Contents
1 Resume 4
2 Positron Emission Tomography fundamentals 7
2.1 Working principles of PET . . . 7
2.1.1 Time Of Flight PET . . . 9
2.1.2 Combined PET/Magnetic Resonance Imaging . . . 11
2.2 Figures of merit in PET . . . 13
2.2.1 Spatial resolution . . . 13
2.2.2 Energy resolution . . . 14
2.2.3 Timing resolution . . . 15
2.3 Detectors for PET, TOF PET and PET+MRI . . . 16
2.3.1 Detectors for PET . . . 16
2.3.2 Detectors for TOF PET . . . 19
2.3.3 Detectors for PET+MRI . . . 20
3 Scintillators 22 3.1 Physical principles of inorganic scintillators . . . 22
3.2 Lutetium Oxyorthosilicate inorganic scintillators: LSO:Ce and LSO:Ce,Ca . . . 24
4.1 Introduction to photodetectors . . . 27
4.2 Solid state photodetectors . . . 28
4.2.1 Silicon Photomultipliers . . . 32
4.2.2 SiPM parameters . . . 34
5 Simulations 37 5.1 Analytic model of the scintillator . . . 37
5.2 Electric model of the SiPM . . . 42
5.3 Output of the complete system . . . 46
6 Spectral characterization of LSO:Ce,Ca crystals 50 6.1 Absorption spectra . . . 51
6.2 Emission and excitation spectra . . . 55
7 Static characterization of SiPM 61 7.1 I-V measurements . . . 61
7.2 Dark noise . . . 63
8 Characterization of the LSO:Ce,Ca and SiPM detector with radioactive sources 67 8.1 Linearity . . . 69
8.2 Energy resolution . . . 73
8.3 LSO:Ce,Ca decay time . . . 76
8.3.1 Decay time with 1x1 mm2SiPM . . . 77
8.3.2 Decay time with 3x3 mm2SiPM . . . 79
8.4 Timing resolution . . . 81
8.4.1 Jitter results from simulations . . . 86
8.4.2 Comparison between simulations and experimental data . . . 89
10 Acknowledgements 94
Chapter 1
Resume
Positron Emission Tomography (PET) is a nuclear medicine imaging technique that produces images of functional processes in the patient by means of radiotracers injected in the body and metabolized by the organ under examination. A radiotracer is a biologically active molecule linked to a β+ radionuclide: a positron annihilates with an electron in the body producing two opposite 511 keV gamma rays. The annihilation photons are then detected by a system composed by a ring of detectors in temporal coincidence in order to identify the Line Of Response (LOR) of the emitted photons. The intersection of several LORs allows to determine the gamma rays emission site. The informations obtained by PET can give feedback on blood flow, oxygen or glucose consumption and protein synthesis.
One of the major limitation of PET is the low sensitivity. A way to improve it is to measure with high precision the arrival time difference between the two annihilation photons in order to constrain the emission point to a particular segment along the LOR. This technique is called Time Of Flight (TOF) PET: using TOF algorithm it would be possible to improve the PET performances in terms of noise variance, reduced random event rate, axial blurring and total scan time.
The detector modules used in PET are usually composed by scintillating crystals like LSO:Ce coupled with PhotoMultiplier Tubes (PMT). To develop TOF PET it is necessary to study a fast detector system: several researches are being performed to improve the time performances of the PET detectors.
Recent studies demonstrate that LSO:Ce codoped with Ca (LSO:Ce,Ca) shows reduced decay time, higher light output and better energy resolution compared to the standard LSO:Ce. For what concerns the photodetectors, a valid alternative to PMTs is represented by the Silicon PhotoMultipliers (SiPM). They are inherently fast (the single photon timing resolution is of 60 ps), show high gain at rather low operating bias (order of 50 V) and are insensitive to magnetic fields, making them attractive for new development of PET like TOF PET and hybrid PET+MRI imaging. For these reasons, a detector based on SiPM coupled to an LSO:Ce,Ca crystal could introduce several improvements with respect to the currently used PET modules, especially for what concerns their timing performances.
To optimise the detector performances, a study of the shape of the current pulse produced in response to the incident photons is required. The aim of this thesis is to assess the overall performance of a PET detector composed by a SiPM coupled to LSO:Ce,Ca (with 0, 0.1, 0.2 and 0.3 % Ca concentration) and connected to a fast transimpedance amplifier.
Initially, an overview of PET, TOF PET and PET+MRI imaging techniques is presented, focusing on their basic working principles, detection systems and figures of merit.
The detection system composed by SiPM and LSO:Ce,Ca is then described. The SiPM working principles and the physics of the scintillating crystals are presented, mainly focusing on the suitability of the detector components for PET, TOF PET and PET+MRI applications.
Then, a modelling of the detector is described: it considers a PET detector module composed by a scintillator, a SiPM and its amplification circuit. A suitable electric model for the SiPM and an analytic model for the scintillator have been considered to estimate the system characteristics, like the time jitter of the signals.
A spectral characterization of LSO:Ce,Ca has been performed in terms of absorption, emission and excitation spectra in order to study the Ca influence on the optical properties of the crystals.
Several measurements have been performed in order to fully characterize the detector composed by SiPM and LSO:Ce,Ca and the results have been compared with the simulations. The photodetector has been studied in terms of the current drawn as a function of the applied bias voltage (I-V curve) and
in terms of dark noise. Subsequently, the detector linearity and energy resolution have been measured by using crystals with different Ca concentration. A timing study has been carried out, focusing on the measurements of the scintillators decay time and of the timing resolution achievable in coincidence evaluated for different Ca codoping. The experimental data of timing resolution have been compared with the simulation results.
Chapter 2
Positron Emission Tomography
fundamentals
2.1
Working principles of PET
Imaging techniques are necessary to improve the accuracy of many medical practices, such as oncology or neurology. In the field of Nuclear Medicine, PET is a powerful and sensitive technique which produces images of functional processes measured by the concentration of a radiotracer in organs or tissues. A radiotracer is a biologically active molecule linked to a β+ radionuclide. It is administered to a patient; physiologic processes cause the distribution of the drug throughout the body and the radiotracer is metabolized by the organ under examination. Emitted positrons travel a short distance (above 1 mm) and then annihilate with the electrons of the body emitting two opposite 511 keV γ rays. The annihilation photons are then detected by a system composed by a ring of detectors in temporal coincidence in order to identify the Line Of Response (LOR) of the emitted photons. The intersection of several LORs allows to determine the gamma rays emission site.
The most diffuse tracers are summarized in tab.2.1, with their half-lives1.
Radioactive nuclide Half-life (min)
C11 20.4
N13 10
O15 2
F18 110
Table 2.1: Some of the most commonly used radionuclides with their half-lives (in minutes) [13].
A fluorine isotope, F18 (half life ∼110 min), can be included by radiochemical synthesis in several natural substances in order to study a wide variety of metabolic and physiologic functions. The F18 isotope is commonly used to tag a glucose analogue, deoxyglucose (DG), producing Fluorodeoxyglucose (FDG). In PET imaging, FDG can be used for the assessment of glucose metabolism in glucose-avid cells such as brain, kidney and cancer cells. Cancer cells are characterized by an high proliferation rate, which makes tumour an iper-consumer of glucose: this is the reason why FDG can be used for tumour identification. After the detection process, 2D or 3D images of the tracer concentration within the body are then reconstructed by computer analysis.
