Let us first consider light penetration in

silicon. Figure 4.24 shows the wavelength dependence of the absorption coefficient

for different materials: the longer the wavelength, the longer the distance the light

can travel without being absorbed.

Let us now consider the simplest geometry of a p/n junction, showed in figure

4.25. The electric field within the depletion region is directed from the n-doped

region to the p-doped one, and its profile can be derived by solving the Poisson

equation. When impinging on the active area of the device, a photon will create

a hole-electron pair: because of the electric field, the electron and the hole will

respectively drift (in this particular case) towards the right and the left, eventually

initiating an avalanche multiplication process with probability Pt.

Pt depends on both Pe(x) and Ph(x), defined as the probabilities that an electron or

a hole starting at a position x within the depletion layer will trigger an avalanche,

as reported by Oldham [30]. Oldham’s treatment is developed for a n+/p structure:

the results can be easily applied to the symmetric case of a p/n device. The

coordinate x = 0 is taken at the n+ edge of the space-charge region, while the

coordinate x = w is taken at the p edge.


If one electron-hole pair is created at position x, the probability that neither the

electron nor the hole causes an avalanche is given by (1 − Pe)(1 − Ph). As a

consequence, the probability for an avalanche to be triggered is given by:

Pt = Pe + Ph − PePh (4.6)

Similarly, the probability Pe(x+∆x) that an electron starting at a position x+∆x

triggers an avalanche is the sum of three terms:

• The probability that it triggers an avalanche after it reaches the position x.

• The probability that in the transit from x + ∆x to x an ionization occurs

that leads to an avalanche multiplication. This term is given by the product

of Pt with the probability that a pair is generated in the transit αe∆x (αe is

the electron ionization coefficient).

• The negative of the product of the first two terms.

The equation for Pe(x+ ∆x) is then:

Figure 4.24: Wavelength dependence of the absorption coefficients for differentmaterials, from http://www.photonics.com/.

http://www.photonics.com/


Figure 4.25: Schematic diagram of a p/n junction (a), including the chargedensity (b), the electric field intensity (c) and the potential energy barriers at

the junction ((d) and (e)) [19].

Pe(x+ ∆x) =Pe(x) + αe∆x[Pe(x) + Ph(x)− Pe(x)Ph(x)]

− Pe(x)αe∆x[Pe(x) + Ph(x)− Pe(x)Ph(x)](4.7)

In differential form, the following expressions for electrons and holes can be written:

dPedx

= (1− Pe)αe[Pe + Ph − PePh]

dPhdx

= −(1− Ph)αh[Pe + Ph − PePh](4.8)


with boundary conditions

Pe(0) = 0

Ph(w) = 0(4.9)

Equations (4.8) with boundary conditions (4.9) can be solved numerically. Figure

4.26 shows the triggering probabilities calculated for both electrons and holes at

different over-voltages.

Figure 4.26: Triggering probabilities Pe and Ph of an n+/p diode at differentover-voltages. Pe(x,∆V ) is the probability that an electron starting at positionx will trigger an avalanche in a diode biased ∆V volts beyond the breakdown.

Ph refers to holes [30].

In the case of a NUV device (i.e. with a p/n structure), a short wavelength

photon will create a hole-electron pair near the p edge of the depletion layer: the

ignition of the avalanche process will be practically caused by an electron. A long

wavelength photon, instead, will generate a pair deeper within the device, near


the n edge of the depletion region: in this case the avalanche will be started by a

hole. Moreover, it can be noticed that, in these extreme cases, the curves in figure

4.26 show a higher triggering probability for the electrons, at a fixed bias beyond

the breakdown (this difference is more evident for low over-voltages). This means

that, as the plot in figure 4.23 highlights, the over-voltage needed to saturate the

PDE is higher for the holes than for the electrons. In the intermediate wavelength

region, both electrons and holes contribute to the avalanche triggering.

As it can be observed, the higher fill factor for the 40µm cell technology results in a

higher PDE for a fixed OV with respect to the 50µm cell, while the presence of the

resin slightly worsens the device performances in the violet-blue region, perhaps

because of light absorption in that wavelength range.

PDE measurements with SiPMs showed similar results. By way of example figure

4.27 shows the charge and the Poisson distributions for a 1x1mm2 SiPM with

40µm cell.


