Multichannel Digital Silicon Photomultipliers for Time-of-Flight PET

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Multichannel Digital Silicon

Photomultipliers for Time-of-Flight PET

Proefschrift

ter verkrijging van de graad van doctor

aan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. ir. K. C. A. M. Luyben,

voorzitter van het College voor Promoties,

in het openbaar te verdedigen

op dinsdag 1 juli 2014 om 10:00 uur

door

Shingo MANDAI

Master of Science

in Electrical Engineering and Information Systems

The University of Tokyo

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Dit proefschrift is goedgekeurd door de promotor: Prof. dr. ir. E. Charbon

Samenstelling promotiecommissie:

Rector Magnificus, voorzitter

Prof. Dr. ir. E. Charbon, ... Technische Universiteit Delft, promotor Prof. Dr. ir. A. J. P. Theuwissen, ... Technische Universiteit Delft

Prof. Dr. ir. R. B. Staszewski, ... Technische Universiteit Delft Prof. Dr. ir. M. Ikeda, ... The University of Tokyo

Prof. Dr. ir. L. Benini, ... Eidgen¨ossische Technische Hochschule Z¨urich Dr. ir. P. Lecoq, ... European Organization for Nuclear Research Dr. ir. T. Frach, ... Philips Digital Photon Counting

Prof. Dr. ir. L. K. Nanver, ... Technische Universiteit Delft, reservelid

CopyrightO 2014 by Shingo MandaiC

All rights reserved. No part of material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author.

ISBN 978-94-6259-234-6

Author website : http://sites.google.com/site/shingomandai/ email : mandai@silicon.u-tokyo.ac.jp

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Nomenclature

2-D Two-Dimension 3-D Three-Dimension

A-SiPM Analog Silicon Photomultiplier ADC Analog-to-Digital Converter APD Avalanche Photodiode APS Active Pixel Sensor

ASIC Application Specific Integrated Circuit BOM Bill of Materials

c.d.f. Cumulative Density function CCD Charge-Coupled Device CML Current Mode Logic

CMOS Complementary Metal-Oxide Semiconductor CT Computed Tomography

CTR Coincidence Time Resolution D-FF D Flip-Flop

D-SiPM Digital Silicon Photomultiplier DAQ Data Acquisition System

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DCP Digitally Controlled Charge Pump DCR Dark Count Rate

DNL Diﬀerential Non-Linearity DR Dynamic Range

FCS Fluorescence Correlation Spectroscopy FLIM Fluorescence Lifetime Imaging Microscopy FPGA Field-Programmable Gate Array

i.i.d. Independent and Identically Distributed I/O Input/Output

INL Integral Non-Linearity LET Light Emission Test LOR Line of Response LSB Least Significant Bit LUT Look-Up Table

MD-SiPM Multichannel Digital SiPM MLE Maximum-Likelihood Estimation MRI Magnetic Resonance Imaging n+ n-type diﬀusion

n-well n-type well

NDF Neutral Density Filter

NMOS N-type Metal-Oxide-Semiconductor p+ p-type diﬀusion

p-well p-type well

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p.d.f. Probability Density Function PDE Photon Detection Eﬃciency PDP Photon Detection Probability PET Positron Emission Tomography PMOS P-type Metal-Oxide-Semiconductor PMT Photomultiplier Tube

PWDC Pulse-Width-to-Digital Converter QE Quantum Eﬃciency

SNR Signal-to-Noise Ratio

SPAD Single-Photon Avalanche Diode

SPECT Single-Photon Emission Computed Tomography SPTR Single-Photon Timing Resolution

SRH Shockley Read Hall STI Shallow Trench Isolation

TCSPC Time-Correlated Single Photon Counting TDA Time Diﬀerence Amplifier

TDC Time-to-Digital Converter TOA Time-of-Arrival

TOF Time-of-Flight TSV Through-Silicon Via

VCO Voltage-Controlled Oscillator WSS Wide-Sense Stationary

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Chapter 1 Introduction

1.1 Nuclear medicine

Medical imaging is a collection of techniques utilized to construct images of the human body for clinical and scientific purposes. It is classified in nuclear medicine, magnetic resonance imaging (MRI), thermography, photoacoustic imaging, tomography, ultrasound and radiography (see Figure 1.1). In particular, nuclear medicine is employed as an ef-fective diagnostic tool using small amounts of radioactive material to check the severity of diseases, including many types of cancers, heart disease, gastrointestinal, endocrine, neurological disorders and other abnormalities within the human body. Because nuclear medicine can pinpoint the biological activity of molecules inside the body, it can identify various diseases in their earliest stages. It can also monitor a patient’s immediate response to therapeutic interventions. In nuclear medicine imaging, radiopharmaceuticals are injected internally, for example, intravenously. Radiation detectors outside the body (gamma cam-eras) capture radiation emitted by the radiopharmaceuticals and construct images of such emissions. There are several techniques used in diagnostic nuclear medicine. Scintigraphy is a two-dimensional (2-D) image technique, while Single-Photon Emission Computed To-mography (SPECT) and Positron emission toTo-mography (PET) are three-dimensional (3-D) tomographic techniques. The most important advantage of PET imaging over SPECT is that it can obtain images with a much higher sensitivity (by approximately two to three orders of magnitude); i.e. the ability to collect a higher percentage of the emitted events, which has very important implications [1, 2].

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Medical imaging Nuclear medicine MRI Thermography Photoacoustic imaging Tomography Ultrasound Radiography Scintigraphy SPECT PET

Figure 1.1: Medical imaging classification.

1.2 PET systems

1.2.1 Overview

Before conducting the scan by a PET machine, a radiopharmaceutical, which is labeled with a short-lived radioactive tracer isotope, is injected into the human body. The tracer is combined into a biologically active molecule; after the absorption of the tracer in tissues of interest, the subject is placed in the imaging scanner. The most common tracer is flu-orodeoxyglucose (FDG), a sugar, for which the waiting period before conducting the scan is typically an hour. As the radioisotope undergoes positron emission decay (also known as positive beta decay) during the scan, it emits a positron. The emitted positron travels in tissue for a short distance, which is typically less than 1 mm, before it annihilates with an electron available in the surrounding medium. After the annihilation, a pair of gamma photons is produced with approximately opposite directions (180o) as shown in Figure 1.2. The coincident gamma photons reach a scintillator in the detector ring, creating a burst of visible light, which is detected by photomultiplier tubes (PMTs) or silicon based photon sensors. After collecting tens of thousands of coincidence events along with straight lines of coincidences or lines of response (LORs), it is possible to localize their source using statistics. Photons that do not arrive coincidentally (i.e. within a coincident timing window of a few nanoseconds) are ignored.

In many centers, nuclear medicine images can be superimposed with computed tomog-raphy (CT) or magnetic resonance imaging (MRI) to produce special views known as

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Body PMT Scintillator Gamma ray Detector ring Gamma ray Origin of emission LOR Photo sensor

Figure 1.2: Structure of PET scanner.

modal reconstructions, image fusion or co-registration. These views allow the information from two diﬀerent exams to be correlated and interpreted in one image, leading to more precise information and accurate diagnoses. In addition, manufacturers are now producing PET/CT and PET/MRI units that are able to perform both imaging exams at the same time.