A typical PET scanner is composed by several thousands of γ ray detectors organized in rings. Each detector is composed by a scintillating crystal, a photodetector and the readout electronics. When two γs are detected in a short time window, they are supposed to originate from the same annihilation event. This consideration permits to define a line, called LOR, between the pair of detector involved in two γ event. The intersection of several LORs indicates a region of high density of positron annihilation, for example where FDG is accumulated [13]. The union of all the possible LORs gives the field of view (FOV), which is therefore the volume between the two opposing detectors that can be reconstructed. Fig.2.1 reports an example of patient slice, characterized by a zone at high emission rate, with an example of LOR identification. Fig.2.2 shows an example of PET image. The spatial resolution of a PET image is estimated to be around 3 mm, limited by the size of the crystals, by the non collinearity of the γ pair production, by the positron range before annihilation and by the internal scattering of γ in the body. All these factors do not permit to localize precisely the unhealthy tissues in the patient’s anatomy.
Figure 2.1: Example of patient slice with a zone with high rate of annihilation events (green in figure). An example of LOR is the red line, involving the two red detectors along the ring.
Figure 2.2: An example of PET image, show-ing a FDG total body.
2.1.1
Time Of Flight PET
A way to improve the image contrast and the background rejection, is to include in the image recon-struction algorithmes the Time Of Flight (TOF) information. The TOF is the time of flight of the γ rays from the pair annihilation site to the detectors: where it is possible to discriminate the time difference in detection between the two annihilation photons, it could be possible to determine the annihilation point along the LOR. Conventional PET reconstruction uses the TOF information only to identify the line along which the annihilation occurred. It is unable, though, to determine which voxel along the line is the source of the two photons; therefore all the voxels along the line are given the same probability of emission.
TOF PET uses the time of flight difference to better locate the annihilation position of the emitted positron. When a point source is placed at the centre of a scanner, the distance from the source to any detector is the same. Therefore, the flight time of any gamma rays couple produced by positron annihilation in the source should be the same. On the contrary, when the source is not at the centre of the scanner, the photons travel different distances and, therefore, they take different times since the annihilation event to the detectors. The limitation in localizing the annihilation point is mainly due to uncertainty in the measured time resolution ∆t of the coincidence system. The time resolution is used in the reconstruction algorithm as a kernel for a localization probability function. The FWHM
of the probability function is the localization uncertainty ∆x =2c∆t in identifying the γ emission site, as shown in fig.2.3 [29].
Figure 2.3: Comparison between traditional PET (a) and TOF PET (b): in the traditional PET technique it is possible to determine only the event LOR, but not the event location along the LOR. In TOF PET the information of the ∆t between the 2γ could help to localize the origin of the annihilation, improving image quality.
The capability of the system in distinguishing a small ∆t could help to evaluate the annihilation point and to have a gain during the reconstruction process. In this respect, there are some difficulties in realizing a TOF system. Firstly, there is the finite duration of the scintillation emission of the detection crystal; secondly, there is the technological issue of measuring a very short time difference that is of the order of a few hundred picoseconds. However, TOF information acquired on a dedicated system could offer a significant reduction in statistical variance.
By accurately measuring the difference in arrival times of the 511 keV photons coming from positron annihilation, the statistical noise in PET can be reduced. This is possible because the position of the positron emitting point would be constrained along the LOR with a spatial precision of ∆x = c
2∆t, as explained before. To get sub-centimetre resolution, timing resolution of less than 50 ps is necessary, which is at present hard to achieve. However, if we evaluate the factor:
f = 2D
c∆t (2.1)
where D is the diameter of the object being imaged and ∆t is the coincidence timing resolution, we can consider f as the value quantifying the reduction noise in variance [12]. For example, if we consider an organ like the brain (D ∼ 20cm), f > 1 (so it is possible to obtain an advantage in image reconstruction) if ∆t < 1.3 ns: this order of magnitude of time resolution is achievable by the existing technology and the goal is to improve it as much as possible.
TOF information could help to reduce the background during the subsequent image reconstruction. In standard PET reconstruction, the fundamental measurement is the number of counts in a detector-detector pair, so the measurement of the activity in one voxel (a volume emitting element) is coupled with the measurement of activity in all the other voxels. In TOF PET, timing information can be used to remove the coupling between voxels that are separated by more than the TOF measurement distance, reducing the background noise (see fig.2.4).
The reduction in background noise is not the only advantage achievable by using TOF information. This innovative technique could reduce the time necessary to the exam and the motion artefacts. Furthermore, the dose could be reduced and the spatial resolution could be increased, improving the diagnostic accuracy and opening new perspective in nuclear imaging involving, for example, heart and other organs in movement. The informations obtained by PET and TOF PET can give feedback on blood flow, oxygen or glucose consumption and protein synthesis.
2.1.2
Combined PET/Magnetic Resonance Imaging
PET data are more meaningful if coupled with elevated spatial resolution images made by magnetic resonance imaging (MRI) that provide informations about the surrounding body structure. This imaging method analyses the Hydrogen atom proton spin in the water molecules: MRI needs a strong static magnetic field (above 1.5-3 T in human studies) that aligns the magnetic moments of the proton. A magnetic field gradient is used in order to obtain the requested slice selection giving the spatial
Figure 2.4: Image from [12]: a representation of the reduction in background noise due to TOF information. In a all the voxels are coupled, without exclusions. In b the voxels separated by more than the TOF measurement distance are not coupled, reducing the background noise.
location of the analysed points. The circularly polarized RF radiation generated by RF coils excites protons magnetic moment and causes them to precess. This causes the nuclei to produce a rotating magnetic field detectable by the scanner. This information is recorded to construct an image of the scanned area of the body. See fig.2.5 for examples of PET+MRI images.
Figure 2.5: Examples of PET+MRI images from [9].
PET and MRI could be integrated by merging the images obtained separately from two different exams, but the elapsed time is biochemically significant. Patient orientation could be different between the two scanning sessions or the interested organs could have functional or anatomical changes. If stand-alone PET and MR imaging systems are used and image data are fused manually, movements from one
imaging device to another or long examination times often make coregistration impossible, especially in small regions such as lymph nodes. A hybrid PET+MR scanner could provide metabolic and anatomical informations in a single imaging session, eliminating the drawbacks of patient movement, time delays between studies and uncertainty in registration techniques: so, current developments aim to combine PET and MR imaging in order to obtain simultaneous data acquisition.
Some problems are connected to the functioning of a PET+MRI scanner, above all because of the strong magnetic field. The most efficient photodetectors for PET, the Photomultiplier Tubes (PMT), do not operated with a similar magnetic field because charged particles in motion (the cascading electrons in a PMT) experience the Lorentz force and are deflected: it is necessary to use insensitive magnetic field detectors. Besides, the additional MRI components increase the backscattering of them because they are very close to the PET detector modules. PET+MRI technique needs restriction of PET camera field of view in order to fit inside the magnetic bores, reducing PET resolution. PET electronics influences MRI creating spikes in MRI images. Finally, magnetic compatibility of materials is crucial for the improvement of PET+MRI.
2.2
Figures of merit in PET
2.2.1
Spatial resolution
The value of spatial resolution is crucial to evaluate the PET detector performances: it represents the capability of the system in distinguishing two different sources at a fixed distance. The spatial resolution in standard PET can be evaluated by estimating the FWHM of a single point source and can be estimated as [40]: F W HM = 1.2 r (d 2) 2+ b2+ (0.0022D)2+ r2
• the factor d
2 quantifies the effects due to the crystal size d. This effect is dominant until the detector size is above 3 mm, when other factors such as not collinearity and light sharing statistics become important;
• the factor b is an additional factor that quantifies the block decoding scheme;
• the factor 0.0022D quantifies the effects due to not collinearity. The positrons do not come to a complete rest before annihilation: the two 511 keV annihilation photons are not emitted in exactly opposite directions. The result is a Gaussian angular distribution with about 0.5o FWHM. At the centre of the tomograph, this translates to a contribution quantified by using the detector ring diameter D;
• the factor r is the effective positron range. For example, r = 0.58mm for F18 [13].