(a) 1x1mm2 with 40µm cell, charge distribution

(b) 1x1mm2 with 40µm cell, Poisson Distribution

Figure 4.27: Figures 4.27a and 4.27b respectively show the charge and Poissondistributions for a given wavelength and applied bias. The blue line representsthe simple Poisson fit, while the black one uses expression (4.4), correctly taking

into account correlated noise probability (the black line is fictitious).


The FBK NUV technology with 40µm cell shows relatively low DCR (up to a few

hundreds of kHz at room temperature) as well as low cross-talk probabilities.

The enhanced fill factor with respect to the 50µm cell SiPMs results in a higher

PDE (up to 45% with SPADs).

Moreover, the presence of the resin does not affect the SiPM performances, neither

in terms of dark counts nor for what concerns the measurements under pulsed LED

illumination.

4.2 The work at INFN Bari

In this section, the work conducted at the Laboratory of the INFN group in Bari

will be described. A comparison between FBK 1x1mm2 NUV SiPM with 40µm

and 50µm cell will be presented. The devices have been characterized in terms of

their gain (expressed in mV/P.E.), signal-to-noise ratio (SNR) and mean number

of photons detected.

4.2.1 Experimental Procedure

The setup employed for the measurements is schematically shown by the block

diagram in figure 4.28.

The SiPM and the amplifier are placed in a dark box, and properly biased by

means of a voltage supply (a picture of the dark box is shown in figure 4.30).

Before starting the measurements under pulsed led illumination, an I-V charac-

teristic of the device is acquired. Figure 4.29 shows the reverse I-V plot of the

Figure 4.28: Block diagram of the setup for measurements at INFN - Bari.


Figure 4.29: Reverse I-V characteristic of a NUV 1x1mm2 SiPM with 40µmcell. The errors are of the order of 1pA and hence not visible in the plot.

NUV FBK SiPM with 40µm cell: as already found in the measurements at FBK,

this device exhibits breakdown voltages in the range of 25V at room temperature

(25±0.2◦C).

The light of a 380nm pulsed diode laser is sent on the device, with frequency 10Hz;

the pulses are controlled by means of a pulse generator. The laser head, as well as

the SiPM, are kept at a fixed temperature (∼ 25◦C) using Peltier cells. Once the

system is stable, 5000 10ns long waveforms are acquired by means of an oscilloscope

and then fed to a LabView software. The software searches the maximum of each

acquired waveform at a fixed time, chosen as the mean value of the distribution of

times at which each minimum is detected. It can be noticed that this distribution

has a width of about 150 bins around the mean value, corresponding to about

600ps with the chosen time resolution: this number can be considered as a rough

estimate of the laser time jitter. The acquired amplitude values are then printed

on a text file and analysed. A view of the user interface of this program is shown

in figure 4.31.

The recorded amplitudes are histogrammed and then fitted with a multigauss

function, where each peak is fitted with a simple gaussian function:


Figure 4.30: Detail of the apparatus employed for the measurements. Thediode laser head is placed on top of the box, where the SiPM (properly placed

on its support) can be inserted.

Figure 4.31: On top of the figure the online-built histogram. Each point ofthe histogram corresponds to the amplitude recorded at the mean value of the

time distribution in red. On the right, the pedestal amplitude distribution.

f(x) = ce−12(x−µσ )

2

(4.10)

µ and σ are the mean value and the standard deviation of the gaussian function.

The first peak represents the so called pedestal : it corresponds to those events in

which the pulser triggers the acquisition but no signal falls in the time window.

The other peaks collect the amplitudes of the signal originated from one or more

photoelectrons.


(a)

(b)

Figure 4.32: Top (4.32a): another view of the acquisition software. Some ofthe input parameters are: the total number of waveforms to acquire and process,the output oscilloscope channel and the time value at which the minimum is

searched. Bottom (4.32b): oscilloscope acquisition.

Therefore, depending on the number of pixel fired, a signal with an amplitude

around a given peak mean value will be observed, as shown in figure 4.33. Each

photoelectron corresponds to an amplitude gain that can be evaluated from the

following expression:


Figure 4.33: Signals from a different number of photoelectrons show differentamplitudes.

G(mV/P.E.) = µi − µped (4.11)

where µi is the mean value of the i -th peak.

The device performances can be analysed in terms of its signal-to-noise (SNR)

ratio, defined as the ratio between the mean value of the a peak and the pedestal

standard deviation. Finally, to extract the mean number of photoelectrons de-

tected, the areas under each peak are evaluated and fitted with a Poisson distri-

bution after being normalized.