1.2.2 Radiation detection

Radiation detection is a key component of any imaging systems. The radiation detection module is composed of a scintillation material (scintillator) and photon counting sensors as shown in Figure 1.2. The scintillation material converts high-energy photons into visible light which can be detectable with a conventional photo sensor. The integral of the visible photons is proportional to the total energy deposited in the scintillators by radiation. Figure 1.3 shows the photon energy spectrum of a LYSO:Ce (LYSO) crystal scintillator, which was acquired by counting detected photons, primary photons. The continuous portion of the energy spectrum shows the Compton scattering region. The Compton scattered gamma photons exit the detector with partial deposition of energy. The peak position marks the mean energy of the radiation after complete deposition in the detector. The ability of the radiation detector to measure the deposited energy accurately is of paramount importance. This accuracy is referred to as the energy resolution of the detector. The energy resolution of the system is defined as the ratio of the full-width at half-maximum (FWHM) of the full energy peak,∆N511keV, and the energy value of the full energy peak maximum, N511keV, as

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0 # of primary photon (

n

) 0 100 1000 3000 300 500 Counts 200 2000 400 FWHM (ΔN_511keV) Photopeak Compton region N_511keV

Figure 1.3: Photon energy spectrum.

calculated

Energy resolution= ∆N511keV N511keV .

(1.1) The properties of some important scintillators are shown in Table 1.1. A high scin-tillation light yield is essential for suitable energy, timing, and spatial resolution, while a high density and eﬀective atomic number (Ze f f) is required to increase the detection

sen-sitivity. For optimum timing, decay time needs to be fast. Some of materials, e.g. sodium iodide doped with thallium (NaI) and Cerium-doped lutetium oxy-orthosilicate (LSO), re-quire doping with an activator substance in order to obtain optimum scintillation properties, while NaI, which has been used in SPECT mainly, is both hygroscopic and fragile. The scintillator for PET cameras has been Bismuth germanate (BGO), which has a high Ze f f, is

not hygroscopic and does not have long-lived secondary scintillation components. LSO is a suitable scintillator for detecting precise TOAs because of its good timing response while it is more expensive than BGO to manufacture.

1.2.3 Timing resolution and coincidence detection

The timing resolution of a PET detector is the statistical timing fluctuations or uncertainty due to the timing characteristics of the scintillator and a photo sensor. Figure 1.4 shows the coincident detection of two detectors. The output from each detector is discriminated by a certain threshold from detector noise or Scattered gamma events which has low energy, and sent to a data acquisition system (DAQ). Since the timing resolution represents the

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Table 1.1: Performance summary of scintillator materials for a PET application [3]. Material Density Ze f f Light yield Decay time Peak wavelength

(g/cm3₎ _(ph/MeV) _(ns) _(nm)

NaI:TI 3.67 51 41000 230 410

BieGe4O12(BGO) 7.13 75.2 8200 300 505

LuAlO3:CeO (LuAP) 8.34 64.9 11400 17 365

Lu2SiO5:Ce (LSO) 7.4 66 27000 40 420

(Lu-Y)2SiO5:Ce (LYSO) 7.1 60 32000 41 420

Gd2SiO5:Ce (GSO) 6.7 57 12500 60 430

Lu2Si2O7:Ce (LPS) 6.23 64.4 30000 30 380 LaBr3 5.29 47 63000 17-35 380 DAQ Threshold t₁ Threshold t₂ Detector 1 Detector 2 Detector 1 Detector 2 TOF (t₂- t₁) t₁ t₂ CTR_sigma = σ(t₂- t₁) = √2σ(t₁) (σ(t₁)==σ(t₂)) σ(t₁) σ(t₂) Coincident timing window

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Gamma generation

Figure 1.4: Detecting coincident events in two detectors.

variability in the signal arrival times (time-of-arrival, TOA) for diﬀerent events, it needs to be properly measured for detecting coincident events to distinguish true events from false events. True coincidences occur when both photons from an annihilation event are detected by detectors in coincidence, and no other event is detected within the coincident timing window. On the other hand, Figure 1.5 shows various kinds of false events. A scattered coincidence occurs when at least one gamma photon is scattered before the detection. Since the direction of the gamma photon has changed during the Compton scattering process, the resulting coincidence event will be registered to the wrong LOR. Random coincidences also generate false events. Multiple coincidences are similar to random events, except that three events from two annihilations are detected within the coincidence timing window. Scattered and random coincidences cannot be discriminated from true coincidences though they can add statistical noise to the data. Multiple coincidences are rejected not to add statistical noise.

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(a) (b) (c)

Figure 1.5: False events. (a) Scattered events. (b) Random events. (c) Multiple events.

The accuracy of the coincidence detection is defined as coincidence time resolution (CTR) as shown in Figure 1.4. When each detector is assumed to have an identical timing uncertainty,σ1(t), CTR is calculated as follows,

{ CT Rsigma= √ 2σ1(t) CT Rf whm≈ 2.35 √ 2σ1(t). (1.2)

Good timing resolution of a PET detector, besides helping reduce the number of random coincidences, can also be used to estimate the annihilation point between the two detec-tors by measuring the arrival time diﬀerence of the two photons [4]. This PET scanner is called time-of-flight PET (TOF PET) [4, 5, 6]. The advantage of estimating the location of the annihilation point is the improved signal-to-noise ratio (SNR) obtained in the acquired image, arising due to a reduction in noise propagation during the image reconstruction pro-cess. Figure 1.6 shows a comparison between non TOF PET and TOF PET. The constructed picture by TOF PET will be sharper with high contrast.

1.3 Photo sensors

Photo sensors are coupled to a scintillator to detect visible photons generated by the in-teraction with gamma photons. They are required to collect as many photons as possible with the accurate TOA acquisition of the corresponding gamma photons. In addition, low cost, tolerance to radiations, robustness to magnetic fields and small size are also important factors. This section introduces currently available or potentially useful photo sensors for PET application.

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Detector ring Gamma ray Origin of emission t1 t₂ w/o TOF w/i TOF LOR (a) (b)

Figure 1.6: Advantage of TOF PET. (a) The lack of precise TOA prevents the identification of a most likely annihilation region in the LOR. (b) High CTR enables the identification of a more precise annihilation region.

1.3.1 CCD and CMOS APS sensors

Charge-coupled devices (CCDs) and CMOS active pixel sensors (CMOS APSs) are a pop-ular silicon based photo sensor. The technology has been improved over the years to have extremely low noise and high quantum eﬃciency (QE), while timing response is still too slow for a single photon detection. Thus, CCDs and CMOS APSs are rarely used as photo sensors for a PET application. However, CMOS APSs have a potential of improving timing response because of maturely developed CMOS APS technology.

1.3.2 PMTs

Figure 1.7 shows the structure of a PMT. A PMT consists of a photo cathode and a series of electrodes in an evacuated glass enclosure. When a photon of sufficient energy strikes the photo cathode, it ejects a photoelectron by photoelectric effect. The photo cathode is at a high negative voltage, typically -500 to -1500 volts. The photoelectron is accelerated to-wards a series of additional electrodes called dynodes, additional electrons, are generated at each dynode. This cascading effect creates 105_{to 10}7_{electrons for each photoelectron that}

is ejected from the photocathode. The amplification depends on the number of dynodes and the accelerating voltage. However, PMTs with large distances between the photocathode and the first dynode are especially sensitive to magnetic fields since strong magnetic fields can bend the electrons’ trajectories. In addition, PMTs are bulky.

