Characterisation of the Timepix3 chip using a gaseous detector

Transcription

1 Characterisation of the Timepix3 chip using a gaseous detector Mijke Schut

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3 Characterisation of the Timepix3 chip using a gaseous detector Mijke Schut February 215 MASTER THESIS Particle and Astroparticle Physics University of Amsterdam Detector Research and Development Nikhef Daily supervisor: Dr. Martin van Beuzekom Examiners: Dr. Els Koffeman Dr. Ivo van Vulpen

4 Abstract The Timepix3 chip is the latest member of the Medipix family of readout chips. It is based on 13 nm CMOS technology. The main advantage of Timepix3 with respect to its predecessor Timepix1 is that it can operate in the combined ToA&ToT mode. This means that both the time of arrival as well as the charge of a hit can be read out simultaneously. Timepix3 will be used in various detectors. One of these is the LHCb VELO for which VeloPix, derived from Timepix3, is developed. Before Timepix3 can be applied in a large scale detector its characteristics have to be determined. To do so a gaseous micromegas detector has been constructed with Timepix3 as readout chip. Testbeam measurements were performed at DESY, Hamburg, with a 6 GeV electron beam. Data was taken at various grid voltages and with two different gas mixtures. A charge calibration was executed at Nikhef. Williamson s and York s method was used for fitting tracks. By track reconstruction, the spatial and time resolution of the detector are determined. Residual distributions show diffusion as well as timewalk. A promising result is the calculation of an average timewalk of 2 ±.17 ns.

5 Contents 1 Introduction 1 2 Timepix From Medipix to Timepix Timepix Operation Modes ToA and ToT information ToA ToT Readout Gaseous gridpix The working of a TPC Ionisation Electrons Drift Diffusion Signal amplification Signal formation Gridpix DESY testbeam Feb DESY Testbeam facility Detector setup Measurements Threshold equalisation ToT-charge calibration Method Results Implementation Gridpix characterisation Some parameter checks Gas amplification Distribution of hits and ToT Polýa function Grid plots

6 6.4 Krumenacher current Timewalk ToT values Timewalk as function of ToT Mean timewalk value Conclusion Track fitting From data to tracks York s method Errors Residuals Diffusion Timewalk Conclusion Summary and Conclusions Improvements Outlook Appendices 6 A Properties of gas mixtures 6 A.1 He/iC 4 H 1 95/ A.2 Ar/iC 4 H 1 9/ B Testbeam data 65 B.1 He/iC 4 H 1 data B.2 Ar/iC 4 H 1 data C DAC scan 68 D Hit and ToT distributions 7 D.1 Distributions of number of hits D.2 Distributions of ToT values Bibliography 75 Samenvatting 78 Acknowledgements 79

7 Chapter 1 Introduction This master s thesis describes a research on the Timepix3 chip. The goal of this research is the characterisation of the chip and the micromegas detector constructed with it. The research was performed at the Detector R&D (Research and Development) group at Nikhef, the Dutch National Institute for Subatomic Physics. The experiment was executed as part of the master s programme in Particle and Astroparticle Physics at the University of Amsterdam. In this introduction the background of the research will be described. Furthermore the objectives and approach are presented. The introduction ends with an overview of the content of the following chapters. At the Detector R&D department, new detectors or detector parts are being developed and tested such that they can be implemented in large particle physics experiments like those at the Large Hadron Collider (LHC) at CERN. At the LHC two proton bundles collide at high energy (13 TeV centre-of-mass in 215 [1]). The detectors along the LHC are positioned such that these interactions happen inside the detectors. From the proton collisions, many particles are created which themselves often decay again very quickly into other particles. The point of collision between two protons is called the primary vertex. The point at which one of the products of the proton collision decays is called the secondary or displaced vertex. The reconstruction of these vertices is very important to understand the details of the physics processes of charged particles [2]. Since most of these charged particles have a short lifetime, the primary and secondary vertex are not far apart and high resolution detectors are needed to reconstruct both. To reconstruct the tracks of charged particles, and thereby locate the displaced vertices, a medium is needed to produce a signal that can be read out. Most commonly this is a gas or a semi-conductor. The signal in the medium is mainly formed by ionisation of the atoms of this medium. For gaseous detectors, the electrons or ions that are released by the ionisation process are called primary charge. This primary charge is directed towards the readout device and amplified such that the signal is sufficiently large to be read out. The point of ionisation above the readout chip can be located by using a pixel chip as readout device. The hits on the pixel chip determine the location of ionisation and thereby tracks of charged particles can be reconstructed. In this thesis the Timepix3 readout chip is characterized. It is a pixel chip which is part of the so-called Medipix family and is the successor of the earlier developed Timepix chip (26) 1. One of the main advantages of Timepix3 with respect to Timepix1 is that it can 1 In this thesis, Timepix (26) will be called Timepix1, to prevent confusion with Timepix3. 1

8 CHAPTER 1. INTRODUCTION 2 measure both the time of an incoming signal as well as its charge simultaneously. The first Timepix3 chip became available mid-213. The aim of this project is to characterize the Timepix3 chip and the micromegas detector constructed with it. To investigate detailed properties of the detector, particle tracks are studied, therefore a great part of the project is dedicated to fitting tracks from a testbeam experiment. The project started by collecting data at the testbeam facility at DESY, Hamburg. This was done together with Martin van Beuzekom and Panagiotis Tsopelas. The testbeam consisted of highly energetic electrons. Using a micromegas foil, the signal of single electrons, as formed by ionisation of a gas, could be amplified to make readout with Timepix3 possible. The focus in the analysis of the data lies on properties of the different gases that were used, tracking and characterizing Timepix3. The last was mainly concentrated on examining timewalk. This effect delays the incoming signal and therefore causes an error on the position measurement of the primary ionisation. The track quality thereby decreases. All of these points, and more, are described in much more detail in this report. Structure of the Report This report is structured as follows. Chapter 2 describes the Timepix3 chip. In Chapter 3 the micromegas detector that was tested is described as well as the working of gaseous detectors. Chapter 4 discusses the experimental setup and the performance of the testbeam at DESY and lists the data that was taken. Chapter 5 describes the ToT-charge calibration that was done in the Nikhef lab, necessary for determining the charge of incoming signals. Chapters 6, 7 and 8 contain results of the measurements. In Chapter 6 the focus is on the properties of the micromegas detector. Chapter 7 is about determining an important error in the measurements, timewalk. Chapter 8 focuses on tracking. Finally, Chapter 9 gives the main conclusions of this research and a short outlook on the development of Timepix3 based detectors in the coming years.

9 Chapter 2 Timepix3 The object of study in this report is the Timepix3 readout chip. In this chapter a bit of history on the development of the chip will be given. Furthermore, the operation of the Timepix3 chip will be described. Figure 2.1: A Timepix3 chip of 14.1 mm side-length. At the bottom the periphery, the interface between pixels and outside of the chip, is visible. 3

10 CHAPTER 2. TIMEPIX From Medipix to Timepix3 Medipix Timepix3 is the most novel pixel readout ASIC in a family of pixel chips. The first of these to be developed was the Medipix1 or Photon Counting Chip (PCC) in 1997 [3]. Medipix1 is a CMOS (complementary metal-oxide-semi-conductor) imaging chip. By implementing bump-bonds to Si and GaAs sensors 1, direct charge conversion of photons was made possible which provides minimum image blurring. Its hybrid pixel technology supplied noise-free single photon counting which was needed at the Large Hadron Collider (LHC) experiments at CERN. A threshold is set and a comparator checks whether the amplified incoming charge from the semi-conductor sensor exceeds this threshold. When this is the case the event is counted. The threshold could be set for each pixel individually. A Medipix1 chip consists of 64 x 64 pixels of 17 µm side-length. It has a per pixel counter of 15 bits which leads to a high dynamic range. Because of the developments in CMOS technology, Medipix could be improved. Medipix2, the successor of Medipix1, has three main novelties. First, the pixel size is reduced to 55 µm x 55 µm which gives a better spatial resolution. Second, the number of pixels per chip has increased to 256 x 256, leading to an active area of 2 cm 2 compared to 1.2 for Medipix1. Third, the chip can accept either positive or negative charge input which makes it possible to use different sensor materials, whereas Medipix1 only accepts positive charge. The aim of Medipix3, the successor of Medipix2, was to facilitate colour imaging by improving the energy resolution. This is done by reducing the effect of charge sharing. Charge sharing happens due to diffusion and it means that charge from one hit is collected by more than one pixel. Often there is one pixel that has received most of the charge, however not all charge coming from the hit. Medipix3 compensates for this effect by summing the charge of neighbouring pixels and assigning this to the pixel that obtained the highest charge. Timepix From Medipix2 the first Timepix chip evolved in 26. The pixel size stayed the same, however the functionality of the pixels was extended. Timepix1 has three modes of operation which can be set for each pixel individually. First, the counting mode, identical to Medipix2, in which hits are counted. Second, the Time-over-Threshold (ToT) mode in which the charge of a hit can be measured. Third, the Time-of-Arrival (ToA) mode in which the arrival time of a hit is measured. The measurement of the arrival time of a hit is novel with respect to Medipix2. Timepix1 was developed to be used as readout chip for Time Projection Chambers (TPCs) which are discussed in the next chapter. This is done by attaching a gas gain grid to the chip to amplify the signal from electrons deposited in a gas volume. Timepix1 can only be used at low event rate because for each event the whole chip has to be read out, even if the event only involves just a few pixels. Due to the effect of timewalk, which will be discussed in much more detail later on in this thesis, the accuracy in the time measurement is not optimal. 1 Silicon (Si) and gallium arsenide (GaAs) are both semi-conductor detector materials.