2.2.2
Energy resolution
The energy resolution quantifies the system capability in distinguishing different energy peaks in the spectrum. By assuming that the detector is exposed to radiation quanta of a single fixed energy (for example, a radioisotope emitting a single gamma-ray energy in its decay), many radiation quanta deposit the same energy in the detector and ideally should produce exactly the same charge. Interaction effects, such as transport efficiency, not proportional effects, statistical effects and electronic noise, blur the ideal energy spectrum. A formal definition of energy resolution is shown in fig.2.6, expressed as the ratio of the FWHM of the peak divided by its centroid position, normally expressed as a percentage.
R = F W HM H0
(2.2)
Small values of R correspond to narrow peaks and good energy resolution. If the incident radiation consists of multiple discrete energies, good energy resolution will help in separating the resulting peaks in the recorded pulse-height spectrum.
Figure 2.6: Example of spectra with illustrated the method to evaluate the energy resolution.
statistics, but if N in significantly large the process can be described by using Gaussian statistics. The standard deviation of the distribution is proportional to the square rout of N (F W HM ∼√N ) and the energy resolution trend can be evaluated as:
R = F W HM H0 ∼ √ N N ∼ 1 √ N
Large N can help to achieve the best energy resolution: for what concerns PET detectors it is necessary to improve the light production in the crystal (use crystal with high light yield), light collection efficiency from the crystal to the photodetector and generation of charge carriers in the photodetector. Other factors, such as the electronic noise and the digitalization of the signal, collaborate to the final energy resolution achievable.
2.2.3
Timing resolution
The timing resolution in PET and in TOF PET determines the system ability to improve the true event rate. The overall timing resolution is determined by the contribution of the crystal, the photodetector and the readout electronic:
σtot2 ∼ σ2 cryst+ σ 2 det+ σ 2 el (2.3)
Other factors influencing the timing resolution are the trigger system and the digitalization of the signal. The timing resolution will be deeply treated in the following chapters, after having described the scintillator and the photodetector.
2.3
Detectors for PET, TOF PET and PET+MRI
This section aims to broadly describe the detection system for PET, TOF PET and PET+MRI, in order to introduce their general requirements. The physics of the different detector components will be treated more deeply in the following chapter, focusing on the devices used in this work.
2.3.1
Detectors for PET
The detectors used for PET technique are composed by a scintillator converting γ rays, a photodetector converting the light absorbed into a measurable electrical signal and the readout electronics analysing the signal. The 511 keV photons from annihilation have to be converted because their energy is nearly invisible to most of the materials employed for photodetection and scintillators have to be used. They permit an indirect detection: the radiation energy is transformed into light of a different (lower) energy detectable by the coupled photodetector. The output of the photodetector is then sent to a customized electronic, specific for the different applications of PET.
A photodetector is a device that converts an optical signal into an electrical signal, which can be processed and stored. Photon detectors are based on the photoelectric effect, where the photon ab-sorption produces the emission of orbital electrons. The response is proportional to the number of photons absorbed by the photodetector. They can be extremely sensitive and have a high response speed capable of following very fast optical signals.
The currently used PET cameras are composed by several block detectors arranged in rings around the patient. In a block detector, a 2D array of scintillating crystals are attached to 4 Photomultiplier tubes (PMTs) (see fig.2.7) via a light guide.
Figure 2.7: Schematic of a block detector used in PET, with scintillator crystals and PMTs.
When a photon is incident on one of the crystals, the resultant light is shared by all 4 PMTs. Infor-mation on the position of the detecting crystal may be obtained from the PMT outputs by calculating the following ratios and comparing them to pre-set values:
Rx= A + B A + B + C + D (2.4) Ry= A + C A + B + C + D (2.5)
where A, B, C and D are the fractional amounts of light detected by each PMT [13].
PMTs are the traditional photodetectors used in PET because of their high gain (up to 106) and high sensitivity. A PMT is made by a glass envelope with a high vacuum inside and with an exposed photocathode at one end: when an incident photon strikes the photocathode, an electron is emitted by photoelectric effect. The electron multiplier consists of a number of electrodes called dynodes positioned along the tube: each dynode supplies a more positive voltage than the previous one. When the first electron leaves the photocathode, it feels the effect of the electric field generated by the first dynode and increases its energy. Upon striking the first dynode, more low energy electrons are emitted, and these electrons in turn are accelerated toward the second dynode and so on. At the end of tube, electrons reach the anode where the accumulation of charge results in a sharp current pulse indicating
the arrival of a photon at the photocathode. An example of PMT is shown in fig.2.8. The anode to cathode supply voltage required to operate a PMT is typically 1000 V. [16].
Figure 2.8: PMT scheme [2].
A scintillator can be defined as a wavelength shifter: it converts the energy of an incident particle or a energetic photon into a number of photons of lower energy easily detectable by the photodetector. Several parameters have to be considered in order to determine the most effective scintillator for the different techniques: decay time, rise time, peak emission wavelength, light yield and so on. Fast scintillators have to be studied and characterized in order to improve the performances of the system. LSO (lutetium oxyorthosilicate: Lu2(SiO4)O) is the standard crystal used in PET because it represents a good compromise between the mentioned parameters. It consists of a matrix of silicate crystal mixed with the lutetium rare earth. This crystal is doped with cerium rare earth and in this case we speak of cerium doped lutetium oxyorthosilicate (LSO:Ce).
Several researches are being performed in order to improve the performances of the detector. Recent studies demonstrate that LSO:Ce codoped with Ca (LSO:Ce,Ca) shows an higher light output, a reduced decay time and better energy resolution [25, 14] compared to the standard LSO:Ce. For these reasons, a detector based on photodetectors coupled to LSO:Ce,Ca crystals could introduce several improvements with respect to the currently used PET modules. This is the reason why this thesis focus on the characterization of a detector composed by a solid state photodetector coupled to LSO:Ce,Ca.
2.3.2
Detectors for TOF PET
At present, the commercial machines mounting a TOF PET technology use PMTs as photodetectors. For example, Philips GEMINI TF PET/CT machine is characterized by a PET detector composed by LYSO and PMTs, with a reported timing resolution of 585 ps [30]. Siemens mCT uses a PET detector composed by LSO and PMTs with a timing resolution of 550 ps [31]. In the contest of existing researches, advances in semiconductor photodiodes have led to the progressive replacement of PMTs with solid state devices. Solid state photodetectors are used because of their higher quantum efficiency, better energy resolution, lower power consumption and a more compact size. Because of the short distance over which the carriers have to move in these devices, their time response starts to compete with that of the PMTs: for this reasons several studies are focusing on their usage in timing experiments and in TOF technique.
An avalanche photodiode (APD) is a highly sensitive semiconductor electronic device that exploits the photoelectric effect to convert light to electricity. APD works with a reverse voltage below breakdown (typically tens of volts). In this regime, carriers (electrons and holes) excited by absorbed photons are strongly accelerated in the internal electric field, so that they can generate secondary carriers. The avalanche process, which may take place over a distance of only a few micrometers, effectively amplifies the photocurrent by a significant factor. Therefore, avalanche photodiodes can be used for very sensitive detectors, which need less electronic signal amplification and are thus less susceptible to electronic noise.
APDs have internal gain which improves the signal to noise ratio but still some 20 photons are needed for a detectable light pulse. The excess noise factor, the fluctuation of the avalanche multiplication, limits the useful range of the gain.