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Current output

HV Photo

cathode Photo electron

anode Dinodes Scintillation photon Figure 1.7: Structure of a PMT. 1.3.3 SiPM

SiPMs are a solid-state alternative to PMTs because of their robustness to magnetic fields, compactness, and low bias voltage [7]. SiPMs consist of an array of avalanche photodiodes (APDs) operating in Geiger mode. These are known as Geiger mode APDs (GAPD) or single-photon avalanche diodes (SPADs) as shown in Figure 1.8. In SPADs, the diode is biased above the breakdown voltage (the extra voltage is called excess bias or over voltage), the absorbed light generates an electron-hole pair, which in the multiplication region may trigger an avalanche, resulting in large number charges. To quench the avalanche, a ballast resistance called quenching resistor is placed either at the cathode or the anode of the diode. The voltage pulse forming across the quenching resistance is used to detect the avalanche. Two flavors exist for SiPMs: analog and digital. An analog SiPM (A-SiPM) is composed of an array of APDs or SPADs, whose avalanche currents are summed in one node, and the output is processed with oﬀ-chip components, as shown in Figure 1.9 (a) [7, 8, 9, 10, 11, 12, 13]. On the contrary, digital SiPMs (D-SiPMs) were firstly reported by Thomas Frach in Philips Digital Photon Counting utilizing an advanced CMOS technology [14]. In D-SiPMs, all of the SPAD digital outputs are combined together by means of a digital OR, and the output is directly routed to an on-chip time-to-digital converter (TDC) to reduce external components and temporal noise as shown in Figure 1.9 (b) [14, 15, 16, 17, 18]. A D-SiPM with multiple TDCs, called Multichannel D-SiPM (MD-SiPM), was also proposed to achieve the statistical approach for TOA estimation, which is one of the topic of this thesis. MD-SiPMs will be discussed in Chapters 2 and 3.

Table 1.2 shows the summary of photo sensors. SiPMs and PMTs are preferred for a 8

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HV n-type substrate p-type HV Photon HV Quenching resistor APD or SPAD

detector cell (pixel)

Avalanche multiplication

Figure 1.8: Structure of SiPMs.

i1 i2 in I = i1 + i2 + ... + in OR t1 t2 tn (a) (b) TDC Quenching resistor Active or passive quenching transistor

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Table 1.2: Summary of photo sensors.

Device Gain PDE Pixel Noise Timing MRI Cost integration

(QE) res. compatible

CCD No High High Low Slow Yes Expensive Middle

CMOS APS No High High Low Slow Yes Middle High

PMT Yes Middle Low High Fast No Cheap Middle

A-SiPM Yes Middle Middle High Fast Yes Expensive Low

D-SiPM Yes Middle Middle High Fast Yes Middle High

PET application because of the sharp timing response, and especially SiPMs can be inte-grated to a PET MRI unit with strong magnetic fields. Moreover, D-SiPMs can achieve high integration while A-SiPMs need external components.

1.4 Photo sensor terminology

The definition of various terms in photo sensors, mainly SiPMs, for a PET application is introduced in this section.

1.4.1 Photon detection eﬃciency

Photon detection eﬃciency (PDE), is the probability to detect photons impinging on the SiPM. PDE is calculated using QE, avalanche probability, Pavalanche, and fill factor, FF, as

follows,

PDE= QE × Pavahanche× FF. (1.3)

Note that Pavalancheis a function of excess bias voltage, and FF is the ratio of the geometrical

sensitive area where photons can be detected to the total SiPM area.

1.4.2 Timing resolution

Timing resolution describes how fast a photo sensor responds to photons. Timing resolution is characterized using a single photon and multiple photons. Single-photon timing resolu-tion is abbreviated as SPTR; it is the convoluresolu-tion of a detector cell jitter, e.g. single APD cell or SPAD cell, and the electrical jitter due to routing and a TDC. The timing resolution can be improved by increasing the number of detected photons, but it saturates indicating the limit of the timing resolution which corresponds to the TDC timing uncertainty. In PET, photo sensors need to have high PDE to receive as many photons as possible from a scintillator so as to achieve better timing resolution.

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1.4.3 Energy resolution

The energy resolution of the system is defined as the ratio of FWHM of the full energy peak and the energy value of the full energy peak maximum as explained in Section 1.3. An SiPM is required to have enough number of photo-detecting cells, pixels, to determine the energy of gamma photons. However, there is a trade-oﬀ between fill factor and energy resolution. Photo sensors should have enough pixels to achieve good linearity for photon counting without saturation eﬀect due to the finite number of pixels, while they also need to avoid small fill factor. Since fill factor increase with pixel size, these two parameter requirements are contradictory.

1.4.4 Gain

PMTs and SiPMs have a high gain to multiply input photons in a short period, while CCDs and CMOS APSs have unity gain. This is the reason why PMTs and SiPMs are preferred in a PET application. In SiPMs, gain is defined by the number of multiplied charges, which determines optical crosstalk and afterpulsing. In A-SiPMs, the gain is an important parame-ter for the design of a front end circuit, while, in D-SiPMs, the gain is not important because the produced charges are converted to digital values, 1 or 0.

1.4.5 Dead time

The dead time of an A-SiPM is the time to restore the output current to zero after an SiPM detects a photon, around 200-300 ns assuming a LYSO crystal scintillator. Depending on its architecture, the dead time of a digital SiPM is much longer than that of an analog SiPM, because all data of pixels may have to be read out before entering the next detection phase.

1.4.6 Noise Dark count noise

SPADs generate pulses called dark count noise, triggered by non-photo-generated carriers, such as thermal or tunneling generation at or near to the surface of silicon. The dark count rate (DCR) of an SiPM is a summation of this dark count noise of all SPADs in an SiPM per second. DCR and PDE are a trade-oﬀ relationship because both PDE and DCR increase as the excess bias increases. In a D-SiPM, each pixel has a specific circuit element added to turn oﬀ the SPAD when its activity is deemed too high (this SPAD is known as screamer).

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Afterpulsing

Afterpulsing is an unwanted avalanche triggered by trapped carriers released during the SPAD’s recharge [19, 20]. The probability of afterpusing is a function of SPAD dead time when the SPAD can not detect another photon. The probability also depends on the size of a SPAD. The afterpulsing could overestimate PDE and DCR, and thus it needs to be avoided.

Crosstalk

Crosstalk is an unwanted avalanche following neighbor SPADs’ avalanches triggered op-tically and/or electrically [21, 22]. Optical crosstalk is counted by spurious avalanches triggered by photons emitted by nearby pixels. In electrical crosstalk, a large amount of charges is generated and diﬀuses very quickly in all directions during an avalanche, in such a way that some holes or electrons can trigger a new avalanche in the neighboring multi-plication region. In a D-SiPM, crosstalk can be suppressed by turning oﬀ active pixels as screamers.

1.5 Goals of this thesis

Figure 1.10 shows the relation between CTR and energy resolution of commercial PET scanners, including clinical and preclinical TOF/non-TOF PET scanners [23, 24, 25, 26, 27]. Commercial clinical TOF PET scanners have already been available and achieved 500– 600 ps CTR, while preclinical PET scanners do not utilize TOF information, because the localization in the small ring diameter requires the dramatic improvement of CTR though it is tough to achieve with the current technology. The first objective of this thesis is to propose and design a photo sensor which can improve the timing performance for both clinical and preclinical PET scanners. The proposed photo sensor provides a novel feature to acquire and analyze generated photons due to the scintillation.

The second major objective of this thesis is to achieve high integration of the photo sensor. SiPMs are a powerful alternative to PMTs, preferred to PMTs because of low op-erating voltage, tolerance to magnetic fields, and small size. Nevertheless, both PMTs and A-SiPMs require extra components, such as amplifiers, discriminators, TDCs, and ADCs, which make the system complicated and bulky. However, thanks to use of a CMOS pro-cess, D-SiPMs can integrate many functions on the same chip rather than just photodiodes, resulting in the reduction of bill of materials (BOM). The high integration also improves timing performance, operating speed, and signal integrity.