11 CHAPTER 2. TIMEPIX3 5 Timepix3 is the successor of Timepix1. The aim of use is in gaseous detectors as well as in semi-conductor detectors [4]. With respect to Timepix1, Timepix3 has a higher time resolution and reduced timewalk. Data can be read out continuously with zerosuppression and at high speed. The most important novelty with respect to Timepix1 in its functionality is the possibility of collecting ToA and ToT information simultaneously. This makes Timepix3 an excellent chip for tracking applications. Figure 2.2 shows two images taken with detectors based on Medipix and Timepix. (a) Medipix1: m (b) Timepix1: bug Figure 2.2: Images taken with Medipix / Timepix detectors. (a) Medipix1 image of an m shaped 5 µm thick tungsten wire. It is captured using a 9 Sr source of electrons, made by the Medipix group at CERN [3]. (b) Timepix1 image of a bug taken with a silicon sensor, made by X-ray Imaging Europe, Germany [5]. 2.2 Timepix3 The Timepix3 chip consists, just as Timepix1, of 256 x 256 square pixels with a size of 55 x 55 µm [4] [6]. Figure 2.3 shows how it is divided in 128 double columns consisting of so-called super pixels: 4 x 2 pixel groups. Each individual pixel is divided into an analogue and a digital part. The analogue part or front end circuit has fast response and low threshold (5 electrons). This enables high resolution time measurement. It is possible to detect both positive and negative charge, because the preamplifier in the analogue circuit, Figure 2.6, is capable of sinking or sourcing the current. The digital part consists, amongst other things, of a time-over-threshold counter, a coarse-time stamp register and a fine-time counter. A fast clock of 64 MHz is needed for the fine-time stamping and is generated by a local start-stop ring oscillator for each super pixel. On-pixel data goes via the super pixel FIFO 2 to the End-Of-Column FIFO via a double column data bus with a speed of 4 MHz. The double column ID is added to the data packet and then transferred 2 FIFO means first in, first out. It is an often used, well structured, data buffer.

12 CHAPTER 2. TIMEPIX3 6 to the end-of-the chip logic, the Data Output Block. The bandwidth of the output block limits the data transfer rate to 2.56 Gbps. An 8b1b encoder, which turns 8 bit symbols into 1 bit symbols to make high speed serial readout possible, is implemented so that the data is ready to be transported off the chip. Figure 2.3: Block diagram of the Timepix3 chip [6]. 2.3 Operation Modes Timepix3 can be operated in three modes. The OnlyToA mode, the EventCount&IntegralToT mode or the combined ToA&ToT mode. In my experiment only the latter was used, therefore the other modes are not discussed here. A pixel data package of a hit collected in

13 CHAPTER 2. TIMEPIX3 7 the combined ToA&ToT mode contains the following information: First, PixAddr is the pixel coordinate (Row,Column or x,y) of the hit. Second, coarse ToA and FToA, (Fast)Time of Arrival, contain information on the arrival time of the hit. Third, ToT, Time over Threshold, represents the measured deposited charge which can be up to 15 ke. At the pixel level, dead time is caused by the transportation of the data package to the super pixel memory which takes 7 ns. For experiments in which ToT information is not needed, the OnlyToA mode can be used to reduce the transportation time to 45 ns. From the super pixel the data is sent to the super pixel FIFO and periphery data bus, the interface between the pixels and the outside of the chip. This happens without any delay and therefore the information at readout has as little dead time as possible. There is no data loss up to a hit rate of 4M hits (4 1 6 ) per cm 2 per second. 2.4 ToA and ToT information Both ToA and ToT information are obtained by counting clock edges. Figure 2.4 shows how signals are counted for coarse ToA, FToA and ToT. Time over Threshold is counted when the signal is above threshold. The threshold level is chosen and can be changed to vary ToT response. Also the Ikrum, Krumenacher current, can be set to modify the ToT value. This will be discussed in more detail in Section One ToT count is 25 ns. The number of ToT counts is related to the charge of the signal. To find the relation between ToT counts and charge the Timepix3 chip must be calibrated, see Chapter 5. The arrival time of a signal is measured by two clocks: coarse ToA and FToA. One coarse ToA count represent 25 ns, whereas an FToA count is 1.56 ns. Figure 2.4: Two signals from hits and the corresponding output in ToT, coarse ToA and FToA counts. The dotted lines for threshold (THL) and Ikrum show that these values can be changed and thereby influence the signal.

14 CHAPTER 2. TIMEPIX ToA Time of Arrival consists of two measurements, coarse ToA and FToA. The signal comes from a Time-to-Digital Converter (TDC) which is apparent in each pixel of the Timepix3 chip. In the periphery a continuous counter of 4 MHz, the clock, assigns a timestamp to every hit, which is called the coarse ToA. To measure FToA, there is one ring oscillator of 64 MHz per super pixel. It starts counting when a signal arrives from the preamplifier and stops at the next rising edge of the clock signal. The number of pulses in this time period is counted, which indicates a 1.56 precise arrival time of a hit within one coarse ToA count. Thus, together the coarse ToA and FToA determine the Time of Arrival according to: ToA = coarse ToA - FToA. The FToA improves the resolution of ToA from 25 (only coarse ToA) to 1.56 ns. Figure 2.5 shows the signal progress in the TDC. Figure 2.5: The progress of the timing signals in the TDC [4] ToT Time over Threshold information is coming from the ToT counter in the digital part of the circuit [7]. However, the front end circuit (analogue part) determines the shape of the ToT signal. It consists of a preamplifier and a discriminator, see the schematics in Figure 2.6. A DAC (Digital-to-Analogue Converter) is used to set the threshold. Figure 2.6: Schematics of the front end circuit of a pixel [7]. Let us start with the preamplifier. The preamplifier circuit is based on the Krumenacher scheme. The Krumenacher current, Ikrum, can be set. This controls the discharge time and therefore the ToT signal (see Figure 2.4). A higher Ikrum value gives shorter discharge time. The preamplifier is characterized by high gain (5 mv/ 1 e ) and low noise (75

15 CHAPTER 2. TIMEPIX3 9 e ). As can be seen from Figure 2.4, the signal needs some time to reach threshold. The discriminator will fire later than the actual arrival time of the hit on the chip. This delay in the signal is called timewalk and depends on the signal amplitude. It will be discussed in detail in Chapter 7. The preamplifier circuit in Timepix3 has fast peaking time (about 1 ns) with respect to Timepix1 (about 1 ns), which decreases the error due to timewalk. The discriminator determines whether a signal is above threshold. A linear voltage DAC is used to set this threshold. There is a threshold setting of 1 bits which is set for the whole chip. Each individual pixel is equipped with another DAC of 4 bits to equalize variations between the pixels. It can compensate for a mismatch of about 6 electrons. 2.5 Readout To readout the Timepix3 chip, all data is multiplexed into one signal. Every system clock cycle a data packet is sent to one of the readout channels. From the readout channels the data is sent to a readout board. In my experiment the Speedy PIxel Detector Readout (SPIDR) module is used [8]. The module is developed on a Xilinx evaluation board. The chip board, on which the Timepix3 chip is mounted, is connected to the SPIDR board. It can read out one Timepix3 chip at full speed (8 Mhits/s) or multiple chips at lower speed. I used only one Timepix3 chip. Figure 2.7 shows a picture of the Xilinx development board as used in my experiment. The blue FMC to FMC cable is attached to the chip board with the Timepix3 chip on it. Figure 2.7: A Xilinx evaluation board as Speedy PIxel Detector Readout module. The board is, via the blue FMC to FMC cable, connected to the chip board with the Timepix3 chip mounted on it (outside the picture).

