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 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
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
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 transmission experiment . . . 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 electron energy for different dynode materials . . . 28
3.4 Statistical broadening of the secondary electron yield from the first dynode 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
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 40µm cell and a resin layer . . . 59
4.21 Primary and correlated noise in a NUV 1x1mm2 SiPM with 40µm cell and 50µm cell . . . 60
4.22 Photon Detection Efficiency comparison between 40µm and 50µm NUV 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
A.9 N-type semiconductor . . . 88 A.10 P-type semiconductor . . . 89
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
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.
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
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.
• 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 production1, 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 Cherenkov light, 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 for the highest, blue-violet for the lowest). Shower images produced by Konrad
Bernl¨ohr [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 in the 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 the focal plane of the Whipple Observatorya camera (diameter 3.5◦). Images of gamma-ray showers coming from a source along the optic axis (cross) are shown by full lines; they are narrow and point towards the center. The images from background cosmic rays are broader and have no preferred pointing direction [5].
aThe Fred Lawrence Whipple Observatory is an astronomical observatory owned and operated by the Smithsonian Astrophysical Observatory (SAO) and is their largest field installation outside of their main site in Cambridge, Massachusetts. It is located near Amado, Arizona on the slopes of Mount Hopkins. The observatory is known for its pioneering work in ground-based gamma ray astronomy through the development of the IACT technique with the Whipple 10-meter telescope in 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 gamma rays 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 derived from 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 than the 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., MAGIC and 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 current IACTs 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].
too . 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.
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
Eγ = hν = hc λ pγ = h
λ
(2.1)
where h is the Planck’s constant (h = 6.626 × 10−34J s), 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:
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 Eγand Z, an approximation of the photoelectric effect probability may be given by the following equation:
τ ≈ constant × Zn
Eγ3.5 (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]
hν0 = hν
1 + hν
m0c2(1 − cosθ)
(2.5)
m0c2is 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 and lead, showing the contribution of different processes[13].
σp.e.= Atomic photoelectric effect
σRayleigh= Rayleigh (coherent) scattering - atom neither ionized nor excited σCompton= Compton scattering
knuc= Pair production, nuclear field ke= 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 transmission experiment[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 = R∞
0 xe−µxdx R∞
0 e−µxdx = 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 photodetector materials[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.
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
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.
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 electron energy 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 the first 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 . 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
(3.5)
where 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 = s
2V0(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 = A
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). On the right, the application of a forward bias narrows the depletion region [18].
Figure 3.10: The diode during the short transition time immediately after reverse-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 redrawn to 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.
Figure 3.15: Simplified structure of a common APD. On the left is shown the electric 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.
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 is at the interface between the p+ and the n region.
41
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
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 direct cross-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.