When operated in the so-called Geiger mode with carefully designed electronics, avalanche photodiodes can be used for photon counting with a quantum efficiency of several tens of percent. The Geiger mode means that the diode is operated slightly above the breakdown threshold voltage, where a single electron-hole pair (generated by absorption of a photon or by a thermal fluctuation) can trigger a
strong avalanche. In the case of such an event, an electronic quenching circuit reduces the voltage at the diode below the threshold voltage for a short time, so that the avalanche is stopped and the photodetector is ready for detection of further photons. Photon-counting APDs are also called GM-APDs (Geiger Mode GM-APDs) [15].
Silicon Photomultipliers (SiPM) are Silicon photo sensitive devices built on Si substrate. They are composed by microcell arrays connected in parallel: each one is a diode APD working in Geiger mode. The supply voltage typically varies between 25 V and 70 V, thus being about 30-40 times lower than the voltage required for a traditional photomultiplier tubes. Making SiPM microcells very small (from 20 to 100 µm) and using them in parallel is possible to eliminate the problems of noise and scalability related to the size of the photodetector. The microcells have a common output and generate a signal proportional to the photons hitting the photodetector. Many feasibility studies show that SiPMs are a very promising new class of light sensors for use in PET because of their reliability and good timing resolution [3, 4].
The requirement of excellent timing performance for TOF PET imposes the use of fast photodetector like SiPM [12]. It is necessary to estimate how the timing performance of a SiPM-based detector would compare to the performances of conventional PMTs-based ones. The single photon timing resolution of SiPMs is reported to be relatively small (60 ps) [27].
Academical and industrial studies have been developping in order to integrate SiPMs in TOF PET scanners (for example, SUBLIMA project [32], ENDO TOFPET US project [33], PicoSEC project [34]). A new acquisition system based on SiPM matrices and fast scintillating crystals is under development at University of Pisa and INFN with 4DMPET project. This thesis work has been carried out in this project and aims to characterize a PET detector based on SiPM.
2.3.3
Detectors for PET+MRI
Detectors for PET+MRI need to be performant as the traditional photomultiplier tubes and insensitive to static magnetic fields and electromagnetic noise. For these reasons solid state photodetectors are
being developed as detector for combined PET+MRI. Photodiodes are much less sensitive to magnetic fields than PMTs, in which external field components distort the intended trajectory of the cascading electrons, reducing the number of electrons detected by the anode.
The currently available PET+MRI machines are based on APD photodetectors. For example, Siemens MAGNETOM Trio is a PET+MRI machine with whole-body 3T MR system mounting LSO crystals and Hamamatzu APDs [35].
Several studies have been carrying out in order to use SiPMs as photodetectors for hybrid PET+MRI imaging because of their potential better performances with respect to APDs, as explained before. In the context of existing studies, SiPM stability while integrated with the electromagnetic field has been proved up to 7 Tesla [5]. For this reason, the detector proposed in this thesis could operate in a large multi-Tesla magnetic field.
Chapter 3
Scintillators
3.1
Physical principles of inorganic scintillators
A scintillator is a material capable to emit light when excited by ionizing radiation. It converts the energy of an incident charged particle or energetic photon into photons, in the visible or near visible range (UV), easily detectable with photodetectors. Different scintillators will be preferred depending on the specific application: among the desirable properties of a good scintillator, high efficiency, fast decay time, high light yield, linearity and good energy resolution are interesting in a number of cases. For what concerns PET applications, inorganic crystalline media are the most diffuse scintillating materials. For this class of crystals, it is possible to describe the scintillation process by using schemes of the electronic band structure of the crystal. The valence band and the conduction band of the crystal are separated by the gap energy Eg (fig.3.1, [22, 23]). After high energy excitation a electron-hole pair is produced. Subsequently, the electron end the electron-hole relax through inelastic scattering and Auger processes, exciting the surrounding electrons in the medium, during a typical time of 10−18 s. Then the created electrons and holes thermalize and, after about 10−16 s, the electrons are at the bottom of the conduction band and the holes at the top of the valence band. These first three steps are responsible to the typical rise time of the scintillator. During the subsequent step, during about 10−12
s, the electron-hole pairs may recombine through non radiative processes, or they might be trapped by defects or impurities in the crystal, or they might be trapped by the luminescent centres of the rare earth present in the crystal lattice (codoping). The codoping favours the radiative de-excitation in the crystal. The last step is the recombination of electron-hole pairs from the luminescent centre, leading to the emission of luminescent photons. This mechanism can have a typical duration range from 10−9 s to some seconds depending on the radiative transition involved and it is responsible for the decay time of the scintillator.
Figure 3.1: Scintillation mechanism in inorganic crystalline media.
The main characteristics of a scintillator can be summarized in:
• Light yield: it measures the luminosity of the crystal and it is expressed as number of produced photons over the energy released in the crystal. It is usually expressed as a percentage of the NaI light yield (38000 photons per Mev, [13]).
• Decay time: is the time required for scintillation emission to decrease to e−1 of its maximum. The light output from the crystal can be described as f (t) ∼ e−
t
time of the crystal.
• Refractive index: it has to be as similar as possible to the photodetector refractive index, in order to reduce the light losses at the interfaces.
• Density and Atomic number: high density and high atomic number are necessary to guarantee an efficient detection of incident photons.
• Peak emission: it has to be compatible with the photodetector characteristics.
• Linearity: the light output of the scintillator has to be proportional to the energy of the incident radiation.
• Hygroscopicity: several inorganic scintillators will deteriorate due to water absorption if ex-posed to air. This sensitivity to moisture is called hygroscopicity.
Tab.3.1 summarizes the listed characteristics for some of the most diffuse scintillators in PET.
Material NaI(Tl) LSO(Ce) BGO CsI(Tl)
Light yield (%) 100 85 21 165
Decay time (ns) 245 40 300 1220
Refractive index 1.85 1.82 2.15 1.79
Density (cmg3) 3.67 7.40 7.13 4.51
Peak emission (nm) 410 420 480 550
Hygroscopic Yes No No Slightly
Table 3.1: Typical parameters of the most commonly used inorganic scintillators in PET [24].
3.2
Lutetium Oxyorthosilicate inorganic scintillators: LSO:Ce
and LSO:Ce,Ca
The scintillator representing the best compromise between the characteristics reported in the previous section is LSO. Its name stands for lutetium oxyorthosilicate (molecular formula Lu2(SiO4)O). LSO is typically doped with 0.05 to 0.5% cerium (Ce). In case of Ce the luminescent centres are the 4f and 5d Ce bands, present in the band-gap of the LSO. LSO is widely used in PET because of its good light
yield, fast decay time, refractive index compatible with the glass and photodetector ones, high density and peak emission compatible with the detection spectrum of the most common photodetectors. Various researches investigated the effect of additional codopants to improve the LSO performances. Recent studies [25, 26, 14] found that LSO light output and decay time may be improved by codoping it with divalent cation such as Ca (Ca2+). Recently developed LSO:Ce scintillators, co-doped with Ca, have been produced by the University of Tennessee [25]. They are characterized by the improved performance of most the above-mentioned characteristics. The better performances are achievable with Ca2+ ions with concentration in the initial starting materials in the range of 0.1-0.4 %. Scintillation light output and decay times of LSO:Ce are listed as a function of Ca in tab.3.2:
Ca concentration Scintillation light yield (Nphper MeV) [26] Decay time τ (ns) [25]
LSO:Ce,Ca (0% Ca) 30900 43.0
LSO:Ce,Ca (0.1% Ca) 38800 36.7
LSO:Ce,Ca (0.2% Ca) 36200 33.3
LSO:Ce,Ca (0.3% Ca) 32400 31.3
Table 3.2: Decay time and light output of the Ca codoped LSO crystals. Values from literature: [25, 26].