16 Chapter 3 Gaseous gridpix The detector used for this research is called a Time Projection Chamber or TPC. The very first TPC was developed by David R. Nygren in the seventies of last century [9]. It was used in the PEP4/PEP9 experiment at the electron-positron collider in Stanford [1]. The predecessor of the TPC, however still in use, was the Multi-Wire Proportional Chamber or MWPC. This detector can measure the position of hits left by particles travelling through it and their energy. However, it is hard to determine the trajectory of a particle in all three dimensions with an MWPC. To this problem the TPC was the solution. In this chapter the working of a TPC will be explained. Subjects like ionisation, drift, diffusion and gas gain are clarified. This chapter therefore provides the necessary background to understand how the signal in the detector I used is formed. 1

17 CHAPTER 3. GASEOUS GRIDPIX The working of a TPC A TPC consists of two crucial ingredients, namely a gas volume in which the signal originates, and something to collect and read out the signal. In the case of my experiment the latter is a pixel chip (Timepix3), whereas it could also be wires or pads. When a particle travels through the gas it ionizes gas atoms. This means that an electron gets kicked out of the atom and that the atom is left with a positive charge. This is called an ion. The charge released by the ionisations, i.e. the electrons, is called primary charge. Figure 3.1: A sketch of a TPC with drift volume (D) and amplification region (A). When a particle traverses the detector it ionizes the gas. The electrons that are released in this process drift through the drift region towards the anode. In the amplification region the signal of single electrons is amplified, avalanches are created, in order to make detection with the Timepix3 chip possible. Figure 3.1 shows a sketch of a TPC as used in my experiment. An electric field is applied across the drift volume (D). This causes the ions to drift towards the cathode and the electrons to drift towards the anode. At the anode, the signal is collected by the readout chip. However, the detection of a single electron is electronically impossible. Therefore, the signal must be amplified prior to detection, and an amplification region (A) is created. This is realized by placing a grid, which is kept at a certain potential, close to the anode. Across the amplification region the electric field is high. Therefore, the electrons are accelerated and cause ionisation. The number of ionisations increases as the number of electrons increases. Assuming that the amount of electrons doubles at each ionisation,

18 CHAPTER 3. GASEOUS GRIDPIX 12 the signal at the anode is intensively amplified with respect to the signal at the grid. In this way, a cloud of electrons originates which is called an avalanche. Due to the creation of avalanches, a single electron at the grid gives an electronically detectable signal. Therefore, the creation of avalanches makes the detector much more sensitive to primary charge. Since the readout is done using a pixel chip, the pixels that were hit by the charge indicate the path of the original particle. The chip consists of 256 x 256 pixels which thus form a grid of x and y coordinates. In this way the x,y-position of a hit can be read out directly. Note that there is an uncertainty in the x,y-position of ionisation due to diffusion, which is explained in Section 3.4. The time that an electron needed to drift from the point of ionisation to the chip is called the drift time. This drift time is proportional to the distance the electron crossed and therefore indicates the height (z-position) of the ionisation point above the anode. This is where the name Time Projection Chamber comes from. 3.2 Ionisation The primary charge is formed by ionisation. The process of ionisation was briefly described in the previous section and is sketched in Figure 3.2. Ionisation happens only when the incoming particle has sufficient energy to release an electron from the atom. This mostly depends on the electron configuration of the (gas) atom. The gas mixtures that I used were helium-isobutane (He/iC 4 H 1 ) with a ratio of 95/5 and argon-isobutane (Ar/iC 4 H 1 ) with a ratio of 9/1. For helium the ionisation energy is ev/atom and for argon ev/atom. Because of the lower ionisation energy, the ionisation rate in the argon-mixture is higher. (a) Process of ionisation (b) Feynman diagram of ionisation process Figure 3.2: (a) A charged particle with high enough energy releases an electron from the outer shell of an atom and thus ionizes the atom. (b) Feynman diagram of this process [11]. When ionisation happens, the incoming particle loses some of its energy to the electron that is kicked out of the outer shell of the atom. The rate of this energy loss for relativistic charged heavy 1 particles is described by the Bethe Bloch equation [12]: 1 In this case heavy means significantly more massive than electrons. Electrons are discussed later on.

19 CHAPTER 3. GASEOUS GRIDPIX 13 de dx = Kz 2 Z A 1 β 2 [ 1 2 ln2m ec 2 β 2 γ 2 T max β 2 δ(βγ) ] I 2 2 (3.1) Here, K = 4πN A rem 2 e c 2, where N A is Avogadro s number, r e is the electron radius and m e is the electron mass. Z and A are the atomic number and mass of the absorber, the atom, respectively. β = v/c is the velocity of the incoming particle, γ = 1/ 1 v2 and c 2 M is the mass of the incoming particle. T max is the maximum kinetic energy that can be imparted to a free electron per collision and I is the mean excitation energy. δ(βγ) is a factor to correct for the density change of the absorbing material. The latter is only apparent in dense materials where shielding is present. This causes the energy loss to be lower. However, the effect of shielding is absent in gaseous detectors because gas is not dense. Thus, the factor δ(βγ) can be omitted when dealing with gaseous detectors Electrons When the incoming particle is an electron or positron the Bethe Bloch formula needs to be modified for two reasons. First, because of the small mass of electrons and positrons, the incident particle may be deflected at the ionisation. Second, because the collision happens between two identical particles. The modified Bethe Bloch equation becomes [13]: de dx = Kz 2 Z A 1 β 2 [ 1 2 ln τ 2 (τ + 2) 2(I/m e c 2 ) + F (τ) δβ ] (3.2) 1 β 2 + τ 2 8 (2τ+1)ln2 F (τ) = ( (τ+1) 2 2ln2 β τ+2 (τ+2) 2 (τ+2) 3 ) for electrons for positrons Here τ = γ 1 and again δ = when dealing with gaseous detectors. Figure 3.3 shows the energy loss or stopping power of electrons in helium and argon gas. On the left side in Figure 3.3 the drop in ionisation is proportional to 1/β 2 [11]. This follows from the momentum transfer of a particle by the Coulomb force described by p = F dt = F dx. This explains that the faster a particle travels, the shorter it feels v the electric force of an atomic electron, and thus the stopping power decreases. From a certain velocity, by Lorentz contraction of the E field, the stopping power will increase for higher velocities of the incoming particle. This is called relativistic rise.

20 CHAPTER 3. GASEOUS GRIDPIX 14 Figure 3.3: de/dx for electrons in helium (thin line) and argon gas [14] A particle that has a velocity due to which it loses the minimum amount of energy possible is called a Minimum Ionising Particle, or MIP. A very important advantage of MIPs is that since they lose only little energy, they remain minimum ionising. Hence, the energy is constant and thus MIPs do not deflect. 3.3 Drift When the electrons are able to move freely after ionisation their velocity can be calculated. If there is no electric field applied the direction of motion of the electrons is random, it is determined by collisions in the gas. Their kinetic energy depends on the temperature of the gas. Therefore, the kinetic energy ( 1 2 mv2 ) equates to the thermal energy. As for the velocity only the translational thermal energy plays a role, this is given by n 1 2 k BT, where k B is Boltzman s constant. The constant n is the number of degrees of freedom so that n = 3 in the case of three dimensions. From equating kinetic energy and thermal energy, the velocity of the electrons is found to be: v = 3kB T m (3.3) This is about 11 cm/µs for electrons and 1 2 cm/µs for noble gas atoms at room temperatures [15].

21 CHAPTER 3. GASEOUS GRIDPIX 15 In the case of a detector as sketched in Figure 3.1, the primary electrons are formed by ionisation, and thus indicate where a particle passed through the detector. To collect them, the electrons should be directed towards the readout chip. This is done by applying an electric field. The electrons and ions will move in a net direction, namely opposite to (in) the direction of the electric field for electrons (ions). This movement is called drift. The equation of motion of electrons in an electric and magnetic field are described by P. Langevin and are given by the following equation [16]: m e d v e dt = e E + e( v e B) K v e (3.4) Here v e is the drift velocity of the electron, e the electron charge, E the strength and direction of the electric field and B the strength and direction of the magnetic field. Since there was no magnetic field applied in my experiment, this equation can be simplified to: m e d v e dt = e E K v e (3.5) The last term in the equation describes the energy loss due to collisions with gas atoms, where K is a friction factor. When this energy loss and the energy gain by electric acceleration reach equilibrium, which is soon after the ionisation has happened, the electron will move with constant velocity in the direction of the electric field lines, the drift velocity. This drift velocity can be found by setting the left part of Equation 3.5 to and writing K as m e /τ, where m e is the mass of the electron and τ a characteristic time. The average net velocity between two collisions, the drift velocity, is given by: v e = e m e τ E µ e E (3.6) The electron mobility, µ e = e m e τ, is characteristic for a gas (mixture). Here τ is the average time between two collisions. Relevant drift velocities are given below. With the helium-isobutane mixture measurements were taken at different electric field strengths, ranging from 38 to 424 V/cm. This corresponds to drift speeds of 1.36 to 1.44 cm/µs. The drift speed in the argon-isobutane mixture was much higher, namely 4.65 cm/µs for an electric field strength of 435 V/cm. The numbers above come from simulations with Magboltz [17] of which the results can be found in Appendix A. 3.4 Diffusion After ionisation, the electrons and ions start drifting towards the anode and cathode respectively. However, there is yet another phenomenon that plays a role in the transportation of electrons in a gas. When a cloud of electrons is released in the gas, it will expand in all three spatial directions. This is called diffusion 2. 2 It must be noted that diffusion is not a property of the electron cloud. The notion of a cloud is used here to describe the diffusion of single electrons. By visualizing this as an expanding cloud, the possible