The third objective is the modeling and analysis of the timing performance based on 12

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En e rg y re so lu tio n [ % ]

Coincidence timing resolution [s] Preclinical PET

Clinical non TOF PET

1.0n 2.0n 3.0n

5 10 15 20

Clinical TOF PET

25 4.0n 5.0n 6.0n 5 10 15 20 25 Preclinical non TOF PET

Clinical non TOF PET

Clinical TOF PET

TOF PET

Figure 1.10: Coincidence timing resolution and energy resolution of commercial PET scan-ners [23, 24, 25, 26, 27].

order statistics and Fisher information with the various type of SiPMs. The timing perfor-mance is improved by utilizing the proposed photo sensor, which has been also verified by the measurement.

These objectives have been achieved in the design a novel D-SiPM including periph-eral components achieving high levels of integration. Each function in the D-SiPM has been successfully measured and the new capabilities of the proposed D-SiPM have been demonstrated.

1.6 Thesis organization

In chapter 2, timing analysis of conventional SiPMs is shown. A new concept of D-SiPMs along with its advantage of utilizing multiple timestamps is also presented. Chapter 3 explains the proposed D-SiPM architecture and its operation. SPAD, TDC, high voltage generator design and their characterization are described in chapters 4, 5, and 6, respec-tively. In chapter 7, the characterizations of the proposed D-SiPM is shown. The advantage of utilizing multiple timestamps is also demonstrated. Finally, chapter 8 gives the conclu-sion of this thesis.

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Chapter 2 D-SiPM : A proposal for a sensor

architecture

This chapter introduces architecture and timing analysis of conventional D-SiPMs. Gen-erally, D-SiPMs have a FWHM SPTR of more than 100 ps, often of several hundred pi-coseconds. This is primarily due to detector jitter, circuit noise, and routing skew. Circuit noise and skew, in turn, strongly depend on the SiPM design; this dependency has been investigated by varying transistor size and transistor channel length, wire resistance, and capacitance. The scalability of the method has been validated by considering D-SiPMs of diﬀerent sizes and with a variety of signal distribution architectures. This chapter also presents a comprehensive statistical analysis of timing resolution for a TOF PET applica-tion with a D-SiPM and a LYSO scintillator, based on the research by Matthew Fishburn and Stefan Seifert [28, 29]. Compared to A-SiPMs, DCR of D-SiPMs must be carefully an-alyzed as it has an important impact on timing resolution. The analysis here includes DCR, SPAD and electrical jitter of the detector when coupled with a LYSO crystal. Next, the advantage of utilizing multiple timestamps assuming an ideal D-SiPM is described. Sim-ulation results show that D-SiPMs utilizing multiple timestamps can be more tolerant to DCR than those utilizing a single timestamp. Finally, based on these findings, a new type of D-SiPM is proposed to acquire multiple timestamps without sacrificing fill-factor. This chapter is based on results published in [30, 31, 32, 33]

2.1 Conventional D-SiPM

In D-SiPMs, all of the SPAD digital outputs are combined together by means of a digital OR, and the output is directly routed to an on-chip TDC to reduce external components and

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OR A D-SiPM chip TDC Energy counter OR TDC t1 _t2 tn

SPAD SPAD SPAD

Buffer Buffer Buffer

v1 v2 v3 Energy counter L a tch SPAD Circuit (a) (b) L a tch L a tch

Figure 2.1: The concept of (a) a D-SiPM and (b) geographical configuration. The timing response of each SPAD is read together to a single point where a TDC captures and digitizes it. The photon hits are individually captured and accumulated in energy counter.

temporal noise as shown in Figure 2.1 (a). Each pixel consists of a SPAD, specific circuit elements are added to generate digital signals for each photon detection. Timing resolution for single-photon detection is limited by SPAD jitter and circuit noise, as well as systematic skew due to mismatches of wire and circuit components from pixels to the single TDC, as shown in Figure 2.1 (b). However, timing resolution of D-SiPMs is not discussed com-prehensively in literature even though some papers investigate the timing performance of A-SiPMs [8, 34]. This section investigates how SPTR is related to architectural choices and design parameters. Design parameters include transistor size and transistor channel length, wire resistance and capacitance, assuming that the D-SiPM is implemented in a 0.35 µm standard CMOS process with special random process variations for the transistor channel length (assuming it includes threshold voltage and mobility variations) and wire resistance and capacitance [35]. However, the method can be easily extended to other processes with-out loss of generality. Diﬀerent sizes of D-SiPMs with a variety of signal distribution ar-chitectures are considered, often discussing the eﬀects of architectural choices and other design parameters on timing resolution; SPTR is important to determine the CTR in PET.

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Nth OR 1st (N+1)th OR 2nd 2(int)(N/2)th (b) N+1 Rw C_w C_in(N) Unit wire SPAD R_w C_w R_w C_w C_in(N+1) Buffer 1st R_w C_w Unit wire 1st OR C_in(1) Mth OR C_in(M) (c) (a) 2-input OR SPAD pitch 50μm Unit wire 25μm 1 2 3 4 5 6 7 8 OR Test input TDC Photon TOA T_ph Detected time by TDC after a photon hits at pixel #n and propagete

T_n T₁ T₂ T₃ T₄ T₂₅₆ Overall statistics Propagation delay Skew N+2 M 2 1

Simplified the simulation model

T_ph

σ(T_n-T_ph) E(T_n-T_ph)

INV1 INV2 OR1 OR2 OR3 OR4 OR5 OR6 OR7 OR8 OR9 OR10 OR11 OR12 OR13

Cout/CinWire cap(fF) 0 7 7 14 14 28 28 56 56 112 112 224 224 448 0

NMOS (μm) 0.7 1.5 2.0 2.9 3.9 5.8 7.5 11.0 14.0 20.0 24.0 32.1 32.1 32.3 0.5 PMOS (μm） 1.2 2.4 6.3 9.4 12.4 18.4 24.0 35.2 44.8 64.1 76.9 102.6 102.8 103.2 1.6 2 NMOS (μm) 0.2 0.6 0.7 1.1 1.4 2.3 2.9 4.6 5.7 9.0 10.9 16.6 17.8 21.5 0.5 PMOS (μm） 0.3 0.9 2.3 3.7 4.6 7.3 9.1 14.6 18.1 28.7 34.8 53.2 57.1 68.8 1.6 3 NMOS (μm) 0.1 0.4 0.4 0.7 0.9 1.4 1.7 2.9 3.4 5.7 6.8 11.0 12.0 16.1 0.5 PMOS (μm） 0.1 0.6 1.4 2.3 2.7 4.6 5.5 9.1 11.0 18.2 21.6 35.2 38.5 51.6 1.6 4 NMOS (μm) 0.1 0.3 0.3 0.5 0.6 1.0 1.2 2.1 2.4 4.2 4.8 8.2 9.0 12.9 0.5 PMOS (μm） 0.1 0.4 1.0 1.7 1.9 3.3 3.9 6.7 7.8 13.3 15.5 26.2 28.7 41.3 1.6 5 NMOS (μm) 0.0 0.2 0.2 0.4 0.5 0.8 0.9 1.6 1.9 3.3 3.8 6.5 7.1 10.8 0.5 PMOS (μm） 0.1 0.3 0.8 1.3 1.5 2.6 3.0 5.3 6.0 10.5 12.0 20.9 22.8 34.4 1.6 6 NMOS (μm) 0.0 0.2 0.2 0.3 0.4 0.7 0.8 1.4 1.5 2.7 3.1 5.4 5.9 9.2 0.5 PMOS (μm） 0.0 0.3 0.6 1.1 1.2 2.2 2.5 4.4 4.9 8.7 9.8 17.3 18.8 29.5 1.6 Red cells show smaller values than the minimum size of transistors, thus the minimum size will be used for them.