An explanation of the improved optical properties of Ca codoped LSO is reported in [26]. Ca2+ codoping was originally introduced in LSO to study the oxygen defect structure. The concentration of oxygen vacancies is crucial for the scintillation mechanism: they are caused by the introduction of Ce codoping and they are one of the most significative defects in LSO:Ce. The calcium dopants fix the concentration of oxygen vacancies and raise the crystal scintillation efficiency.
Ca codoping does not appear to alter the energy level structure of Ce centres and has relatively small influence on the intrinsic decay of Ce. The energy transfer process is thought to be the key in under-standing the shortening of scintillation decay time.
Charge traps are considered to slow the energy transfer process and, as a consequence, to increase decay time. Thermoluminescence measurements reported in [26] show that Ca codoping significantly suppresses the charge trap population in LSO:Ce crystals as a function of Ca concentration, explaining the decrease in decay time.
The suppression of charge traps in the LSO matrix may have two possible explanations. Oxygen va-cancies are common defects in oxide crystals: it is possible that the observed charge traps are, in fact, caused by such vacancies and that the addition of Ca may inhibit the formation of oxygen vacancies during crystal growth, suppressing trap formation. Another possible explanation is that Ca may in-hibits the capture of electrons by the traps, and therefore suppresses the trapped charge population, although the oxygen vacancies (i.e., traps) may exist.
In the contest of these studies, this thesis aims to characterize a detector using LSO:Ce,Ca as scintil-lator, focusing on its reliability for TOF PET application.
Chapter 4
Silicon Photomultipliers
4.1
Introduction to photodetectors
The aim of a photodetector is to convert the energy of absorbed photons into a measurable electrical signal. Photodetectors can be:
• Vacuum photodetectors: by using vacuum photodetectors, visible photons interact through external photoelectric effect into a photocathode and the emitted photoelectrons are then mul-tiplied in the vacuum tube through secondary emission thanks to the high electric field applied across the electrodes. PMTs, for example, belong to this class of photodetectors;
• Solid state photodetectors: these photodetectors mainly rely on photons interaction through internal photoelectric effect in a semiconductor. Electrons are multiplied through the impact ionization mechanism, under an electric field above 106 Vm. In this category we can find, for example, SiPM.
The photoelectric effect is a quantum electronic phenomenon in which the energy from the incident electromagnetic radiation is fully transferred to one electron, which is ejected from its bound shell. The electron is ejected if the absorbed energy overcomes a threshold energy. If the photon energy
is too low, the electron is unable to escape the material. Increasing the intensity of the light beam, increases the number of photons in the light beam, and thus increases the number of electrons excited, but does not increase the energy that each electron possesses. The energy of the emitted electrons does not depend on the intensity of the incoming light, but only on the energy or frequency of the individual photons. The maximum kinetic energy of the ejected electron is:
Tmax= hf − Ethr (4.1)
where h is the Planck constant, f is the incident photon frequency and Ethr is the energy thresh-old. The electron can remain confined in the matter (internal photoelectric effect) or can escape from the surface of the matter (external photoelectric effect). If the photoelectric effect is internal, Ethr is the energy gap between the conduction band and the valence band. For example, in semiconductor materials used to built solid state photodetectors, the excited electron does not escape from the semi-conductor surface, but it is released from the valence band to the conduction band. Otherwise, if the photoelectric effect is external, Ethr is the material work function, which is the minimum energy that must be given to an electron to liberate it from the surface of a particular substance.
4.2
Solid state photodetectors
Advances in semiconductor photodiodes led to the progressive replacement of PMTs with solid state devices in some applications. Solid state photodetectors are characterized by higher quantum efficiency and potentially better energy resolution; they have lower power consumption and a more compact size. A Silicon based photodetector is a particular kind of solid state photodetector based on Si as semicon-ductor material.
In solid-state physics, the electronic band structure of a solid describes those ranges of energy an electron is forbidden or allowed to have. The band structure of a material determines several char-acteristics, in particular the material’s electronic and optical properties. Fig.4.1 shows a simplified
picture of the bands in a solid that allows the three major types of materials to be identified: metals, semiconductors and insulators.
Figure 4.1: Bands in metals, semiconductors and insulators.
A semiconductor is a material with electrical conductivity intermediate in magnitude between that of a conductor and an insulator. The valence band in any given metal is nearly filled with electrons, while very few (semiconductor) or virtually none (insulator) of them are available in the conduction band, the band immediately above the valence band. The ease with which electrons in the semiconductor can be excited from the valence band to the conduction band depends on the energy gap between them. The semiconductor materials, such as Si or Ge, are characterized by a band gap of few eV: at room temperature, some electrons can pass in conduction band because of this low value. Some physical properties of Si are reported in tab.4.1.
Atomic number Z 14
Atomic weight A 28.1 Density 2.3 cmg3 Energy gap (300 K) 1.1 eV Energy gap (0 K) 1.21 eV Table 4.1: Physical properties of Si [16].
K, this average energy is 3.62 eV and at 77 K 3.81 eV [16]. For the same radiation energy, the numbers of charge carriers created in Si will be an order of magnitude greater than in gaseous photodetector (i.e. for Ar the mean energy for ion-pair creation is 26 eV [16]). Compared to the energy gap in Si, the average energy necessary to create a pair is bigger, because it takes into account of probabilistic effects like recombination, lattice vibrations and so on.
The electrical properties of semiconductor can be modulated by doping, that is the intentional in-troduction of impurities into an intrinsic semiconductor. The impurities depend upon the type of semiconductor: for example, Si and Ge (Group IV semiconductors) are usually doped with Group III (for example B) or Group V (for example N, P) elements. Lightly and moderately doped semiconduc-tors are referred to as ”extrinsic”.
In semiconductor physics, acceptor is a dopant atom that when added to a semiconductor can form p-type regions. For example, when Si, having four valence electrons, is doped with elements from group III like boron (B) or aluminium (Al), having three valence electrons, is called p-type semiconductor. A donor is a dopant atom that, when added to a semiconductor, can form n-type region. For example, when Si is doped with elements from group V like phosphorus (P) or arsenic (As), with five valence electrons, is called n-type semiconductor,. The effect of n-type and p-type codoping is shown in fig.4.2. Small numbers of dopant atoms can change the ability of a semiconductor to conduct electricity. When on the order of one dopant atom is added per 100 million atoms, the doping is said to be low or light. When many more dopant atoms are added, on the order of one per ten thousand atoms, the doping is referred to as heavy or high. This is often shown as n+ for n-type doping or p+ for p-type doping [16].
A p-doped semiconductor and a n-doped semiconductor can be joined, in order to create a ”p-n ju”p-nctio”p-n”. At the i”p-nterface, the differe”p-nt electro”p-n a”p-nd hole co”p-nce”p-ntratio”p-n, a”p-nd their subseque”p-nt recombination, creates an electric field gradient between the junction, causing the presence of a contact potential barrier. This region is called ”depletion region”: it is a region where the charge carriers have diffused away. The only charge left in the depletion region are ionized donor or acceptor impurities.
Figure 4.2: A representation of Si codoping with an acceptor (B) and a donor (P), leaving, respectively, a free hole and a free electron.