22 CHAPTER 3. GASEOUS GRIDPIX 16 When there is no electric field applied, the deviation of the electrons is the same in all three spatial directions, the extension of the charge cloud follows a Gaussian distribution. With τ the average time between two collisions, λ the mean free path of an electron and v e = λ/τ the electron velocity, the width of the electron cloud at the time of the first collision is found to be [18]: σ 2 = 1 t τ e τ (ve t) 2 dt = 1 t τ e τ ( λ τ t)2 dt = 2λ 2 (3.7) Here, 1 τ e t τ is the probability that no collision took place within a time t and v e t is the length of the electron path. This equation can be multiplied with the number of collisions in a time t (n = t/τ) to get the width of the electron cloud after n collisions: σ 2 = 2λ 2 t τ = 2Dt (3.8) Here, D = λ2 is called the diffusion coefficient. In the case of isotropic diffusion, the τ expansion of the electron cloud in all three spatial directions is equal. A distinction can be made between the transversal and the longitudinal direction, where transversal spans the x and y-directions, and longitudinal the z-direction. Therefore: σ T = 2/3 2Dt and σ L = 1/3 2Dt (3.9) It is clear that the width of the electron cloud grows with time. Figure 3.4(a) shows the expansion of the electron cloud in the situation without an electric field. However, when there is an electric field applied, the longitudinal diffusion (parallel to the electric field lines) changes. The diffusion in this direction is then given by: σ 2 = 2Dt = 2D L = 2DL v e µ e E = 2k BT L ee (3.1) Here, L is the drift distance and the last step is made by applying the Nernst-Townsend or Einstein formula D = k BT [19]. To minimize diffusion the drift time should be kept µ e short. Equation 3.1 shows that this is influenced by the gas that is used and the applied electric field. Due to the velocity of the electrons in the drift direction the shape of the cloud is deformed. This can be seen in Figure 3.4(b). Instead of saying that σ 2 is different in the longitudinal and transverse direction, one could also say that the diffusion coefficient D differs. The longitudinal diffusion coefficient D L increases when an electric field is applied, whereas the transverse coefficient D T stays the same. From Figure 3.4(b) it seems that D L > D T. However, since D T spans two dimensions and D L one, this does not have to be the case. It is hard to find the exact diffusion coefficients D L and D T and therefore they should be found numerically. This can be done using simulations. The results of these, performed with Magboltz, can be found in Appendix A. Measurements were taken at electric field strengths of about 4 V/cm. This corresponds to diffusion coefficients D L = 21 and directions of movement of the electrons are easily seen.

23 CHAPTER 3. GASEOUS GRIDPIX 17 (a) No electric and magnetic field (b) Electric field Figure 3.4: (a) The Gaussian expansion of an electron cloud in the case that there is no electric or magnetic field applied. (b) The deformed expansion of an electron cloud due to the application of an electric field. D T = 28 µm/cm for the helium-isobutane mixture and D L = 21 and D T = 36 µm/cm for the argon-isobutane mixture. Diffusion is easily recognized when looking at the projection of a track in the x,y-plane. It causes the position of detection of electrons to be displaced with respect to the ionisation point. When ionisation happens further away from the anode, electrons have a longer time to diffuse and the displacement is more significant. Figure 3.5 illustrates this by showing how hits from a straight line track do not end up on the same straight line on the chip. It shows a track that is angled in the x,z-plane and therefore the ionisation points differ in height, as is the case in Figure 3.1. Diffusion is taken into account as an error on the hit position while fitting tracks, see Section 8.2. Figure 3.5: A track that causes ionisation inside the gas volume. The electrons are diffused and therefore are detected at a certain distance from their point of ionisation.

24 CHAPTER 3. GASEOUS GRIDPIX Signal amplification When the electrons have drifted through the drift region towards the grid they enter the amplification or gain region. In this region, between grid and anode, there is a high electric field causing many ionisations. The electrons that are released in these ionisation processes have such high energies that they can release even more electrons. This process, in which the number of electrons is multiplied, is called an avalanche process. The creation of avalanches is necessary to create a signal that has high enough charge (enough electrons) to be measurable by the readout chip. The amount of electrons in an avalanche doubles after each length l i, the mean distance between two ionisations. Therefore, the average amount of electrons in an avalanche, when starting from one electron at the grid, is [15]: N e = 2 X l i = 2 Xa i (3.11) With a i = 1/l i is the number of ionisations per unit length and X is the total length of the avalanche. The amount of ionisations per unit length depends on the strength of the electric field. In the case of my experiment the electric field in the gain region can be assumed to be homogeneous. The gas amplification is therefore given by: G(X) = e (αx) (3.12) The factor α is called the Townsend coefficient. It depends on the electric field which is controlled by the voltage on the grid. In my experiment, different voltages were applied, and thus the gas amplification changed, which can be seen from the data. The gas amplification depends largely on the moment of the first ionisation in the gain region. This is due to the exponential nature of the development of avalanches and therefore the charge within the avalanches varies significantly. The gas gain is mostly described as the mean magnitude of the avalanches. The spectrum, how the gas amplifications differ, is described by the Polýa distribution [2]: ( ) G p = Nm ( m G ) m 1 e m(g/g ) G Γ(m) G (3.13) The value p is the probability of ionisation for certain gas gain G. N is the size of an avalanche and m a dimensionless parameter depending on the strength of the electric field. G is the average effective gas gain. There are two effects that determine the probability of ionisation. First, directly after an ionisation the probability of releasing another electron is reduced since the original and released electron are regarded to be at rest. Second, the more an electron has drifted, the more energy it has acquired due to acceleration in the electric field, which increases the probability of ionisation. To illustrate this, Figure 3.6 shows the Polýa distribution for a gas gain of G = 5 for different values of m.

25 CHAPTER 3. GASEOUS GRIDPIX 19 Figure 3.6: Polýa distributions for a gas gain of 5. As the value of m increases, the distribution becomes less exponential and the average approaches the most likely value [15]. 3.6 Signal formation The signal that is read out by the electronics consists of two components [15]. The first one comes directly from the electrons that were developed in the avalanche. This component is fast but small. The second component comes from the ions that keep a significant part of the electrons inside the amplification region because of induction. The ions slowly drift away towards the grid and so the electrons are released and can reach the readout electronics. This part of the signal is larger and slower. By comparing the work done on one electron and one ion, it can be shown that most of the signal comes from the ions. The work done on a charge by the electric field for a constant potential across the gap is: W = Q V = V gap Q (3.14) Where V gap is the electric potential in the amplification region. The work on both an electron and an ion can be calculated by plugging in the height of the amplification region L gap and the distance of an ionisation to the anode d i. In terms of L gap and d i the electron has to travel a distance d i from ionisation to the anode, and the ion has to travel L gap d i to the grid. The work on both an electron and ion is then: W both = W e + W ion = (V gap e d i L gap ) + ( V gap e L gap d i L gap ) = ev gap (3.15) Now the fraction of signal that comes from the electron is calculated to be: W e W both = W e W e + W ion = d i L gap (3.16) Most of the ionisations inside an avalanche happen close to the anode because of the exponential nature of the avalanche. This implies that d i on average is small compared to

26 CHAPTER 3. GASEOUS GRIDPIX 2 L gap. Therefore, as can be seen from Equation 3.16, the main part of the signal is induced by the ions. When having a gas gain of 1, and an amplification region of L gap = 5 µm, half of the ionisations occur within a distance of 5 µm to the anode. Therefore the most probable value of d i = 5 µm is used in the following calculation. For a higher gas gain, d i will be smaller. To get an idea of how long it takes to develop the signal in the amplification region a first order calculation is made. Because most of the ionisations occur close to the anode, the ions have to travel almost the entire length L gap d i = 45 µm. The electric field inside the amplification region is about 3 V, which is 6 kv/cm. The ion mobility µ ion in the argon-isobutane mixture is about 1.4 cm 2 /Vs [19] [21]. The ion velocity can thus be calculated: v ion = µ ion E = = 84 cm/s =.84 µm/ns (3.17) Using the drift gap, one can calculate the time the ions need to drift towards the grid, and thus the time it takes to develop the signal: t signal = L gap d i v ion = 45 µm.84 µm/ns 54 ns (3.18) In the drift region the electric field is about 4 V/cm. The electron drift velocity then is 4.6 cm/µs. The primary electrons need about 1/4.6 = 217 ns to drift trough the volume of 1 cm. Therefore, it can be concluded that the time that is needed to develop the signal in the amplification region is small compared to the drift of the primary electrons. 3.7 Gridpix As Figure 3.1 shows, a grid is placed a little above the readout chip, to create the amplification region. The grid that I used is a 5 µm thick micromegas foil made of copper, see Figure 3.7(a). The voltage on the grid can be set independently and so the different regions, drift region and amplification region are created. The micromegas grid is positioned above the chip on 5 µm tall poly-imide pillars. The holes in the grid are about 35 µm in diameter and the centres lay apart from each other by 6 µm. Figure 3.7(b) shows the electric field lines close to the grid. Because of the large field difference between the drift region and the amplification region, electrons are focused into the holes. The frame with the micromegas was placed on top of the Timepix3 chip by two rubber strings, see Figure 3.8(a). When the electric voltage is applied the electric force pulls the micromegas towards the chip [22]. The micromegas mesh has a disadvantage with respect to the later developed Ingrid. Because of the large distance between the holes and the thickness of the foil, the pattern of the holes (mesh) is visible in the data (see Chapter 6). This is called the Moiré effect. Also the pillars are visible, there are absolutely no hits at the pillar coordinates.