7

Figure 2.2: (a) H-tree for timing signals. (b) Model for the route from Nth junction to (N+1)th junction. (c) Summary table of transistor sizes in various λ. Each transistor size is calculated using Eq. 2.1.

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2.1.1 Simulated D-SiPM structure

When photons hit an SiPM, the first photon can impinge at any SPAD in any random loca-tion. Thus timing resolution degrades due to routing skew. H-tree is a well-known topology for clock distribution networks to minimize skew, and it is applicable to a D-SiPM with an OR gate. As shown in Figure 2.2 (a), e.g. a 16× 16 SPAD array in a D-SiPM, H-tree is implemented from each SPAD to the timing output via a buﬀer and 2-input OR gates. After a photon hits the nthpixel at TOA, Tph, the signal is propagated through a buﬀer, wires and

OR gates (one for each H junction), and the time is digitized by a TDC as Tn. The

prop-agation delay and skew,τskew, is defined as E(Tn− Tph) andσ(Tn− Tph), respectively, as

shown in Figure 2.2 (a). Note that the skew is in general defined as a time-invariant random variable and characterized in terms of its standard deviation. Figure 2.2 (b) shows the circuit schematic for our simulation. Following a SPAD, a buﬀer composed of two inverters and unit wires corresponding to the propagation path until the SiPM output inserting an OR gate in each junction (in the figure only these ORs are shown that are considered in an individual simulation, but all of the junctions have one). As an unit wire, which is a half length of the pixel pitch, a simple RC model (Rwand Cw) is employed. An OR gate consists of a NAND

gate and an inverter. In the simulations, it is assumed that the SPAD pitch and unit wire length is 50µm and 25 µm, respectively, and the number of SPADs is 64 × 64.

In an H-tree design, determination of the maximum transition time is important for skew control, area and power dissipation [36]. A parameterλ = Cout/Cin is used to control the

transition time, where Cin is the input capacitance of the OR gate and Cout its output load

capacitance to drive the next stage (including the input capacitance of the next OR gate) [37]. Parameterλ at the Nthjunction is defined using the unit wire capacitance, Cw, as,

λ = Cout/Cin = (Cw× 2[(N/2)]+ Cin(N+1))/Cin(N). (2.1)

The output of the H-tree is connected to an unit size OR gate to minimize the input capaci-tance, so Cin(13)is of known value. Therefore, all Cinwill be calculated successively. After

all Cinare calculated, the transistor size of each OR gate is introduced, as summarized in the

table of Figure 2.2 (c). Red cells show smaller values than the minimum size of transistors in the employed CMOS process, thus the minimum size will be used for them, assuming the eﬀect on the analysis is small since most of the stages can achieve the target lambda value.

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2 3 _λ 1.5n Pro p a g a ti o n d e la y (s) 4 2f (a) (b) 5 6 7 2.0n 2.5n 3.0n 3.5n 4.0n 30p Ske w (s) 35p 40p 45p 50p 55p 60p 2 3 4 _λ 5 6 7 3f 4f 5f 6f 7f 2f 3f4f 5f 6f 7f Unit wire capacitance, C_w (F) Unit wire capacitance, C_w (F)

Figure 2.3: (a) Propagation delay and (b) skew for variousλ values with diﬀerent values of

Cw.

2.1.2 Simulation results

A 2P4M high voltage 0.35µm CMOS process is employed for simulations. 0.35 µm and 0.5µm are set as the minimum channel length and width of transistors, respectively. The simulator is Cadence Virtuoso Spectre (TM) Circuit Simulator, version 7.0.1.076.

Figure 2.3 and 2.4 show the propagation delay and skew for eachλ, varying Cw from

7 fF to 2 fF, and Rw, from 3.5 ohm to 1 ohm, respectively, assuming that each transistor

channel length (Ltr), unit wire capacitance, and unit wire resistance has 5 % (sigma) process

variation. Both the propagation delay and the skew improve dramatically by changingλ from 7 to 2 while the dissipated power increases 1.7 times and the transistor area increases 4.5 times at 7 fF Cw and 3.5 ohm Rwas shown in Figure 2.5. One future option could be

designing the D-SiPM using an advanced CMOS process, such as 180 nm, 130 nm or 90 nm so as to minimize the impact on fill factor, because the wires and transistors occupy smaller area in the advanced CMOS processes. Note that Cwhas more eﬀect on the skew than Rw

in the case of D-SiPMs, while Rwis very important for A-SiPMs [8]. The process variation

for Ltr, Cw, and Rwwere set to vary from 5 % to 1% to see the dominant factor for the skew,

as shown in Figure 2.6, thus demonstrating that Ltr has the highest impact on the skew.

The temporal noise of the D-SiPM is composed of SPAD jitter,σspad, and noise due to

timing signal routing,σroute, including transistor induced noise and kTC noise [38]. The

temporal noise model is shown in Figure 2.7 (a). Figure 2.7 (b) shows the temporal noise by the timing signal routing. The temporal noise by the timing signal routing can be improved by employing a small value ofλ due to small transition time. Assuming that all these sources

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2 3 _λ 1.5n Pro p a g a ti o n d e la y (s) 4 (a) (b) 5 6 7 2.0n 2.5n 3.0n 3.5n 4.0n 30p Ske w (s) 35p 40p 45p 50p 55p 60p 2 3 4 _λ 5 6 7

Unit wire resisitance, R_w (Ω)

1.5 2 2.5 1 1.52 2.5 1 3 3.5 3 3.5 Unit wire resisitance, R_w (Ω)

Figure 2.4: (a) Propagation delay and (b) skew for variousλ values with diﬀerent values of

Rw. Rwwas found to have negligible eﬀects on propagation delays and skews.

2 3 λ 0 Po w e r co n su mp tio n (a . u .) 4 (a) (b) 5 6 7 1 O ccu p ie d a re a (a .u .) 1 2 3 λ 4 5 6 7 2

Unit wire capacitance, C_w (F) Unit wire capacitance, C_w (F)

2f 3f 4f 5f 6f 7f 2f 3f 4f 5f 6f 7f

Figure 2.5: (a) Power consumption and (b) area occupation of H-tree drivers in variousλ values.

of noise are wide-sense stationary (WSS), statistically independent random processes, the total standard deviation of the resulting process is computed as, σ2_jitter = σ2_spad + σ2_route. Figure 2.7 (c) shows simulation results of the noise by routing,σroute, and the total temporal

noise,σspad+route, assuming that the SPAD jitter is 42.6 ps sigma [30]. It is observed that

the SPAD jitter is dominant for the temporal jitter.

Under the same assumption of before, the SPTR of D-SiPMs is calculated as,σ2_sipm = τ2

skew + σ2jitter. Note that the skew is not time-invariant but process-variant. The jitter, on

the contrary, in time-variant but can be assumed to be process-invariant. Therefore,σsipmis

capturing both process and timing uncertainties. Figure 2.8 shows the SPTR of the D-SiPM 20

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1% 2 3 λ 4 (a) (b) 5 6 7 2 3 λ 4 5 6 7 Only Ltr variation 3% 5% 2 3 λ 4 (c) 5 6 7 2% 4% 1% All variations (Ltr, Cw, Rw) 2%3% 4%5% Only Cw variation All variations (Ltr, Cw, Rw) All variations (Ltr, Cw, Rw) Only Rw variation 1%-5% 0 Ske w (s) 10p 20p 30p 40p 50p 60p

Figure 2.6: Skew dependency on (a) Ltr, (b) Cwand (c) Rw. For a broken line, the situation

for which Ltr, Cwand Rwhave 5% sigma process variation at the same time is considered

as a reference. (a) (c) 0 T o ta l te mp o ra l n o ise (s) 10p 20p 30p 40p 2 3 λ 4 5 6 7 σ_spad_{+ route} σ_route SPAD jitter Transistor noise Thermal noise (σ_spad) (σ_route) SPADsBufferOR Wire

(b) 0 T e mp o ra l n o ise b y ro u n ti n g (s) 0.5p 2 3 λ 4 5 6 7 0.4p 0.3p 0.2p 0.1p σ_route

Figure 2.7: (a) Temporal noise sources in the D-SiPM. (b) Temporal noise by the timing signal routing. (c) Temporal noise in the D-SiPM for various values ofλ.