This characteristic is very useful in the photodetectors, because the electron-hole couples created in the depletion region feel the effect of the electric field and are drifted toward the electrical contacts placed at the photodetector sides, creating a current signal. Intrinsically, the junction characteristics are not perfectly suitable for the radiation detection: the electric field is not sufficient for an effective light collection and the depletion region is too small, increasing the noise of the signal output and being suitable just for low energy radiation detection. For these reasons, an inverse voltage is applied through the junction, increasing the depletion region, thus the sensitive region and the charge collection efficiency.
A photodiode is a type of photodetector capable of converting light into a detectable current signal. A photodiode is a p-n junction: when a photon of sufficient energy strikes the diode, it excites an electron, creating a free electron and a free hole, with inner photoelectric effect. If the absorption occurs in the junction’s depletion region these carriers are swept from the junction by the built-in field. Thus holes move toward the cathode, and electrons toward the anode, and a photocurrent is produced. This photocurrent is the sum of both the dark current (the current produced without light hitting the photodetector, but just due to thermal effects) and the light current, so the dark current must be minimised to enhance the sensitivity of the device. [16, 21].
4.2.1
Silicon Photomultipliers
Between the semiconductor-based photodetectors, Avalanche Photodiodes (APD) are photodiodes formed by a n+− p − p−− p+ structure, where n+ is the n-doped side (entrance window), p is the p-doped layer, p− is a slightly p-doped layer and p+ is heavily p-doped. This different concentration of p-doping is necessary to define the shape of the electric field and of the depletion region when bias is reversed: when reverse bias is applied, the depletion region (about 5 µm) in the p-layer widens to reach through the p−-layer. The electric field extends from the thin n+-layer, maximizes in the n+-p junction and decreases through the p-layer and slightly through the p−-layer (because the net space charge density is small in this region) and vanishes at the end of the depletion layer in the p+-layer, as shown in fig.4.3. During the Geiger-mode operation, each APD is biased to a voltage Vbiasabove the breakdown voltage Vbreakdown, defined as the minimum reverse voltage to make the diode conducting in reverse.
Figure 4.3: APD schematic with the trend of electric field.
Photons interact with Si, especially in the p− doped region, where they create electron-hole pairs, separated by the electric field and drifted in the n+ and p+ region, respectively. Electrons are ac-celerated by the increasing field to a sufficiently large kinetic energy that permits, when they reach the p-layer, to cause impact ionization and release new electron-hole pairs which start the avalanche process thanks to the high electric field in n+− p junction. In this way a single photon absorption can produce a sufficiently large current and can be detected [18].
A quenching mechanism is necessary in order to stop the avalanche process after the photon detection and to return to the initial configuration. A resistive layer on the top of Silicon wafer, made for ex-ample of SiC, provides the negative feedback (due to very low tangential conductivity of the resistive layer) in the multiplication area: through it, the avalanche process increases current and causes a charge accumulation on the resistive layer-Silicon interface. Because of the redistribution of charge, an electric field increases in the opposite direction, screening the initial one: it decelerates the avalanche process and causes its termination.
A Silicon PhotoMultiplier (SiPM) is a photodetector composed by Avalanche PhotoDiodes (APD) each working in single photon detection (not-proportional) Geiger mode: each cell works like a binary system activated by the passage of the photon. When all the responses are summed, this value is proportional to the number of involved cells, giving informations about the flux of photons. Avalanche multiplication of charge carriers is responsible for the internal gain in APD (about 102− 103), but in SiPM each microcell operates in independent Geiger mode, producing a very large current flow with gain up to 106. The typical density of microcells in 1000-5000 per mm2. The background noise is defined as the dark count rate, which is estimated from electrical pulses caused by a single thermally generated electron or hole detected in Geiger mode.
Several producers are present, for example Hamamatsu, FBK-irst, SensL, Zecotek. As an example, fig.4.4 shows an example of Fondazione Bruno Kessler FBK-irst microcell array of a SiPM. Fig.4.5 is a picture of the 3x3 mm2 SiPM produced by FBK-irst, Trento (Italy).
Figure 4.5: SiPMs used in the measurements, produced by FBK-irst.
4.2.2
SiPM parameters
Several parameters are used to characterize photodetectors; the first that has to be measured is spectral response, because the response of a photon detector is wavelength dependent and is determined by the material, the structure or the packaging of photodetector. Quantum Efficiency (QE) of a photon detector is the number of detected photoelectron with respect to the number of incident photons. It can be expressed by the following equation [18]:
QE = G(1 − R)(1 − e−αx) (4.2)
where G is the geometrical efficiency (the ratio of the sensitive area on the total photodetector surface), R the reflection coefficient, α is the coefficient of absorption and x is the width of the sensitive region. Thickness of active area is provided in order to increase the QE and minimize the size of the multiplication region: thus, local electric fields are decreased, the avalanche process is stable and useful absorption is maximized. The absorption coefficient of light in Si depends on its wavelength: the absorption coefficient of Si as a function of photon energy at different temperatures is shown in fig.4.6.
The photon detection efficiency (P DE) of an SiPM is the statistical probability than an incident photon produces a Geiger pulse from one of the SiPM microcells. It is given by
Figure 4.6: Absorption coefficient of Si against photon energy at different temperatures [19].
P DE = QE ∗ AP (4.3)
where QE is the quantum efficiency and AP is the avalanche initiation probability (the probability that the generated electron-hole couples will start an avalanche). The fraction of light transmitted to the sensitive region is optimized for the left edge of sensitive spectra (green light). The scintillators used in PET have the emission peak around 350 nm - 500 nm: for this reason, the PET photodetectors need to have a good efficiency in this region.
In a photodetector, the gain is the mean number of photoelectrons produced in response to an incident photon. For what concerns SiPMs, their gain is about 106, making them attractive for radiation detection and competitive with PMTs.
Fig.4.7 reports the P DE of different photodetectors and fig.4.8 their gain, by comparing 1x1 mm2 SiPM supplied by Photonique, FBK-irst, SensL, Hamamatsu HPK.
Figure 4.7: The P DE vs wavelength λ (a) of the Photonique, FBK-irst and SensL devices and (b) HPK devices [20].
Figure 4.8: The gain of the SiPM prototypes vs. overvoltage ∆V=Vbias− Vbreakdown [20].
part of the reported photodetectors. This means that they can be coupled with scintillating crystals emitting in this wavelength range and have a good detection efficiency. As shown in fig.4.8, the photodetectors show high gain at rather low bias overvoltage too, and they reach gain values up to (3 − 4) ∗ 106 if the overvoltage increases.
Chapter 5
Simulations
The model presented in this work considers a PET detector module composed by a scintillator, a SiPM and its amplification circuit. The contribution of the LSO crystal for various Ca concentration is described by an analytic model of the light emitted by the scintillator. The information achievable by using the crystal model is joined with the SiPM and amplifier electric models, used in the experimental setup, to reproduce the final signal.
