Download Characterisation of the Timepix3 chip using a

Characterisation of the Timepix3 chip
using a gaseous detector
Mijke Schut
Characterisation of the Timepix3 chip
using a gaseous detector
Mijke Schut
February 2015
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
Abstract
The Timepix3 chip is the latest member of the Medipix family of readout chips. It is
based on 130 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 20 ± 0.17 ns.
Contents
1 Introduction
1
2 Timepix3
2.1 From Medipix to Timepix3
2.2 Timepix3 . . . . . . . . .
2.3 Operation Modes . . . . .
2.4 ToA and ToT information
2.4.1 ToA . . . . . . . .
2.4.2 ToT . . . . . . . .
2.5 Readout . . . . . . . . . .
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5 ToT-charge calibration
5.1 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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6 Gridpix characterisation
6.1 Some parameter checks . . . . . . .
6.2 Gas amplification . . . . . . . . . .
6.2.1 Distribution of hits and ToT
6.2.2 Polýa function . . . . . . . .
6.3 Grid plots . . . . . . . . . . . . . .
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3 Gaseous gridpix
3.1 The working of a TPC
3.2 Ionisation . . . . . . .
3.2.1 Electrons . . .
3.3 Drift . . . . . . . . . .
3.4 Diffusion . . . . . . . .
3.5 Signal amplification . .
3.6 Signal formation . . .
3.7 Gridpix . . . . . . . .
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4 DESY testbeam Feb 2014
4.1 DESY . . . . . . . . . .
4.1.1 Testbeam facility
4.2 Detector setup . . . . . .
4.3 Measurements . . . . . .
4.4 Threshold equalisation .
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6.4
Krumenacher current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
7 Timewalk
7.1 ToT values . . . . . .
7.2 Timewalk as function
7.3 Mean timewalk value
7.4 Conclusion . . . . . .
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of ToT .
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8 Track fitting
8.1 From data to tracks
8.2 York’s method . . .
8.2.1 Errors . . .
8.3 Residuals . . . . .
8.3.1 Diffusion . .
8.3.2 Timewalk .
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9 Conclusion
9.1 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 Improvements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.3 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Appendices
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A Properties of gas mixtures
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A.1 He/i C4 H10 95/5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
A.2 Ar/i C4 H10 90/10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
B Testbeam data
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B.1 He/i C4 H10 data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
B.2 Ar/i C4 H10 data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
C DAC scan
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D Hit and ToT distributions
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D.1 Distributions of number of hits . . . . . . . . . . . . . . . . . . . . . . . . 71
D.2 Distributions of ToT values . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Bibliography
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Samenvatting
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Acknowledgements
79
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 2015 [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
(2006)1 . One of the main advantages of Timepix3 with respect to Timepix1 is that it can
1
In this thesis, Timepix (2006) will be called Timepix1, to prevent confusion with Timepix3.
1
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-2013.
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.
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
CHAPTER 2. TIMEPIX3
2.1
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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 sensors1 , 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 170 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 cm2 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 2006. 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.
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 500 µm thick tungsten wire. It is captured using a 90 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 (500 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 640 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 FIFO2 to the End-Of-Column FIFO via a double column data bus with a
speed of 40 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.
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 8b10b encoder, which turns 8 bit symbols
into 10 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
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 150 ke− . At the pixel level, dead time is caused by the transportation of the
data package to the super pixel memory which takes 700 ns. For experiments in which
ToT information is not needed, the OnlyToA mode can be used to reduce the transportation time to 450 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 40M hits (40·106 ) per cm2 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 2.4.2. 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.
CHAPTER 2. TIMEPIX3
2.4.1
8
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 40 MHz, the clock, assigns a timestamp to
every hit, which is called the coarse ToA. To measure FToA, there is one ring oscillator of
640 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].
2.4.2
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 (50 mV/ 1000 e− ) and low noise (75
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
10 ns) with respect to Timepix1 (about 100 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 10 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 60 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 (80 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).
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 [10].
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.