27 CHAPTER 3. GASEOUS GRIDPIX 21 (a) Micromegas (b) Amplification region Figure 3.7: (a) The micromegas mesh which is placed on 5 µm tall pillars above the readout chip [23]. (b) The holes in the grid and the electric field lines in the drift and amplification region. Electrons are focused into the holes [15]. The Ingrid is an aluminium grid of about 1 µm thick, see Figure 3.8(b). Data taken with the Ingrid does not show a Moiré pattern. Also the pillars are placed between the pads of pixels and thus they do not cause dead regions. The Ingrid is therefore preferable to the micromegas. However, at the time my experiment was performed the Ingrid was not yet available for Timepix3. Furthermore, normally one would protect the readout chip against discharges using a highly resistive layer. Also this protection layer was not yet implemented on Timepix3 when the measurements were performed. (a) Micromegas frame (b) Ingrid Figure 3.8: (a) The micromegas frame attached by two rubber strings [24]. (b) A Scanning Electron Microscopy (SEM) picture of an Ingrid on 5 µm pillars above the readout chip [15].

28 Chapter 4 DESY testbeam Feb 214 The data for this research was taken at the Deutches Elektron-Synchrotron (DESY) in Hamburg. The testbeam measurements were performed from 11 to 14 February 214. This chapter gives an introduction to DESY and its testbeam facility. Furthermore the setup and method of measurement taking are described. 22

29 CHAPTER 4. DESY TESTBEAM FEB DESY DESY was founded in 1959 [25]. Its first success was the realization of a 6 GeV electron synchrotron in 1964 [26]. In 1969 the two ring electron-positron collider DORIS was built, at which the mixing of neutral B mesons was discovered. Later, completed in 1978, a new electron-positron collider was built at the DESY site in Hamburg, PETRA. It had a final centre-of-mass energy of 46 GeV and was the key in the discovery of the gluon. The next big accelerator that was built at DESY is HERA, finished in HERA is an electron-proton collider which runs at a centre-of-mass energy of 3 GeV. HERA has been operating until 27. Nowadays research at DESY is focused on photon science. This is the study of synchrotron and free-electron laser radiation. In photon science PE- TRA III, the improved version of PETRA which was finished in 29, plays a prominent role as synchrotron radiation source. Also, DESY serves as a testbeam facility Testbeam facility There are three testbeam lines at the beam facility [27]. The data for this research was taken in beam line 21 of the DESY II ring. The maximum beam energy was 6 GeV. The electron beam is a converted bremsstrahlung beam produced by a carbon fibre target. Figure 4.1 shows a schematic overview of how the testbeam is generated. In the synchrotron DESY II ring electrons or positrons circulate. Photons are created when these electrons or positrons hit the fibre. With the converter, a metal plate, the photons are turned into electron/positron pairs with a range of energies. A dipole magnet deflects the beam depending on energy. Electrons and positron can thus be separated and the required momenta can be selected. The collimator cuts out the final beam, in this case the electron part. The beam is continuous. e+/e Converter Fiber γ e+ e Magnet e+ Collimator e DESY II Spill Counter Figure 4.1: Formation of an electron testbeam at the DESY II facility [27].

30 CHAPTER 4. DESY TESTBEAM FEB Detector setup The experiment was built up first at Nikhef and then brought to DESY. The whole setup was placed on a translation stage so that it could be moved in and out the beam line. Figure 4.2 shows the schematics of the setup. Figure 4.3 shows an actual photograph of it. The detector itself (A) consisted of a gas chamber, in which the charge could be collected, and an unprotected Timepix3 chip with a micromegas foil on top. The chip, on the chip board (B), was placed on a rotatable and tiltable device so that measurements could be performed at different angles with respect to the beam line, see Figure 4.6. From a gas bottle (C) the gas was offered through a tube to the gas chamber. It was possible to constantly monitor its features via a labview program, for example pressure, temperature and humidity. The chip was connected to a SPIDR board (D) for readout, from which the data was sent to the computer. We used a scintillator (not connected to the SPIDR board, but to a counter) for alignment with the beam (E). 1 cm beam line A 4 cm E 3 cm B 11.5 cm D 12.5 cm C 7 cm 26.5 cm 22 cm Figure 4.2: Schematics of the experimental setup. The different components are not scaled relatively, however dimensions are given. The detector, a Timepix3 chip with a gas chamber on top (A), is mounted on the chip board (B). The gas bottle (C) provides the gas flow. The signal from the chip board goes via the SPIDR readout board (D) to the computer. The signal from the scintillator (E) is sent to a counter and used for beam alignment. The electron beam goes through the detector and scintillator.

31 CHAPTER 4. DESY TESTBEAM FEB Figure 4.3: The experimental setup. Showing the Timepix3 detector (A), chip board (B), gas bottle (C), SPIDR readout board (D) and scintillator (E). The beam line comes in from the back, drawn with purple line. 4.3 Measurements Figure 4.4: The relation between the energy of the electrons and their rate. In this experiment a copper target of 5 mm was used, corresponding to the uppermost graph [27]. Before we could do measurements, the detector had to be aligned with the beam line. This was done roughly first using a laser to align scintillator and detector. After that, the

32 CHAPTER 4. DESY TESTBEAM FEB beam was turned on, and the particle rate through the scintillator could be measured. By lifting and shifting the stage the detector and scintillator were placed in the beam line. This was done when the magnet current was A which corresponded to a 3 GeV electron beam. When the settings were optimal we obtained a particle rate of 28 Hz. The magnet current was changed to provide higher particle rates. Figure 4.4 shows that at an electron energy of 2 GeV the particle rate takes its maximum value. This corresponded to a magnet current of 74.8 A. The particle rate through the detector at this current was 32 Hz. During the measurements the magnet current was kept at 74.8 A. Now that optimal settings were applied the data taking could start. As mentioned in the previous chapter, we took measurements with two different gases. The first was a helium-isobutane (He/iC 4 H 1 ) mixture of ratio 95/5 and the second an argon-isobutane (Ar/iC 4 H 1 ) mixture of ratio 9/1. We took measurements with different grid voltages and different angles of the detector with respect to the beam line. Most measurements were taken with the chip positioned at an angle of 45 degrees with respect to the beam line (yaw 45 ). Sometimes this was combined with a tilting angle of 3 degrees (roll 3 ) to allow the electrons to travel a longer distance inside the gas volume. The relevant coordinate system is shown in Figure 4.5. Figure 4.6 shows a photograph of the detector in straight position (a), and in tilted position (b). Figure 4.5: The definition of the angles in which the detector was used. A rotation around the y-axis is called yaw, a rotation around the x-axis roll. Measurements were taken at different chip settings for Ikrum and threshold. Changing these values resulted in differences in the amount of detected hits per track. An overview of all the obtained data can be found in Appendix B.

33 CHAPTER 4. DESY TESTBEAM FEB For the helium-isobutane mixture data was taken with grid voltages from 32 up to 39 V. The data in Tables B.3 and B.4 is used mostly in the analysis since it has the largest data files and thus the most significant tracks. For the argon-isobutane mixture data was taken with grid voltages from 3 to 34 V. Because of the higher ionisation rate inside the gas the voltage we started at could and should be lower. We were careful with ramping the voltage up because the Timepix3 chip did not have a protection layer. However, after 3 minutes of operation at a grid voltage of 34 V the chip broke down. The obtained data can be found in Table B.5. (a) No tilt (b) Tilted Figure 4.6: (a) The dectector in straight position, however at an angle of 45 degrees with respect to the beam line (yaw: 45, roll: ). (b) The detector in tilted position (yaw: 45, roll: 3). The scintillator is visible in the back of the photograph. Beam line goes into the page.