4.2.2 Results

In this section, the amplitude distributions for different over-voltages are here

presented for both the devices, as well as their gains, SNRs and mean values of

detected photons.

As it can be noticed, the gain of the 50µm-cell device is greater than the 40µm-

cell one, as well as the SNR. In both cases, the signal-to-noise ratio eventually


saturates with the device gain: it would then be useless to further increase the

device operating voltage.

However, the SiPM with 40µm cell detects more photons than the device with

50µm cell, as it can be noticed from the plot in figure 4.39. Moreover, at a fixed

gain (i.e. 9.3 mV/P.E., corresponding to an over-voltage of 2V and 4V for the

50µm and the 40µm device respectively), the detection efficiency of the 40µm-cell

(a)

(b)

(c)

Figure 4.34: Amplitude distributions for the 1x1mm2 with 50µm cell device,at different over-voltages.


device is greater by a factor ∼ 2− 3 than the efficiency of the 50µm-cell one. This

result confirms the observations with the SPAD.

The observed discrepancy between the mean number of photoelectrons extracted

from the different fits is due to the cross-talk events. As already discussed, cross-

talk events take their roots in the avalanche developing: there is a finite probability

for a generated hole-electron pair to recombine, thus producing a photon that may

eventually trigger an avalanche in a neighbouring cell. The net effect of this noise

source is to shift the amplitude distribution to higher values of detected photons:

the device actually “sees” a higher number of photons, as shown in figure 4.39.


(a)

(b)

(c)

(d)

Figure 4.35: Amplitude distributions for the 1x1mm2 with 40µm cell device,at different over-voltages.


(a)

(b)

Figure 4.36: Gains for the 1x1mm2 with 50µm and 40µm cell devices.


(a)

(b)

Figure 4.37: SNR for the 1x1mm2 with 50µm and 40µm cell devices.


(a)

(b)

Figure 4.38: SNR for the 1x1mm2 with 50µm and 40µm cell devices as afunction of the bias.


(a)

(b)

(c)

Figure 4.39: Poisson distributions for the 1x1mm2 with 50µm cell device.

Conclusions

As it has been outlined throughout this work, Silicon Photomultipliers are nowa-

days mature and competitive detectors. Their application as sensors for a Cherenkov

camera in the framework of the CTA experiment is being studied. In this contest,

the research efforts are concentrated on the development of high detection effi-

ciency photodetectors for the realisation of SST and MST telescopes, which will

make up the major number of the telescopes array. For what concerns LST, the

challenge is the realisation of a camera with pixel size around 1 inch as a possible

upgrade of the baseline PMT design. There is then the pressing need for both

cheap and performing instruments.

The analysed FBK devices showed very good performances both in dark and under

pulsed light measurements. They have very low and uniform breakdown voltage

(around 25V), with a slight variation with temperature (25mV/◦C). At room tem-

perature and for an over-voltage of 3V, their dark count rate reaches values of

about 100kHz/mm2, while keeping low cross-talk probability (about 9%). More-

over, they show high detection efficiency in the near ultra-violet region of the e.m.

spectrum (about 30% for an over-voltage of 4V) and there is a net improvement

of the 40µm-cell technology with respect to the 50µm cell one. For the listed

reasons, FBK SiPMs demonstrate to satisfy the Cherenkov camera requirements,

while efforts are currently made to further improve their performances.

81

Appendix A

Seminconductors Basics

A.1 Atomic and band structure

Atomic structure can be pictured as a shell structure. Electrons within an atom

occupy specific energy levels: the more distant they are from the core the less

tightly bound they are.

In a multi-atomic structure (as everyday materials we are used to deal with) these

energy levels have to rearrange in order to respect the Pauli exclusion principle: no

more than one electron per quantum state is allowed. This reorganisation results

in a quasi-continuum of energy levels also called band structure. The valence band

is the upmost band occupied by electrons in a given material.

When an electron acquires enough energy, it can leave the valence band and enter

the so called conduction band. The energy difference between the conduction and

the valence band is named energy gap. The electrical behaviour of a given material

can be classified depending on how these bands are arranged within the material

itself.

Figure A.1 shows energy diagrams for insulators, semiconductors and conductors.

Insulators have a very wide energy gap. Valence electrons do not “jump” into

the conduction band except under breakdown conditions where extremely high

voltages are applied across the material. On the contrary, energy bands in a

conductor overlap: in a conductive material there is always a large number of free

electrons available for conduction. Semiconductors have much narrower energy

83

84 Appendix A. Seminconductors Basics

Figure A.1: Energy diagrams for an insulator, a semiconductor and a conduc-tor [18].