10
CHAPTER 3. GASEOUS GRIDPIX
3.1
11
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,
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/i C4 H10 ) with a ratio of 95/5 and argon-isobutane
(Ar/i C4 H10 ) with a ratio of 90/10. For helium the ionisation energy is 24.587 eV/atom
and for argon 15.760 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.
CHAPTER 3. GASEOUS GRIDPIX
−
dE
dx
13
1 1 2me c2 β 2 γ 2 Tmax
δ(βγ)
2
= Kz
ln
−β −
A β2 2
I2
2
2Z
(3.1)
Here, K = 4πNA re2 me c2 , where NA is Avogadro’s number, re is the electron radius and
me is the electron mass. Z and A are the atomic number and mass of the absorber,
the
q
2
atom, respectively. β = v/c is the velocity of the incoming particle, γ = 1/ 1 − vc2 and
M is the mass of the incoming particle.
Tmax 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.
3.2.1
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]:
−
F (τ ) =
dE
dx
1 1 τ 2 (τ + 2)
F (τ ) δβ
ln
+
−
= Kz
A β 2 2 2(I/me c2 )2
2
2
2Z

1 − β 2 +
2ln2 −
β2
12
τ2
−(2τ +1)ln2
8
(τ +1)2
23 +
14
τ +2
(3.2)
for electrons
+
10
(τ +2)2
+
4
(τ +2)3
for positrons
Here τ = γ − 1 and again δ = 0 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
followsR from the
transfer of a particle by the Coulomb force described by
R momentum
dx
∆p = F dt = F v . This explains that the faster a particle travels, the shorter it feels
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.
CHAPTER 3. GASEOUS GRIDPIX
14
Figure 3.3: h−dE/dxi 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 ( 21 mv 2 ) equates to the thermal energy. As for
the velocity only the translational thermal energy plays a role, this is given by n × 12 kB T ,
where kB 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:
r
v=
3kB T
m
(3.3)
This is about 11 cm/µs for electrons and 10−2 cm/µs for noble gas atoms at room temperatures [15].
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]:
me
d~
ve
~ + e(v~e × B)
~ − K v~e
= eE
dt
(3.4)
~ the strength and
Here v~e is the drift velocity of the electron, e the electron charge, E
~ the strength and direction of the magnetic field. Since
direction of the electric field and B
there was no magnetic field applied in my experiment, this equation can be simplified to:
me
d~
ve
~ − K v~e
= eE
dt
(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 0 and writing
K as me /τ , where me 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 ~
~
τ E ≡ µe E
me
(3.6)
The electron mobility, µe = mee 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 380 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 diffusion2 .
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
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
ve = λ/τ the electron velocity, the width of the electron cloud at the time of the first
collision is found to be [18]:
σ2 =
Z∞
1 −t
e τ · (ve t)2 dt =
τ
Z∞
1 −t λ 2
e τ · ( t) dt = 2λ2
τ
τ
(3.7)
0
0
t
Here, τ1 e− τ is the probability that no collision took place within a time t and ve 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 = 2λ2 ·
t
= 2Dt
τ
(3.8)
2
Here, D = λτ is called the diffusion coefficient. In the case of isotropic diffusion, the
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:
σT =
p
2/3 · 2Dt
and
σL =
p
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
2kB T L
2DL
=
=
ve
µe E
eE
(3.10)
Here, L is the drift distance and the last step is made by applying the Nernst-Townsend
or Einstein formula Dµ = kBeT [19]. To minimize diffusion the drift time should be kept
short. Equation 3.10 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 DL increases when an electric field is applied, whereas the transverse coefficient DT
stays the same. From Figure 3.4(b) it seems that DL > DT . However, since DT spans
two dimensions and DL one, this does not have to be the case.
It is hard to find the exact diffusion coefficients DL and DT 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 400 V/cm. This corresponds to diffusion coefficients DL = 210 and
directions of movement of the electrons are easily seen.
CHAPTER 3. GASEOUS GRIDPIX
(a) No electric and magnetic field
17
(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.
DT = 280 µm/cm for the helium-isobutane mixture and DL = 210 and DT = 360 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.