2 3 λ 4 (a) 5 6 7 σ_jitter τ_skew σ_sipm 2 3 λ 4 (b) 5 6 7 σ_jitter τ_skew σ_sipm 2 3 λ 4 (c) 5 6 7 SPT R 0 20p 40p 60p 80p σ_jitter τ_skew σ_sipm

1% L_tr variation 3% L_tr variation 5% L_tr variation

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Size of SiPM T imi n g re so lu ti o n f o r a si n g le p h o to n (s) 40p 50p 60p 70p 64x64 32x32 16x16 8x8 4x4 λ=2 λ=3 λ=4 λ=5 λ=6 λ=7

Figure 2.9: SPTR of the D-SiPM for diﬀerent sizes of the D-SiPM.

(b) TDC per cluster SPAD cluster SiPM Chip TSVs Routing per cluster TDC Chip SPAD + electronics 3D via SPAD cluster SiPM+TDC Chip Routing per cluster SPAD + electronics (a) TDCs

Figure 2.10: Ideal configuration of a D-SiPM implemented as (a) a one-chip solution (lim-ited applications) and (b) a 3D integrated circuit with TSVs.

for a range ofλ derived from τskewandσjitterat 1, 3 and 5 % process variation. The timing

resolution improves by utilizing smallλ because the skew improves. In addition, the SPTR improves by reducing the transistor channel length variation and approaches to the SPAD jitter. The SPTR dependency on the size of the D-SiPM has also been investigated. Figure 2.9 shows the timing resolution as a function of array size andλ. By reducing the size of the D-SiPM, the D-SiPM will be less sensitive to process variations because the skew becomes small. Therefore, to achieve good SPTR, the D-SiPM should be divided into small groups of SPADs, and connected to TDCs in the side of the chip as shown in Figure 2.10 (a), or in another die with short through-silicon vias (TSVs), as shown in Figure 2.10 (b). At the same time, optimizing the value ofλ and designing transistors carefully is also important

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not to have any geometrical asymmetry thus introducing Ltrvariations.

2.2 Timing analysis with a LYSO crystal scintillator based on

conventional D-SiPMs

In this section, a statistical analysis of timing resolution in conventional D-SiPMs is dis-cussed based on [28, 29], then, a more realistic analysis including the eﬀects of DCR is presented. The analysis here includes DCR, SPAD and electrical jitter of the detector with a LYSO crystal.

2.2.1 Coincidence time resolution

In a LYSO scintillator, it is assumed that photons are detected with the arrival time,θ. Tim-ing information of each photon can be considered as statistically independent and identically distributed (i.i.d.) following a probability density function (p.d.f.), femi(t|θ), which has been

modeled as a double-exponential with rise time trand decay time td [39]

femi(t|θ) = { (exp(−t−θ td )− exp(− t−θ tr ))/(td− tr) (t> θ) 0 (otherwise) (2.2)

Upon photon impingement, the SPAD jitter and an electrical jitter are convolved with the scintillator-based p.d.f., femi(t|θ) to calculate the detection p.d.f., fdet(t|θ). The timing

uncertainty of each rank’s photon can be calculated using order statistics (Eq. 2.3) with the detection p.d.f. and cumulative density function (c.d.f.), Fdet(t|θ),

fk:n(t|θ) = n(n_k−1₋₁) fdet(t|θ)Fdet(t|θ)k−1(1− Fdet(t|θ))n−k (2.3)

Figure 2.11 (a) shows the detection p.d.f. and Figure 2.11 (b) shows the p.d.f. of the k-th primary photon detected after the first detected photon.

Figure 2.12 shows the relation between order statistics and CTR with various numbers of detected photons and rise time. The number of photons and rise time can be varied depending on the PDE of the photo sensor, the aspect ratio of a scintillator, photosensor-scintillator coupling, and reflector material. When a single photon is utilized, CTR is small-est at a certain rank’s photon and degrades at an earlier or later rank’s photon. Thus, a TDC needs to choose the optimal rank of a photon carefully.

2.2.2 Noise eﬀect

D-SiPMs have various types of noise as discussed in Chap. 1.3. Here, dark count noise is focused on because afterpulsing and crosstalk have a negligible eﬀect to timing resolution.

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Time[s] Pro b a b ili ty d e n si ty (a .u .) 0 1 0 Expected TOA : 1st _1n Time uncertainty 2nd ₃rd ₄th ₅th ₆th ₇th ₈th ₉th Detection p.d.f. 1st Photon p.d.f. 2nd 3rd (b) Pro b a b ili ty d e n si ty (a .u .) 0 1 0 _100n Detection p.d.f. Time[s] (a)

Figure 2.11: (a) Detection p.d.f. (b) p.d.f. of the k-th primary photon detected after the first detected photon.

The dark count noise follows an exponential distribution with event rate,µ, and system reset time, tr, as

f (t)=

{

µ exp(−µ(t − tr)) (t> tr)

0 (otherwise) (2.4)

The p.d.f. of dark count noise should also be convolved with electrical jitter, forming DCR-based p.d.f., fdcr(t|tr). The detection cycle or frame starts at the earliest beforeθ and

at the latest frame period, T beforeθ, so the DCR-based p.d.f. is summed up for each reset time and then normalized. Since the gamma events and dark noise can occur independently, the scintillator-based p.d.f. and DCR-based p.d.f. are mixed with a mixing ratio p : (1− p) when p is defined by the percentage of photons emitted from scintillator, N, out of total detectable events, N+ µT, as shown below.

femi+dcr(t|θ) = p femi(t|θ) + (1 − p) ∫_θ θ−T fdcr(t|tr) dr ∫_θ θ−T ∫_∞ tr fdcr(t|tr) dt dr (2.5) 24

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0 10 0 200 400 600 800 1000 F W H M o f C T R (p s) 20 30 40 50 Rise time : 400ps (b) Order statstics Rise time : 300ps Rise time : 200ps Rise time : 100ps 0 10 0 200 400 600 800 1000 F W H M o f C T R (p s) 20 30 40 50 200 photons 500 photons ₁₀₀₀ photons 2000 photons (a) Order statstics

Figure 2.12: Order statistics with a single timestamp with (a) various numbers of detected photons, 200, 500, 1000, and 2000, and (b) various values of rise time, 100, 200, 300, and 400 ps, at 1 Hz DCR. f_1:n(t;θ) or f_2:n(t;θ) or ... or f_n:n(t;θ) + Dark count SPAD jitter Scintillator Emission × (1-p) × p f(t;θ) Single time information (p : mixing ratio) Detection Convolution Electrical jitter Convolution p.d.f. t t t t t p.d.f. p.d.f. p.d.f. p.d.f.

Figure 2.13: Method for calculating the detection p.d.f. considering DCR based on conven-tional D-SiPMs. A detailed description of all components is given in text.