Figure A.2: Diagrams of the silicon and germanium atoms [18].

gap if compared to insulators. The most common single-element semiconductors

are silicon (Si) and germanium (Ge).

The atomic structure of silicon and germanium are compared in figure A.2. Both

of them have four electrons in the outer shell. As it can be noticed, these electrons

occupy the third and the fourth shell in silicon and germanium respectively. This

means that germanium valence electrons are at higher energy levels than those in

silicon and, therefore, require a smaller amount of additional energy to escape from

the atom. This property makes germanium more unstable at high temperatures,

and this is the basic reason why silicon is the most widely used semiconductive

material.

Appendix A. Seminconductors Basics 85

Figure A.3: Illustration of covalent bonds in silicon [18].

Figure A.4: Illustration of covalent bonds in a silicon crystal [18].

A.2 Intrinsic and doped semiconductors

Figure A.3 shows the arrangement of four adjacent silicon atoms to form a silicon

crystal. A Si atom shares a valence electron with each of its neighbours, producing

the covalent bonds that hold the atom together: each valence electron is attracted

equally by two adjacent atoms which share it. Figure A.4 shows covalent bonding

in an intrinsic silicon crystal. A crystal is defined intrinsic when it has no impuri-

ties altering its electrical behaviour. The case of covalent bonding for germanium

is similar to the one just described, because it also has four valence electrons.


Figure A.5: Creation of hole-electron pairs in silicon [18].

Figure A.6: Electron-hole pairs in a silicon crystal. Free electrons are beinggenerated continuously while some recombine with holes [18].

At room temperature, electrons in an intrinsic silicon have enough energy to jump

from the valence to the conduction band, as schematically illustrated in figure A.5.

When this happens, a vacancy is left in the valence band within the crystal: this

vacancy is called a hole. The “promotion” of an electron from the valence to

the conduction band creates what is called an electron-hole pair. Recombination

occurs when a conduction-band electron loses energy and falls back into a hole in

the valence band. The hole-electron pair creation and recombination is pictured

in figure A.6.


Figure A.7: Electron current in intrinsic silicon [18].

Figure A.8: Hole current in intrinsic silicon. When a valence electron movesleft to right to fill a hole while leaving another hole behind, the hole has effec-tively moved from right to left. Gray arrows indicate effective movement of a

hole [18].

When a voltage is applied across a piece of intrinsic silicon, the thermally generated

electrons in the conduction band drift toward the positive end under the action of

the electric field, as shown in figure A.7. This current is known as electron current.

As already mentioned, for each electron moved to the conduction band a hole is left

in the valence band. In this band electrons are not free to move within the crystal

structure as conduction electrons do; however, they can jump to a neighbouring

atom filling a hole and thus leaving another hole where it came from. Effectively

the hole has moved from one place to another in the crystal structure, as illustrated

in figure A.8. This is called hole current.


Figure A.9: Pentavalent impurity atom in a silicon crystal structure [18].

The conductivity of an pure semiconductor can be increased by the doping process,

that is the controlled addition of impurities to an intrinsic semiconductive material.

Doping a semiconductor results in the increase of the number of carriers available

for conduction; the concentration of the doping atoms is usually 10−6 with respect

to the semiconductor atoms’ concentration (∼ 1022atoms/cm3 in Si). There are

two categories of impurities: n−type and p-type impurities.

A.2.1 N-Type Semiconductor

N-type doping consist in the addition of pentavalent impurity atoms (i.e. atoms

with five valence electrons) such as arsenic (As), Phosphorus (P) and antimony

(Sb). Figure A.9 shows the effect of the addition of a Sb atom to the crystal

structure of a Si semiconductor. Each impurity atom forms covalent bonds with the

surrounding silicon atoms, thus leaving one extra electron that becomes available

for conduction, not being attached to any atom. Since pentavalent atoms “give up”

electrons they are often called donor atoms. The number of conduction electrons

can be controlled by properly modifying the dopant concentration.


Figure A.10: Trivalent impurity atom in a silicon crystal structure [18].

A.2.2 P-Type Semiconductor

To increase the number of holes in an intrinsic semiconductor, trivalent impurity

atoms (i.e. with three valence electrons) such as boron (B), indium (In) and

gallium (Ga) are added. As depicted in figure A.10, the formation of covalent

bonds with the neighbouring silicon atoms results in the creation of a hole. Because

the trivalent atom can accept an electron, it is often referred to as an acceptor atom.