34 CHAPTER 4. DESY TESTBEAM FEB Threshold equalisation Before the measurements were carried out, a threshold equalisation was performed on the Timepix3 chip. This is done to have all pixels correspond to the globally set threshold in an equal way. Inhomogeneities due to fabrication or radiation damage 1 are so compensated for. Figure 4.7 shows the result of this threshold scan. Figure 4.7: The result of a threshold equalisation. The black distribution is the average of the red (DAC=) and blue (DAC=15) distributions of threshold values. The narrower the black peak, the better the equalisation. A unit of threshold corresponds to 1 electrons. In a threshold scan, the 4 bit DAC of the individual pixels is set. First, it is set to its minimum value, DAC=, which results in a Gaussian distribution (red in Figure 4.7). Second, it is set to its maximum value, DAC=15, resulting in a Gaussian distribution at higher threshold (blue). Then, for each pixel the threshold is chosen which is closest to the average of the Gaussian mean values. This results in a narrow distribution at the noise level (black). The smaller this distribution, the better the chip is equalised. 1 In the case of this chip that we used radiation damage was not apparent since it was not used before.

35 Chapter 5 ToT-charge calibration To properly characterise detector parameters such as gain and timewalk, one needs to relate the charge of the signal to the measured ToT counts. In principle, the response of the chip should be a linear function of input charge. However, close to the threshold value this is not the case. The relation between ToT counts and input charge in the linear, as well as in the non-linear regime, is well described by the so-called surrogate fit function [28]. The ToT-charge relation varies not only from chip to chip but also from pixel to pixel. Therefore, the Timepix3 chip needs to be calibrated. This means finding the relation between ToT counts and charge for each individual pixel 1. For the calibration an internal testpulse is used. The value of the testpulse [mv] is known and corresponds to a certain number of electrons. Because the calibration shows a clear column to column variation, it is chosen to use the result in terms of a mean surrogate fit function per column. This thus gives a relation for ToT counts to charge for each column, which is implemented in the data. 1 It has to be noted that the chip that was used for taking data at the testbeam is not exactly the same one as the chip used in this calibration. Unfortunately, the data-taking-chip broke down during measurements and was not calibrated in advance. Therefore the calibration is done using another Timepix3 chip, which was the best solution. 29

36 CHAPTER 5. TOT-CHARGE CALIBRATION Method Before the calibration measurement was performed the chip was equalised, as was also done with the chip that was used at the testbeam. The threshold here was set to 1 electrons. After the threshold equalisation was done, the calibration measurements could be performed. To do so, an internal testpulse is used. This implies that one injects a known charge on each pixel individually. In this case testpulses with an increasing amplitude in steps of 2 were used. The testpulse amplitude is set via an internal Digital-to-Analogue Converter (DAC). In order to calibrate the DAC its voltage is measured. One DAC step is measured to correspond to 1.12 mv. Given the testpulse capacitance of 3 ff, one DAC step increases the charge with 21 electrons. The result of the DAC scan, as well as a short calculation for the charge, is shown in detail in Appendix C. The 1.12 mv per DAC step is valid in the linear regime of Figure C.1. Per testpulse step, more than one testpulse must be injected. The reason for this is that the outcome of the measurement could vary due to noise, which would influence the calibration. Therefore it is chosen to inject 1 testpulses and use the mean measured value and its rms error. It is also unwanted to inject testpulses on all pixels simultaneously as this could affect the calibration. Per shutter, only 1 pixel in an 8 by 8 group of pixels is tested at the same time. Therefore, a certain grid like pattern arises. This pattern is then shifted to calibrate also the other pixels. During the testpulse scan, the threshold of the pixels is fixed. The testpulses amplitude is scanned and the corresponding ToT value is measured. After the 1 testpulses are injected, the charge of the testpulse is raised and the same measurement is repeated. This is done 2 times so that input charges between and 448 mv are injected. Figure 5.1(a) shows the mean measured ToT value for each pixel at an input charge of 224 mv. Figure 5.1(b) shows the mean measured ToT value for each pixel at an input charge of 43.2 mv. These were thus calculated from 1 testpulses per shutter. ToT maps like these could be made for all input charges between and 448 mv for every 2.24 mv (2 DAC steps).

37 htot3 Entries Mean x Mean y RMS x RMS y htot3 Entries Mean x Mean y 128 RMS x RMS y CHAPTER 5. TOT-CHARGE CALIBRATION Mean ToT distribution ToT Y X Y 1 5 (a) Input charge 224 mv Mean ToT distribution ToT X (b) Input charge 43.2 mv Figure 5.1: (a) The mean ToT value per pixel from 1 injected testpulses of 224 mv. (b) The mean ToT value per pixel from 1 injected testpulses of 43.2 mv. As can be seen from both pictures there is an evident spread in ToT values.

38 CHAPTER 5. TOT-CHARGE CALIBRATION Results When performing these measurements at the different testpulse values mentioned above, the results can be combined to give the relation between testpulse [mv] and ToT counts for each pixel. Figure 5.2 shows an example of this relation for two different pixels. Figure 5.2: The relation between testpulse [mv] and ToT counts [25 ns] for two pixels (112,16) (lower graph) and (144,168) that were chosen at random. The error bars indicate the rms error from 1 testpulses per shutter. Also here the spread in ToT values is evident. Curves as those shown in Figure 5.2 are fitted per pixel with the following surrogate function [29]: f(x) = ax + b c (5.1) x t Well above threshold the relation is linear, and described by the slope a and intercept b. Close to threshold t and c parametrize the non-linear part. To provide an idea of the values of the fit parameters the ones for the two pixels above are listed in the following table: Fit parameters a b c t pixel (112,16).738 ± ± ± ± 38.1 pixel (144,168).864 ± ± ± ± Table 5.1: The mean and rms values of the surrogate function fit parameters of pixels (112,16) and (144,168).

39 hb_pfx Entries Mean Mean y.8442 RMS RMS y.9576 Underflow Overflow Integral Skewness.4684 CHAPTER 5. TOT-CHARGE CALIBRATION 33 Figure 5.3 shows the value of the mean surrogate function parameter a per column (256 pixels). Since a represents the slope well above threshold, the deviation in ToT is clear. A per collie fit parameter a column number (x) Figure 5.3: The mean of parameter a per column. The error bars indicate the error on this mean. There is a clear fluctuation in the value of a, and thus in the ToT-charge relation. 5.3 Implementation The measured calibration parameters make it possible to calculate the detected charge for a measured ToT value. In units of electrons this is given by the following inverse surrogate function : Q in (e ) = ta + T ot b + (b + ta T ot ) 2 + 4ac 2a (5.2) The factor comes from the built-in capacitor of 3 ff in every Timepix3 pixel. Per step voltage of 1 mv, the corresponding charge is electrons. However, the chip that was used in the calibration was not exactly the same one as the chip used for the measurements. Therefore, the calibration is implemented on the data using the mean fit parameters per column, since Figures 5.1 and 5.3 shows that there is a spread in ToT values from column to column.

40 Chapter 6 Gridpix characterisation In this chapter the characteristics of the gridpix detector constructed of a Timepix3 chip and a micromegas as described in Chapters 2 and 3 are presented. It contains results of the measurements that were performed at the testbeam at DESY as presented in Chapter 4. This chapter treats the distribution of ToA values and some typical events. Furthermore the distribution of hits, ToT values and charge on the chip are examined. From these results the gas gain is calculated. Finally, different values for the Krumenacher current are compared using ToT distributions of many hits. 34

41 htoa Entries 1 Mean 8161 RMS 4717 hftoa Entries 1 Mean 7.56 RMS 4.57 CHAPTER 6. GRIDPIX CHARACTERISATION Some parameter checks In Chapter 2 the clocks that measure the arrival time of a hit were described: coarse Time of Arrival (coarse ToA) and Fast Time of Arrival (FToA). The coarse ToA is not triggered with an external trigger, and thus ticks continuously. The FToA is triggered by the particle that is detected itself. The coarse ToA and FToA clocks measure up to (2 14 ) and 16 (2 4 ) counts, respectively, and then start from zero again. Since the beam is continuous, the arrival time of the particles is random with respect to the clocks and hence a flat coarse ToA and FToA distribution are expected. As can be seen from Figure 6.1 this is indeed the case for the coarse ToA distribution. However, the FToA distribution in Figure 6.2 is not completely flat. This is a feature of the actual circuit and has been reproduced with testpulses in the lab [3]. The effect of this non-flatness on time resolution is small. TOA distribution counts coarse ToA counts [25 ns] Figure 6.1: The distribution of coarse ToA values of a random selection of 1M hits. The coarse ToA spectrum is flat, as expected. [ArIso, GridV. 34] FTOA distribution counts FToA counts [1.56 ns] Figure 6.2: The distribution of FToA values of the same selection of 1M hits. The FToA spectrum is not completely flat due to the circuit. [ArIso, GridV. 34]