5.1
Analytic model of the scintillator
The first part of the model aims to describe the light output from the scintillator. The physical phenomena that contribute to the crystal light output have been explained in the previous chapter. Summarizing, the light output can be described by using two typical time constants: the rise time τrise and the decay time τdecay. If we neglect the rise time contribution, for the case of a scintillator decaying exponentially with a time constant τdecay, with maximum photon emission rate A, the light emission rate as a function of time can be expressed as:
y(t) = Ae− t
The expected number of photons during an interval [0, t] is: f (t) = Z t 0 y(t)dt = Z t 0 Ae− t τdecaydt = −Aτ decay[e − t τdecay]t 0= R(1 − e − t τdecay) (5.2)
where R = Aτdecay is the total photons yield:
Z +∞ 0
y(t)dt = R = Aτdecay (5.3)
The light emission statistics from a scintillator is characterized to be a sequence of events in which the occurrence of any event is independent on the others and can be described by using Poisson statistics. Given f (t), the expected number of photons during an interval [0, t], the emission probability of the Qthphoton is [37]:
PQ(t) =
f (t)Qe−f (t)
Q! (5.4)
The variance of PQ(t) can be evaluated under the hypothesis of R >> 1 and R >> Q [37]:
σ2cryst= Q( τdecay R ) 2(1 + 21 + Q R + ...) ∼ Q( τdecay R ) 2 (5.5)
A first study can be performed by studying how the probability of the emission of the Qthphoton varies as a function of Q, maintaining R and τdecay unchanged. Fig.5.1 shows the emission probability of the Qthphoton by varying Q from 1 to 5 with τdecay=40 ns, R=1000. If we consider the position of the maximum of the probability, it is noticeable that increasing Q both the time when the probability reaches the maximum value and the FWHM of the distribution increases. This means that in order to achieve the better timing performances it is necessary to consider the arrival times of the very first photons from the crystal. A read-out electronics capable to trigger on the first detected photons can improve the time precision of the system.
Figure 5.1: Probability of emission of the Qth photon by varying Q from 1 to 5 with τdecay=40 ns, R=1000.
of τdecay, maintaining R and Q unchanged. Fig.5.2 shows the probability of emission of the third photon (Q = 3) by varying τdecay from 30 ns to 50 ns, with R=1000. If we consider the maximum of the probability function, it is noticeable that increasing τdecay the time when the probability reaches the maximum value and the FWHM of the distribution increase. This means that in order to achieve the better timing performances it is necessary to use a fast scintillator, with short τdecay, like LSO:Ce codoped with Ca. The Ca codoping in LSO could improve the timing performances of the system because of its decreased decay time, in comparison with the not codoped crystal.
Considering the graphs plotted in fig.5.1 and in fig.5.2 it is possible to evaluate of the timing performances degrade by using crystal with long τdecay and threshold at high number of photons. Fig.5.3 shows the FWHM of the curves plotted in figg.5.1, 5.2: these values have to be considered as the ultimate estimation of the timing performance of the single detector since just the crystal contribution is considered while the contribution of the photodetector, of the electronics and of the light transport are neglected. The FWHM increases with increasing Q and τdecay, as expected.
To assess the actual crystal performance in a fast scintillator the contribution of the scintillator rise time τrise could be not negligible. This is the reason why, with respect to the models considered
Figure 5.2: Probability of emission of the third photon by varying τdecay from 30 ns to 50 ns, with R=1000.
Figure 5.3: FWHM of the curves plotted in fig.5.1, 5.2. Fig.5.3a shows FWHM as a function of Q, fig.5.3b as a function of τdecay.
in literature [37], the following function takes into account the contribution of the rise time of the scintillator [38, 39]: f (t) = R(1 −τrise+ τdecay τdecay e −t τdecay + τrise τdecay e−t( 1 τdecay+ 1 τrise)) (5.6)
• with τrise=0 the two forms of f (t) are equivalent, as expected. The bi-exponential model includes the single exponential one if τrise is considered equal to 0;
• if τrise
τdecay is small there is no substantial difference between the two f (t). In this case, the single exponential model can be sufficient to describe the system. It happens when τdecay is large enough to make τrise negligible;
• for a fast scintillator τrise
τdecay is not small enough to be neglected and the bi-exponential model is more appropriate to describe the scintillator light output.
Fig.5.4 shows a comparison between the single exponential model and the bi-exponential model, performed by plotting f (t) with R=1000, τdecay=40 ns, τrise=0 ns (neglected) (red line) and τrise=0.5 ns (blue line). The rise and decay time constants are chosen similar to the corresponding values of the LSO scintillator. The main difference between the functions is at the beginning of the time scale, within the region that is approximately equal to the rise time constant (see the zoom - red square in fig.5.4).
Fig.5.5 shows the probability P(t) of the emission of the third photon (Q=3) from a crystal with R=1000, τdecay=40 ns and τrise varying from 0 to 1 ns. The position of the maximum and the FWHM increases in time by increasing the τrise. From fig.5.5 it can be underlined how the τrise can affect the timing performances of the system. Tab.5.1 reports the values of the FWHM of the curves plotted in fig.5.5.
τrise (ns) FWHM (ns)
0 0.16
0.5 0.27
1 0.37
Table 5.1: FWHM of the curves plotted in fig.5.5.
The LSO:Ce rise time has been measured in several studies: it is estimate to be faster than 30 ps (88%), but there is a slower component (12%) estimated to be 350 ± 70 ps [40, 41]. The contributions to the rise time partly arise from intrinsic crystal properties and from its size, reflection properties and index of refraction. To our knowledge, the influence of Ca on the τrise of LSO:Ce has not been studied
Figure 5.4: Mean number of photons emitted f (t) with R=1000, τdecay=40 ns and τrise from 0 (ne-glected) to 1 ns.
yet. For these reasons, according to the data reported in [40, 41], the following simulations have been performed considering τrise= 0 and τrise= 0.5 ns.
5.2
Electric model of the SiPM
The previous chapter underlined the suitability of SiPM as a promising photodetector for PET, in reason of its high gain, low bias voltage, intrinsic fast timing response and insensitivity to magnetic field. The definition of the most performing detector configuration requires a study of the shape of the current pulse produced in response to an incident photon. This is the reason why an equivalent electric model of SiPM have to be developed and studied, paying attention to its validation with measured
Figure 5.5: P(t) as a function of time (ns) by varying τrise=0.5 ns, with R=1000, Q=3 and τdecay=40 ns.
signals. The simulation of the equivalent SiPM electric circuit has been performed by using Orcad Capture: it is used to develop schematics and perform timing and circuit analysis.
A SiPM is composed by several microcells (usually order of hundreds): the model is based on the equivalent electric circuit of a microcell fired by an incident photon and the other microcells not fired in parallel [42]. When a single microcell is fired, the current pulse delivered to the external circuit is affected by the presence of the other hundreds of microcells in parallel and by internal and external parasitic and load effects. All the contributions have to be considered. The equivalent SiPM electric circuit is shown if fig.5.6.
If we focus on a single microcell, we have to remember that it is an avalanche photodiode working in Geiger mode, quenched by a resistor in series. The quenching process is important in order to allow the fired microcell to reset the signal and detect other particles. The quenching process is modelled by using a circuit with Rq (the quenching resistor) and Cq (a small quenching capacitor) in parallel. CpT OT models the lumped contribution of the parasitic Cp between the substrate of the device and the contact of the quenching resistor from each microcell composing the SiPM.
Figure 5.6: SiPM electric circuit [42].
by using a current source with the diode capacitor Cdin parallel. By considering just the fired microcell, the total collected charge can be expressed as:
Q = (Cd+ Cq)∆V (5.7)
where ∆V is the overvoltage. The quenching circuit has to interrupt the avalanche after a photon hits the microcell. The diode discharge acts through the resistor Rq in series to the diode. The typical RC discharge time can be expressed as:
τdis= Rq(CpT OT + Cq) (5.8)
The diode recharges with a typical time due to the diode capacitance Cd and to the quenching resistance Rq:
τrec= Rq(Cd+ Cq) (5.9)
If the SiPM is composed by N microcells, a single fired microcell acts as described above and the other N − 1 microcells as a circuit in parallel. Their contribution can be included by considering their effects in the quenching circuit (CqN = (N − 1)Cq), RqN =
Rq
N −1) and in the diode capacitance (CdN = (N − 1)Cd). The SiPM electric equivalent circuit includes the value of the bias voltage Vband of the input resistance of the front-end electronics Re. The model can describe SiPMs from different manufacturers simply by changing their typical resistors and capacitors.