Finally, the mixed p.d.f. is used for calculating the Fisher information [40] for the rth-order statistics p.d.f. This procedure is shown in Figure 2.13.

For our simulations, we assumed normal SPAD jitter and electrical jitter distributions with a standard deviation of 100 ps, the rise and decay times of a LYSO scintillator are 200 ps and 40 ns, respectively, while the number of detected photons is varied from 100 to

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Order statstics 0 10 0 200 400 600 800 1000 F W H M o f C T R (p s) 20 30 40 50 20M DCR 10M DCR <100k DCR 1M DCR

Figure 2.14: CTR degradation due to various values of DCR, less than 100 k, 1 MHz, 10 MHz, 20 MHz with 1000 detected photons.

5000, and DCR is varied from 1 Hz to 100 MHz. Figure 2.14 shows the simulation results assuming a detected photon flux of 1 MHz/s with various values of DCR. The x-axis means the rank of a photon. High DCR degrades CTR by occupying a TDC before gamma photons impinge. Figure 2.15 (a) shows the timing of dark count noise and photons generated by gamma events. A TDC cannot always trigger due to photons generated by gamma events because dark count noise is randomly mixed with gamma generated photons. However, some D-SiPMs employs dark count noise rejection technique, as shown in Figure 2.15 (b) [14, 15]. Any diode breakdown is assumed to be a dark count noise and is automatically reset if the first trigger does not lead to another trigger within a certain evaluation period. This embedded refresh logic prevents dark count noise from accumulating and, eventually, interfering with true gamma events. This technique can reduce the eﬀect of DCR. Figure 2.16 shows the improvement of CTR by employing a dark count noise rejection technique with 200 ns and 20 ns evaluation period. However, this technique requires a certain evalu-ation time and recovery time for resetting the TDCs. Figure 2.15 (b) shows an example of missing a gamma event photons. Gamma events and dark count noise can occur at random, thus the recovery time can overlap with a gamma event. Misditection of TOA and the un-derestimation of the radiation energy occur as a result. In other words, the sensitivity of the system is reduced and statistical noise is added to the constructed image. Figure 2.17 shows the evaluation time-related occupancy of TDCs during the detection of gamma events. Two conditions, 20 ns and 10 ns reset period, are shown with diﬀerent DCR values. If a SiPM

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(a)

Dark count noise Photons

(b)

Photons

Recovery time

Dark count noise

Evaluation Reset Missing photons Collect data Detect Recovery time

Figure 2.15: (a) The timing of dark count noise and photons generated by gamma events. (b) Eﬀects by utilizing a dark count noise rejection technique.

0 10 0 200 400 600 800 1000 F W H M o f C T R (p s) 20 30 40 50 w/o checker w/i checker (20 ns evaluation) Order statstics w/i checker (200 ns evaluation)

Figure 2.16: CTR improvement by the dark count noise rejection technique.

has 10 MHz DCR with 20 ns reset period, the recovery time reduces the total detection time to 80 %.

2.3 Timing resolution based on an ideal D-SiPM

Although conventional D-SiPMs can reduce extra components (Preamplifier, ADC, TDC, etc.) compared to A-SiPMs, the routing skew could degrade timing performance and the recovery time due to DCR reduces the sensitivity of the system. However, the approach

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DCR [Hz] 100k 0.01% 0.1% 1% 10% 100% 1M 10M 20 ns reset period 10 ns reset period D e a d t ime o ccu p a n cy

Figure 2.17: Recovery time occupancy with diﬀerent DCR values.

pursued in [41] can achieve perfectly balanced routing by implementing an on-pixel TDC as shown in Figure 2.18. The structure gives minimum SPTR by minimizing the skew, whose eﬀects were discussed in 2.1. Furthermore, the statistical approach to estimate TOA of a gamma photon is possible by detecting timestamps of multiple photons in a single gamma event. In this section, the timing analysis based on the ideal D-SiPM is discussed.

2.3.1 Simulation setup

For our simulations, we assumed the same setup to acquire the mixed p.d.f, used for calcu-lating Fisher information [40, 29] for the joint p.d.f. of the first r-order statistics, then the Cr´amer-Rao lower bound for the unbiased estimator, ˆθ is calculated. Figure 2.19 shows the procedure.

2.3.2 Timing improvement

Figure 2.20 shows the relation between order statistics and CTR with various numbers of detected photons and rise time. The x-axis means the rank of a photon for single timestamp and the ranks of photons for multiple timestamps. By utilizing more photons, CTR is im-proved until it reaches the Cr´amer-Rao lower bound. The lower bound is better than the best CTR utilizing a single timestamp under the same photo-exposure conditions.

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TDC TDC TDC

Figure 2.18: Ideal D-SiPM.

+ Dark count SPAD jitter Scintillator Emission × (1-p) × p f(t;θ) f_1:n(t;θ) or f_1,2:n(t;θ) or ... or f_1,2,..,n:n(t;θ) multi-time information (p : mixing ratio) Detection Convolution Electrical jitter Convolution p.d.f. t t t t t p.d.f. p.d.f. p.d.f. p.d.f.

Figure 2.19: Method for calculating the detection p.d.f. considering DCR based on the ideal D-SiPM.

2.3.3 Noise eﬀects

DCR is considered for the timing analysis. The timing resolution with multiple timestamps does not degrade due to DCR while the timing resolution with a single timestamp degrades

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Order statstics 0 10 0 200 400 600 800 1000 F W H M o f C T R (p s) 20 30 40 50 (b) Single timestamp Multiple timestamps Rise time : 400ps Rise time : 300ps Rise time : 200ps Rise time : 100ps Order statstics 0 10 0 200 400 600 800 1000 F W H M o f C T R (p s) 20 30 40 50 200 photons 500 photons 1000 photons 2000 photons (a) Single timestamp Multiple timestamps

Crámer-Rao Lower bound

Figure 2.20: Utilizing of a single timestamp or multiple timestamps v.s. FWHM of CTR with (a) various numbers of detected photons, 200, 500, 1000, and 2000, and (b) various values of rise time, 100, 200, 300, and 400 ps, at 1 Hz DCR (which is almost negligible).

with a certain amount of DCR, as shown in Figure 2.21. Figure 2.22 summarizes the relation between the number of detected photons and timing resolution using a single timestamp and multiple timestamps. The FWHM with multiple timestamps improves 13% if compared to the FWHM with a single timestamp at less than 100 kHz DCR, however, the FWHM is 20% and 40% better at 1 MHz and 10 MHz DCR at 1000 detected photons, respectively.

A large number of TDCs is implemented in the ideal D-SiPM. Thus, the ideal D-SiPM can still detect the timestamps of photons by gamma events, though the dark count noise may occupy several TDCs. Figure 2.23 shows the timing of dark count noise and photons generated by gamma events. The number of acceptable dark count noise is set to three counts, so the ideal D-SiPM resets all TDCs after it receives three dark count noise, in the example shown in Figure 2.23 (b). By employing the ideal D-SiPM, the second gamma events can be detected, while it was not possible to detect with a conventional D-SiPM.

The recovery time occupancy using the ideal D-SiPM with diﬀerent dark count noise acceptance is shown in Figure 2.24. By increasing the acceptable number of dark counts, the recovery time can be reduced. During accepting dark count noise, the pixel who has dark count noise is not sensitive to a photon, but the eﬀect on the PDE due to loss of fill factor is small since SiPMs have more than hundreds of pixels typically.