42 htot2 Entries 6 Mean x 57.5 Mean y RMS x RMS y htot Entries 18 Mean x 57.5 Mean y RMS x RMS y 1.78 htot2 Entries 48 Mean x Mean y RMS x 35.6 RMS y htot Entries 144 Mean x Mean y RMS x 35.6 RMS y 4.33 CHAPTER 6. GRIDPIX CHARACTERISATION Gas amplification The experiment was performed with two different gases. For the helium-isobutane (95/5) mixture the expected ionisation rate in the gas is much lower than for argon-isobutane (9/1). Figure 6.3 illustrates this difference by showing a typical event for each of these gases at the same grid voltage, namely 34 V. In this case, the beam runs along the x-direction, coming in from the left (x = ). 1 Total (alles ToT waardes opgeteld) ToT distribution xy ToT 1 1 Total (alles ToT waardes opgeteld) ToT distribution xy ToT Z [mm] Z [mm] X X (a) (b) 25 Total (alles ToT waardes opgeteld) ToT distribution on grid (xy) ToT 1 25 Total (alles ToT waardes opgeteld) ToT distribution on grid (xy) ToT Y Y X X (c) Event He/iC 4 H 1 34 V (d) Event Ar/iC 4 H 1 34 V Figure 6.3: Two typical events for a grid voltage of 34 V. For He/iC 4 H 1 (a)(c) the mean number of hits per event is around 1.6, whereas for Ar/iC 4 H 1 (b)(d) it is These plots also show that the amplification in the argon-isobutane mixture is higher, apparent from the higher ToT values. [HeIso I / ArIso, GridV. 34] Note that the track in Figure 6.3(d) shows diffusion very well. Figure 6.3(b) shows that this track is angled in the x,z-plane, yaw 45, so that hits on the left side originate from higher up in the gas volume. Due to the longer drift time the electrons have had more time to diffuse. The number of ionisations does not only depend on the type of gas, but also on the voltage applied to the grid. At higher grid voltages the charge per avalanche is higher. This

43 htot2 Entries 12 Mean x Mean y RMS x RMS y 1.98 htot Entries 36 Mean x Mean y RMS x RMS y 12.5 htot2 Entries 15 Mean x 14.6 Mean y RMS x 5.14 RMS y htot Entries 45 Mean x 14.6 Mean y RMS x 5.14 RMS y CHAPTER 6. GRIDPIX CHARACTERISATION 37 means that more avalanches are detected since those with a charge below the threshold go undetected. The difference in charge per avalanche can be seen by comparing measurements with the same gas, but different voltages applied to the grid. See Figure 6.4. The threshold for these events is 58 electrons. 1 9 Total (alles ToT waardes opgeteld) ToT distribution xy ToT Total (alles ToT waardes opgeteld) ToT distribution xy ToT Z [mm] Z [mm] X X (a) (b) 25 Total (alles ToT waardes opgeteld) ToT distribution on grid (xy) ToT Total (alles ToT waardes opgeteld) ToT distribution on grid (xy) ToT Y Y X X (c) Event He/iC 4 H 1 37 V (d) Event He/iC 4 H 1 39 V Figure 6.4: Two typical events for He/iC 4 H 1 at different grid voltages. It shows that at higher grid voltage the ToT values have increased. At 37 V (a)(c) the mean number of hits is around 3.6, at 39 V (b)(d) it is around 4.8. [HeIso IV, GridV. 37 / 39] Note that the track in Figure 6.4(c) is angled. This is because it is from data that was taken with a roll of 3, see Appendix B, Table B.4. The track in Figure 6.4(d) is not angled since the detector was not tilted, roll, when the measurement was performed Distribution of hits and ToT To clarify more the difference in the number of ionisations and the charge per avalanche, hit and ToT distributions are made for the two different gases and for different grid voltages. These can be found in Appendix D. Trend plots for these values are given below.

44 CHAPTER 6. GRIDPIX CHARACTERISATION 38 ArIso ToT as function of HV mean nhits mean ToT value [25 ns] grid voltage [V] (a) Mean number of hits helium-isobutane (95/5) grid voltage [V] (b) Mean ToT helium-isobutane (95/5) Figure 6.5: (a) The mean number of hits per event as function of grid voltage. (b) The mean ToT value per hit as function of grid voltage. [HeIso II, IV, GridV ] ArIso ToT as function of HV mean nhits mean ToT value [25 ns] grid voltage [V] grid voltage [V] (a) Mean number of hits argon-isobutane (9/1) (b) Mean ToT argon-isobutane (9/1) Figure 6.6: (a) The mean number of hits per event as function of grid voltage. (b) The mean ToT value per hit as function of grid voltage. [ArIso, GridV. 3-34] Polýa function The calibration of Chapter 5 is applied on the ToT distributions that are shown in Appendix D. This provides a charge distribution that should be Polýa distributed, see Chapter 3. Figure 6.7 shows the charge distribution for measurements with the argon-isobutane mixture at a grid voltage of 34 V.

45 hhits Entries e+7 Mean x Mean y RMS x RMS y h21 Entries 1 Mean 2276 RMS χ / ndf 3.289e+5 / 94 Prob 2.421e+4 ± 3.564e+1 N ±.6 m meang 2752 ± 2.2 htot3 Entries Mean x Mean y 125 RMS x 49.3 RMS y CHAPTER 6. GRIDPIX CHARACTERISATION 39 counts x Charge_distributions of all tracks Grid 34 V Charge [electrons] Figure 6.7: The charge distribution for 1M hits fitted with a Polýa function. GridV. 34] [ArIso, The data in Figure 6.7 is fitted by the Polýa function as described by Equation The measured fit parameters are N = 2421±36, m = 5.44±.1 and G = 2752±2. Whether the gain is as expected is verified by comparing the maximum gain in an avalanche to simulations in the next section. 6.3 Grid plots The figures below show distributions of hits, mean ToT (Figure 6.8) and charge (Figure 6.9) on the Timepix3 chip for argon-isobutane mixture data at a grid voltage of 34 V Y Hit distribution on grid (xy) nhits Y Mean ToT distribution on grid (xy) with Divide() ToT X X 7 (a) Hit distribution on chip (b) ToT distribution on chip Figure 6.8: (a) The distribution of hits on the chip for events (tracks), corresponding to a total of hits. (b) The distribution of mean ToT values per hit on the chip for the same events (tracks). [ArIso, GridV. 34]

46 hcharge Entries nan Mean x Mean y 125 RMS x RMS y hcharge Entries nan Mean x Mean y 125 RMS x RMS y CHAPTER 6. GRIDPIX CHARACTERISATION 4 The pillars that attach the micromegas on the chip are very well visible (white spots) in Figure 6.8. A Moiré pattern arises due to the mismatch of the Timepix3 pixel pitch (55 µm) and the micromegas (6 µm). This is a pattern of blobs that repeats itself every 12 (6/5) pixels. The edges of the micromegas appear to be less efficient in the detection of hits. The ToT distribution of figure 6.8(b) is almost flat. However, there seems to be a slight difference between the right and left side of the chip of about 1 ToT count Mean Charge distribution on grid (xy) with Divide() - Charge [e ] Mean Charge distribution on grid (xy) with Divide() - Charge [e ] Y 12 3 Y X X 1 (a) All charge (b) Zoomed charge scale Figure 6.9: The distribution of mean charge [electrons] on the chip for the same events (tracks) as above. (b) The same distribution with different scaling. [ArIso, GridV. 34] The distribution of ToT values in Figure 6.8(b) is transformed into a charge distribution using the per column calibration of Chapter 5. The charge distribution in Figure 6.9 still shows the column to column variation on the chip. However, it was expected that the charge distribution would be more flat after gain equalisation, calibration. The size of the avalanche in terms of electrons indicates the gas gain. Since the centres of the holes in the micromegas were more efficient in the detection of hits it was expected that the gain would be higher there as well. And indeed, the mean gain per hit is higher at the centre of the holes than at the edges. However, the difference is only a few hundreds of electrons. Figure 6.9 shows the gas gain created by one electron. Therefore, the maximum gain (at the centre of a hole) that was achieved with the argon-isobutane mixture at a grid voltage of 34 V is around 3 ± 22 electrons per hit 1. This value is compared with simulations [31]. These simulations give a value of 35 electrons per hit at the centre of the holes, however for an amplification gap of 75 µm with a voltage difference of 5 V. The amplification gap in my experiment was 5 µm and had a voltage difference of 34 V. It is hard to compare the two configurations because of the different gap size. The field strength however in both configurations is about equal. However the gain is not. The 1 22 electrons corresponds on average to 1 ToT count.