The circuit adopted in the simulations describes the FBK-irst SiPM used in measurements, composed by N = 3600 microcells each one with dimensions 50x50 µm2: their characteristic parameters have been reported in [42] and they have to be finally tuned in order to well reproduce the measured signal. Typically, the diode capacitance Cd is sbout 70 fF, the quenching capacitance Cq is about 15 fF and the parasitic capacitance CpT OT is about 20 pF/mm2 (for the modelled SiPM, with dimensions 3x3 mm2, CpT OT ∼180 pF). The quenching resistor Rq is about 400 kΩ and the input resistance of the front-end electronics Reis usually very small (few tens of ohms, ∼50 Ω).
The output of the SiPM is then sent to a fast transimpedance amplifier whose circuit reproduces the actual electric circuit of the amplifier used in the measurements. As compact electronics boards incorporates a SiPM bias circuit and a transimpedance amplifier optimized for the amplification of SiPM signals. The supply voltage is 9V [43]. The Orcad Capture amplifier schematic is represented in fig.5.7 and fig.5.8 shows a picture of the amplifier board.
The whole response of the system composed by SiPM and amplifier is studied. Fig.5.9 shows a superimposition of a typical single photoelectron dark signal (black in figure) and the output of the simulation (red in figure), considering the signal produced by a single fired microcell. The parameters of the model have been optimized in order to have the best agreement between simulations and real data.
Figure 5.7: Schematic of the amplifier circuit.
Figure 5.8: Photo of the amplifier board. Its circuit is schematized in fig.5.7.
5.3
Output of the complete system
The informations obtained by the analytic crystal model and by the electric model of the SiPM and of the amplifier can be joined to perform a suitable modelling of the overall detection system. Calling Signcell(t) the system response when a single microcell is fired by a photon (the red signal in fig.5.9), under the hypothesis that N different photoelectrons from the scintillator trigger N different microcells of the SiPM, the output signal can be described as:
Signtot(t) = N X
Q=1
Signcell(t − tQ) (5.10)
Figure 5.9: Validation of the model: superimposition of a single photoelectron dark count (black line) and the output of the simulated system (red line) when a single microcell is fired.
be performed by evaluating tQ as the time when the probability of the Qth photon emission assumes the maximum value (see fig.5.10: the first five tQ are shown). This method will be called maximum probability method.
Figure 5.10: Example of evaluation of tQ with Q from 1 to 5: for example, t1 is the time where the emission probability of the first photon reaches the maximum, and so on.
Otherwise, the time tQcan be extracted according to the probability curves (see fig.5.2 and 5.1 for examples) with an extraction. This method will be called rejection method. First of all, the parameters
of the scintillator have to be fixed (τdecay, τrise and R). Secondly, for each point, fixing Q, a value of the probability between 0 and Pmax and a value of time were extracted (by using rand function in Matlab). So doing, a point (textr, Pextr) for each Q is extracted in the probability-time space. In conclusion, the (textr, Pextr) point is compared to the probability curve for the fixed Q: if the point is below the probability curve, textris considered as an emission time of the Qthphoton; otherwise, the point is rejected and the extraction procedure restarts. Fig.5.11 is an example of probability plot and relative extracted points.
Figure 5.11: Example of extraction procedure: the red line is the probability curve for Q = 1 with a crystal emitting R = 1000 photons, with τrise = 0 and τdecay = 40 ns. The fifteen blue dots are examples of (textr, Pextr) that could be considered for the evaluation of t1 because they are below the probability curve.
Evaluating the photons emission times with the procedures described above, it is possible to sim-ulate the signal from a complete detector system composed by LSO and SiPM connected to a tran-simpedance amplifier by using the output from Signtot(t). The procedure is performed by using a Matlab code: it starts to sum the contribute of the Qthmicrocell to the final signal just when the Qth photon hits the SiPM surface. Signtot(t) can reproduce signals of different energies by varying the number of photons hitting the SiPM surface.
this case has been performed with the rejection method) and a signal acquired by coupling an LSO:Ce crystal with a SiPM, connected to a transimpedance amplifier, excited by using a Na22 source. Data acquisition has been performed with a LeCroy LC684DM 1.5GHz 2GS/s Oscilloscope.
Figure 5.12: Superimposition of a measured signal (black line) and the output of the simulated system (red line).
It is notifiable from fig.5.12 a good agreement between measured and simulated signals, especially for what concerns the rising edge and the behaviour around the peak. The agreement in the rising edge is very important for what concerns the subsequent measurements of the jitter on crossing several thresholds.
Chapter 6
Spectral characterization of
LSO:Ce,Ca crystals
A spectroscopical study has been performed to analyze the interaction between the LSO:Ce,Ca scintil-lators and the electromagnetic radiation, focusing on absorption, emission and excitation. Absorption occurs when energy from the radiative source is absorbed by the material. Absorption is usually deter-mined by measuring the fraction of energy transmitted through the material. Emission spectroscopy refers to spectral measurements of photons emitted by the crystal when excited by using an electro-magnetic radiation. The excitation spectrum is obtained by measuring the emission intensity at a fixed wavelength, while varying the excitation wavelength. The emission spectrum is obtained by measuring the variation in emission intensity for a fixed excitation wavelength.
The spectral characterization has been performed for LSO:Ce crystals with different Ca concentration, underlying the Ca influence on crystal spectroscopic properties.
This work has been performed under the supervision of Dr. Alessandra Toncelli (INFN and University of Pisa).
6.1
Absorption spectra
The measurements of absorption spectra have been performed by using a Cary 500 UV-VIS-NIR Spectrophotometer. It can be used for optical absorption spectroscopy in the wavelength range 180 nm-3200 nm. For our study, we focused on the range between 180 nm and 800 nm.
The spectrophotometer uses a monochromator with a diffraction grating with 1200 lines/mm. The grating can be scanned stepwise so that the photodetector can measure the light intensity at each wavelength corresponding to each step. The built-in light sources are a Tungsten Halogen (VIS-IR region) and a Deuterium arc (UV region). The Spectrophotometer uses an R928 photomultiplier as a photodetector in the UV-Vis region and a cooled PbS photodiode for the NIR region of the spectrum. The source changeover was set at 340 nm. For both UV and NIR region the signal bandwidth was set 2 nm. The data interval was set 1 nm and the average time 1 sec, defining a scan rate of 60 nm/min. The spectrophotometer quantitatively compares the fraction of light that passes through the crystal and the reference light, obtaining the absorption spectrum as their ratio as a function of λ [55, 56]. All the spectra have been corrected by acquiring a baseline before the acquisitions. The output of the spectrophotometer is in absorbance as a function of wavelength λ(nm). In spectroscopy, the absorbance A is defined as:
A = log10( I0
I) (6.1)
where I is the intensity of light at a specified wavelength that has passed through the sample (transmitted light intensity) and I0 is the intensity of the light before it enters the sample.
For what concerns the crystal preparation, they have been cut in thin slices, in order to avoid the photodetector saturation or blinding, and polished. The crystals dimensions are reported in tab.6.1.
After the baseline acquisition, each crystal has been placed in the spectrophotometer in a sample holder.
![Figure 4.8: The gain of the SiPM prototypes vs. overvoltage ∆V=V bias − V breakdown [20].](https://thumb-eu.123doks.com/thumbv2/123dokorg/7560784.110437/36.918.477.811.279.511/figure-gain-sipm-prototypes-vs-overvoltage-bias-breakdown.webp)