Electrons and holes are the majority carriers in n-type and p-type semiconduc-

tors respectively. However, as previously mentioned, hole-electron pairs can be

thermally generated within a semiconductor. That means that holes can also con-

tribute to conduction in n-doped materials, as well as electrons can do in p-doped

ones. In this case, holes and electrons represent the minority carriers of the n-type

and p-type semiconductors respectively.

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Acknowledgements

It may sound like an abused stereotype, but these few lines are always the harder

to type. Maybe it is because there is always someone to be grateful to or something

to be thankful for, whether we are smart and humble enough to admit it or not.

In any case, the wiser thing to do is to anticipate the apologies for all the people

the feeble memory of a graduating Physics student will certainly forget. Dear All,

I owe you one and I am sorry I did not write down your names.

There is another reason that makes this task the tougher to accomplish, and I will

try to explain it as simply as possible. As anybody who had the privilege to be

a student for such a long time has certainly experienced, schools and universities

are special places to meet new people. They are at the same time a bite of the

bitter work future and the memory of a past where the word “friend” was naively

bestowed. This situation holds good especially in small realities, such as our

Physics Department: it then becomes difficult, at this point, to discern between

“institutional” and more personal acknowledgements.

To close this long preamble, I would like to add the last anticipated apology. I am

aware of the importance of titles: it might seem an old-fashioned and somewhat

presumptuous point of view, but I think there exists a difference between students,

assistants, professors, secretaries and attendants. There is not any doubt about

how much chance can influence this condition, but still it holds and it would be

unfair not to respectfully consider it. Again, however, there are particularly lucky

situations in which titles do not influence the pleasure to work together, as in my

case. Finally, despite all classifications men will ever conceive, names are still the

noblest titles to be honoured with: this is why I will call by name all the people I

will thank hereafter. I hope that nobody will feel hurt because of this choice.

95

96 Acknowledgements

As the most genuine tradition of captatio benevolentiae would teach, I would like

to start with the two supervisors of this thesis: Francesco Giordano and Elisabetta

Bissaldi. Both of them patiently thought me about the subject of this work and

followed its evolution, without caring too much about weekends or nights. An

extra acknowledgement goes to Francesco, for having proposed me to spend my

internship at the Fondazione Bruno Kessler. It turned out to be an essential

period of learning and progress, as well as an important life experience. A special

acknowledgement goes to Simone Garrappa: the acquisition softwares employed

for the measurements in Bari, and whose pictures are shown in the last chapter,

are his creations.

As a logic consequence, I would like to thank Claudio Piemonte and all of its

group, who let me join their laboratory and work with them. Again, it was a

very fruitful training period, and I hope to have the possibility to continue this

cooperation in the future.

The next thanksgiving goes to all my university colleagues, with no exceptions:

from each of them I had the possibility to learn something. It was not always

related to Physics, but this did not make the teaching less significant.

These years’ closest friends must be thanked too. Even in this occasion, I do not

intend to hurt any of the previously thanked colleagues’ sensibility. However, it

goes without saying that friendship manifests itself at different levels, and cannot

arouse the same feelings for anybody, without any discrimination.

I must thank Leonardo Di Venere for each single debate we had: I always learnt

something valuable. I am also grateful to Riccardo Pennetta for his somewhat

British phlegmatic behaviour: when the going gets tough, he will always be drink-

ing his five o’ clock tea. Giancarlo Garnero seems to share my same passion for

comics: I sincerely do not know whether to be pleased or worried about it. I thank

the three of them for the time spent together.

I owe a special acknowledgement to Francesca Santoro, who has been quoted in

this work: her thesis was one of my first readings about SiPMs. It is simple, clear

and coherently developed, in other words a pleasant reading even for a beginner.

I am also grateful to all my other friends. To those I do not see anymore, to those

I used to believe in and to those to come: each of them is a blessing and none of

their teachings will be wasted.

Acknowledgements 97

I must thank Papa, Mamma and Stefania for their support: being loved by Family

should never be taken for granted. For this reason, I would like to thank my family.

Thank you to those who are still there, if any, and to those who simply pretended

to be.

Thank you to those who behaved like family, though not knowing me at all. Thank

you to Alessandra, Elio and Patrizia.

Finally, I would like to thank the reader who had the courage of going so far: I

hope you enjoyed this work.

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