47 CHAPTER 6. GRIDPIX CHARACTERISATION 41 gain depends on the size of the gap. If the mean distance between collisions is the same, there are more duplications in the amplification for larger gap. The gain I measured is lower than the gain in the simulation, which was expected because of the larger gap size. 6.4 Krumenacher current The Krumenacher current (Ikrum) determines the discharge time of a signal, see Chapter 2. Figure 6.1 shows that for a lower Ikrum (Ikrum 1 > Ikrum 2 ) the discharge time is longer and therefore there are more ToT counts for the same charge [7]. A higher number of ToT counts is preferred since this gives a higher resolution. Figure 6.1: The shape of two signals with the same charge but different Ikrum setting. With lower Ikrum (Ikrum 1 > Ikrum 2 ) the discharge time is longer and thus the number of ToT counts increases. To see if a relation between Ikrum and ToT counts is apparent in the data, the mean ToT values of different data sets are compared. mean ToT value [25 ns] Ikrum grid voltage [V] Figure 6.11: The mean ToT value as function of grid voltage. The upper curve belongs to data taken with an Ikrum of 1.2 na, the lower curve to data taken with an Ikrum of 3.6 na. [HeIso III / HeIso IV, GridV ]

48 CHAPTER 6. GRIDPIX CHARACTERISATION 42 Figure 6.11 shows the relation between mean ToT value and grid voltage for different data sets. The data with an Ikrum of 3.6 na is listed in Table B.3 and the data with an Ikrum of 1.2 na in Table B.4. For a higher Krumenacher current the mean ToT values are lower, as expected. However, the ratio between the values is expected to be inverse linear with the Krumenacher current. Therefore a ratio of 3.6 na/1.2 na = 1/3 would be expected. However the measurements shows more a ratio of 1/2. The difference between the expectation and measurement could be explained by the fact that maybe the Krumenacher setting differs from the actual Krumenacher current. Note that the data is taken with a small difference in threshold, about 1 electrons. With a high threshold setting there are less ToT counts than with a low threshold setting (see Figure 6.1) for the same charge. Therefore, to really compare the data there should be added a small value to the ToT values with an Ikrum of 1.2 na. However, since these ToT values are already sufficiently larger than the ones with an Ikrum of 3.6 na, this would not change the relative difference much (it would increase even more). Also note that the difference in threshold of 1 electrons is really marginal compared to a ToT count, which corresponds to 22 electrons.

49 Chapter 7 Timewalk As already explained in Chapter 2, the signal on the Timepix3 chip needs some time to rise until it reaches threshold. Therefore, the time when the signal crosses threshold is delayed with respect to the time that it actually arrived at the chip. This delay is called timewalk. Timewalk leads to an uncertainty in the measurement of the z-position of a hit, which is expressed as an error on the fit of a track (Chapter 8). Fortunately, there is a way to determine this timewalk. Namely, it is related to charge. Figure 7.1 shows the behaviour of two signals of different charge. The signal of high charge rises steeply and therefore does not need a lot of time to reach threshold. The ToT clock starts with only a small delay and thus timewalk is short. However, the signal with low charge takes much more time to reach threshold and thus timewalk is long. Since ToT counts actually are a measurement of the signal charge, determining the relation between ToT counts and timewalk would be of great importance in correcting for the arrival time of a hit. Figure 7.1: The signal of two hits with different charge. Low charge corresponds to little ToT counts and long timewalk t w (lower line). High charge leads to many ToT counts and short timewalk (upper line). 43

50 CHAPTER 7. TIMEWALK ToT values Since timewalk is related to the number of ToT counts (which is a measure of charge), the distribution of ToT values for a certain data set gives an indication of the spread of timewalk and can be used to determine its average. These distributions can be found in Appendix D. Figure 7.2 shows the average ToT value per data set as a function of grid voltage for the argon-isobutane (9/1) mixture. ToT as function of HV mean ToT value [25 ns] grid voltage [V] Figure 7.2: The relation between grid voltage and mean ToT value. [ArIso GridV. 3-34] Compared to other experiments, for example the ones described in [32], the ToT values here are low. This means that the charge on the readout chip is low, which is due to the low gas gain. The low ToT values, and therefore large timewalk, causes quite some uncertainty in the measurement of the arrival time of hits. For measurements with ToT counts of or 1 this uncertainty is so large, see Figure 7.4, that these points hardly influence the fit. 7.2 Timewalk as function of ToT The relation between timewalk and charge for Timepix3 was measured by Szymon Kulis. Figure 7.3(a) shows this relation which is based on testpulse measurements. It is the average of 64 acquisitions. In order to use this relation in my own data, it is fitted with a function, see Figure 7.3(b). It is chosen to assign zero timewalk (t w = ) to the timewalk value in the tail of the distribution 1. This is the reason that the relation in Figure 7.3(b) is shifted down with 1 Zero timewalk could also be assigned to the most probable value in the data. However, since this is very arbitrary, the value lowest possible value for timewalk is chosen to be the zero level.

51 CHAPTER 7. TIMEWALK 45 Timewalk [ns] Graph Timewalk [ns] Graph Charge [ke ] (a) Measured timewalk-charge relation Charge [ke ] (b) Fitted to be used on data Figure 7.3: (a) The measured relation between charge and timewalk for Timepix3 [33]. (b) The same relation fitted with linear and exponential function. respect to the measurement results of Figure 7.3(a). The fit function has an exponential and linear part to properly describe the data: t w [ns] = { 7 62 Q, if.7 < Q < 1 ke exp( Q), if Q 1 ke. (7.1) The above function can now be used to relate charge to a certain timewalk value. The calibration in Chapter 5 gives the relation between charge and ToT counts per pixel and thus ToT can now be used to determine timewalk. However, this calibration was done with a different Timepix3 chip than the one used for data taking. Therefore, it is implemented in the rest of this thesis as a mean ToT-charge relation per column. Yet, in the next section the mean timewalk for a certain data set is calculated. To do so the mean ToT-charge relation of the whole chip is used. 7.3 Mean timewalk value The average timewalk for the data set of ArIso GridV. 34 is calculated. This is done by using the mean ToT-charge relation of the whole chip to convert ToT to charge. The result can be used to find the average relation between timewalk and ToT, which is shown in Figure 7.4. This relation differs per Ikrum setting since that influences the number of ToT counts per measured charge. Here, Ikrum is set to 1.2 na. To get the mean timewalk value, the ToT distribution of data taken with the argonisobutane mixture at a grid voltage of 34 V, Figure D.7, is multiplied by the corresponding timewalk values:

52 CHAPTER 7. TIMEWALK 46 Timewalk as function of charge TPX3 Timewalk [ns] ToT counts [25 ns] Figure 7.4: The average relation between timewalk and ToT counts for Ikrum = 1.2 na. mean timewalk = T ot =5 T ot = fraction (ToT) timewalk (ToT) (7.2) Using the above formula, a value of 4.5 ± 3 ns is calculated for timewalk. The error is large due to the uncertainty in timewalk in general and specially at low ToT. In Chapter 8, timewalk will be calculated again, however in a different way, namely from the residual distribution. 7.4 Conclusion In the data there is a significant fraction of signals with little charge. This leads to a large uncertainty in the time measurement due to timewalk. Indirectly this leads to a significant uncertainty in the z-coordinate of a hit. However, by implementing the value for timewalk a first order correction is made. When further measurements would be done it is recommended to use higher voltage to create higher charge in the avalanches. This was impossible in my experiment since the Timepix3 chip that was used was unprotected against breakdown of the grid voltages which leads to irreversible damage of the chip. The breakdown of the chip at a grid voltage of 34 V demonstrates this.

53 Chapter 8 Track fitting Because this chapter is a little free-standing from the previous ones, it will start with a historical introduction to the topic of track fitting. Essentially the goal of particle physics is to inspect and understand the building blocks of nature. However, the small particles of matter are not visible with the naked eye. Experiments of all kinds are built to detect these particles. An important character of a particle is the path that it travels inside such a detector. This can reveal what kind of particle it is. An example is the discovery of the positron in a cloud chamber in 1932 by Carl Anderson. The direction of bending of its trajectory (Figure 8.1) in the magnetic field was opposite to that of an electron. Therefore, the conclusion was drawn that this must be a parti- Figure 8.1: Positron trajeccle with opposite charge to that of an electron, a tory in cloud chamber [34]. positron [35]. In the case of my experiment the nature of the particle is clear. The testbeam consisted of electrons. However, it is still important getting to know a particle s trajectory. This provides insight in the functionality of the micromegas detector, the characteristics of the Timepix3 chip and the properties of the gases that were used. Unlike the example above, in the gas chamber the track is not directly visible (see Chapter 3). Data from the chip contains, among other things, the position of hits on the chip s plane (x,y). With the Time of Arrival (ToA) information, the drift time inside the gas can be calculated, and so the height (z) is reconstructed. Additionally, information about the charge (ToT) is available which can be used to correct for timewalk, and thereby improve the track fit. This chapter explains the method of track fitting that is used, Williamson s and York s method1. Also, it explains how tracks are exactly constructed. It ends with the results that were obtained from this track fitting. 1 The methods are similar. However, in this thesis York s article is used as reference and therefore the method is just called York s method in the continuation of the report. 47