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0 10 0 200 400 600 800 1000 F W H M o f C T R (p s) 20 30 40 50 Single timestamp 20M DCR 10M DCR <100k DCR Multiple timestamps 1M DCR Order statstics

Figure 2.21: Order statistics with a single timestamp or multiple timestamps v.s. FWHM of timing information with various values of DCR, less than 1 MHz, 10 MHz, 20 MHz at 1000 detected photons.

0 1000

Number of detected photons 0 200 400 600 800 1000 F W H M o f C T R (p s) 2000 3000 4000 5000 1,100k Hz 0 1000

Number of detected photons

2000 3000 4000 5000 1,100k,1M,10M,20M Hz 20M Hz 1M Hz 10M Hz 0 200 400 600 800 1000 F W H M o f C T R (p s) (a) (b)

Figure 2.22: FWHM timing resolution v.s. number of detected photons using (a) a single timestamp and (b) multiple timestamps

2.4 Proposed SiPM structure

The ideal D-SiPM gives the best SPTR by minimizing the skew, and achieves the statistical approach to estimate TOA by detecting TOAs of multiple photons in a single gamma event. However, the main drawback of the approach proposed in [41] is a low fill factor due to the need for a significant silicon real estate to implement per-pixel functionality. In order to

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(a)

Dark count noise Photons

(b)

Photons Dark count noise

Recovery time Evaluation

(Until 3 dark count noise) Reset Collect data

Detect

Collect data

Detect

1 2 3 1 2

Figure 2.23: (a) The timing of dark count noise and photons generated by gamma events. (b) Eﬀects by utilizing the dark count noise rejection technique based on the ideal SiPM.

DCR [Hz] 100k 0.01% 0.1% 1% 10% 100% D e a d t ime o ccu p a n cy 1M 10M

20 ns reset period w/i a conventional D-SiPM (check just

after first dark count noise)

Until 2 dark count noise Until 5 dark count noise Until 10 dark count noise

20 ns reset period w/i the ideal D-SiPM (check until n dark count noise)

Figure 2.24: Recovery time occupancy with diﬀerent DCR values. The ideal D-SiPM with the diﬀerent acceptable values of DCR acceptance is compared with a conventional D-SiPM. (Each p.d.f. component is explained in Subsection 2.2.2).

keep high PDE, the 3-D integration is a promising technique. However, reliable 3D ICs are still unavailable and/or expensive.

2.4.1 Structure of multichannel D-SiPM

To achieve both high fill factor and acquisition of multiple timestamps, a new type of a D-SiPM has been proposed [32, 42, 43]. Sharing one TDC with several pixels has the ad-vantage of increasing the fill factor while still enabling somewhat independent photon TOA

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TDC TDC TDC

OR OR OR

Figure 2.25: Proposed multichannel D-SiPM.

evaluation, as shown in Figure 2.25. The skew problem is also improved when compared to conventional D-SiPMs for single-photon detection, and the multiple timing information can be utilized in a statistical approach for multiple-photon detection. This type of SiPMs is called Multichannel digital SiPM, MD-SiPM. Figure 2.26 shows a simulation result of pre-dicted CTR sweeping D-SiPM SPTR. The simulation compares CTR using a single times-tamp and multiple timestimes-tamps at 500 and 1000 detected photons at 1 Hz DCR. CTR is improved by reducing SPTR and utilizing multiple timestamps.

2.4.2 Acquisition of multiple timestamps

MD-SiPMs share a TDC with several pixels, thus this might aﬀect the acquisition of multi-ple timestamps. To evaluate the feasibility of this approach with the MD-SiPM, a simulation is carried out using first 50 photons impinging on the entire detector with Poissonian arrival statistics. The simulation considers several numbers of TDCs, such as 96 and 192. Figure 2.27 shows simulation results of the probability of detecting the timing information of pho-tons continuously. The simulation suggests the possibility to get multiple time information

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0 100 FWHM of SPTR (ps) 100 200 300 400 200 400 F W H M o f C T R (p s) 300 Single timestamp Multiple timestamps CTR improve ment by SPT R CTR improvement by multiple timestamps 1000 photons 500 photons

Figure 2.26: SPTR of a D-SiPM vs. predicted CTR using a single timestamp and multiple timestamps with 500 or 1000 detected photons at 1 Hz DCR.

0

Order of input photons

10 20 30 40 50 0 1.0 0.8 0.6 0.4 Pro b a b ili ty 0.2 96 192 48 # of TDCs 416 1

Figure 2.27: The probability to detect the time information of photons continuously without skipped data, with 48 TDCs, extrapolating to 96 TDCs, and 192 TDCs.

without any detection interruption. Even with 48 TDCs, 5 timestamps can be acquired with-out detection interruption with 80 % probability. According to section 2.3, first 5 photons are necessary to reach to the Cr´amer-Rao lower bound. This proves that the MD-SiPM can achieve both high fill factor and the acquisition of multiple timestamps enough to improve timing resolution.

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2.5 Conclusion

The timing resolution based on conventional D-SiPMs has been analyzed using a SPICE simulator. It is found that SPAD jitter and skew have a strong impact on the timing reso-lution of the D-SiPMs, though the timing resoreso-lution can be improved by choosing a proper architecture or modifying the design parameters: i.e. transistor width and length, wire re-sistance and capacitance, and their process variations. The analysis has been extended for the timing resolution based on conventional D-SiPMs and the ideal D-SiPM for a TOF PET application. The analysis here includes DCR, SPAD and electrical jitter of the detector with a LYSO crystal. Simulation results show that D-SiPMs utilizing multiple timestamps can be more tolerant to DCR than those utilizing a single timestamp. Finally, based on these findings, a new type of D-SiPMs called Multichannel D-SiPMs or MD-SiPM, has been pro-posed. MD-SiPMs can acquire multiple timestamps without sacrificing fill factor for some applications, such as an endoscope which will be explained in Chap. 3.1.

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Chapter 3 MD-SiPM architecture

This chapter explains the MD-SiPM architecture. Three chips including a 4× 6 MD-SiPM array chip, a 4× 4 MD-SiPM array chip, and a 9 × 18 MD-SiPM array chip, have been fabricated. In this chapter, the structure of the 9× 18 MD-SiPM array chip and its operation are described. The detail of TDCs will be described in Chapter 5. This chapter is based on the results published in [33, 42, 43, 44]

3.1 Requirements for the MD-SiPM design

MD-SiPM array chips are designed and fabricated for the European Union 7th Framework Program under Grant Agreement No. 256984 EndoTOFPET-US. The EndoTOFPET-US project aims ”to design and build one prototype of a bi-modal PET-US (Positron Emission Tomography and Ultrasound) endoscopic probe combining in a miniaturized system a fully digital, 200 ps time resolution Time of Flight PET detector head (TOF-PET) coupled to a commercial ultrasound (US) assisted biopsy endoscope and to launch a pilot clinical study focusing on pancreatic cancer, after a first step of preclinical feasibility tests on pigs” [45, 46]. The external sensor is a large format commercial SiPM array coupled to a pixelated LYSO scintillator and the endoscopic sensor is a miniaturized array of MD-SiPMs coupled to a mini-scintillator. The external sensor has 256 matrices of 44 LYSO crystals with an size of 3.5 mm× 3.5 mm × 15 mm, and the endoscope sensor has 800 µm pitch 9 × 18 matrices with a cross-section of 0.71 mm× 0.71 mm and a length of 10-15 mm [47]. 200 ps CTR can contribute to reject background coincidences outside the organs of interest. In addition, or more importantly, it helps reduce the large number of random coincidences due to the close distance of the probe from the radiation source [4]. Therefore, the endoscope sensor is aimed to achieve the accurate timing resolution regardless of the small size crystal.

Multichannel Digital Silicon Photomultipliers for Time-of-Flight PET