CHAPTER 3. GASEOUS GRIDPIX
3.5
18
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 li , 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]:
X
Ne = 2 li = 2Xai
(3.11)
With ai = 1/li 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 [20]:
p
G
G0
Nm
=
Γ(m)
G
m
G0
m−1
em(G/G0 )
(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. G0 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 = 5000 for different values of m.
CHAPTER 3. GASEOUS GRIDPIX
19
Figure 3.6: Polýa distributions for a gas gain of 5000. 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 = Vgap ∆Q
(3.14)
Where Vgap 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 Lgap and the distance of an ionisation to the anode di . In terms of Lgap and di the
electron has to travel a distance di from ionisation to the anode, and the ion has to travel
Lgap − di to the grid. The work on both an electron and ion is then:
Wboth = We + Wion = (Vgap · −e
Lgap − di
di
) + (−Vgap · e
) = −eVgap
Lgap
Lgap
(3.15)
Now the fraction of signal that comes from the electron is calculated to be:
We
We
di
=
=
Wboth
We + Wion
Lgap
(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 di on average is small compared to
CHAPTER 3. GASEOUS GRIDPIX
20
Lgap . 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 1000, and an amplification region of Lgap = 50 µm, half of the
ionisations occur within a distance of 5 µm to the anode. Therefore the most probable
value of di = 5 µm is used in the following calculation. For a higher gas gain, di 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 Lgap − di = 45 µm. The electric field inside
the amplification region is about 300 V, which is 60 kV/cm. The ion mobility µion in
the argon-isobutane mixture is about 1.4 cm2 /Vs [19] [21]. The ion velocity can thus be
calculated:
vion = µion E = 1.4 · 60000 = 84000 cm/s = 0.84 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:
tsignal =
45 µm
Lgap − di
=
≈ 54 ns
vion
0.84 µm/ns
(3.18)
In the drift region the electric field is about 400 V/cm. The electron drift velocity then
is 4.6 cm/µs. The primary electrons need about 1000/4.6 = 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 50 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 60 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.
CHAPTER 3. GASEOUS GRIDPIX
(a) Micromegas
21
(b) Amplification region
Figure 3.7: (a) The micromegas mesh which is placed on 50 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 50 µm pillars above the readout
chip [15].
Chapter 4
DESY testbeam Feb 2014
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 2014.
This chapter gives an introduction to DESY and its testbeam facility. Furthermore the
setup and method of measurement taking are described.
22
CHAPTER 4. DESY TESTBEAM FEB 2014
4.1
23
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 1991. HERA is
an electron-proton collider which runs at a centre-of-mass energy of 300 GeV. HERA has
been operating until 2007. Nowadays research at DESY is focused on photon science.
This is the study of synchrotron and free-electron laser radiation. In photon science PETRA III, the improved version of PETRA which was finished in 2009, plays a prominent
role as synchrotron radiation source. Also, DESY serves as a testbeam facility.
4.1.1
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.
Converter
γ
e+
/e
−
Fiber
Collim
ator
Magnet
e+
e−
e+
e−
Spill Counter
DESY II
Figure 4.1: Formation of an electron testbeam at the DESY II facility [27].
CHAPTER 4. DESY TESTBEAM FEB 2014
4.2
24
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
4 cm
A
30 cm
B
11.5 cm
E
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.
CHAPTER 4. DESY TESTBEAM FEB 2014
25
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
CHAPTER 4. DESY TESTBEAM FEB 2014
26
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 112.2 A which corresponded to a 3
GeV electron beam. When the settings were optimal we obtained a particle rate of 280 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 74.80 A. The particle rate through the detector at this
current was 320 Hz. During the measurements the magnet current was kept at 74.80 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/i C4 H10 ) mixture of ratio 95/5 and the second an argon-isobutane
(Ar/i C4 H10 ) mixture of ratio 90/10. 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 30 degrees (roll 30◦ )
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.
CHAPTER 4. DESY TESTBEAM FEB 2014
27
For the helium-isobutane mixture data was taken with grid voltages from 320 up to 390
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 300 to 340 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 30 minutes of operation at a grid voltage
of 340 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: 0). (b) The detector in tilted position (yaw: 45,
roll: 30). The scintillator is visible in the back of the photograph. Beam line goes into
the page.
CHAPTER 4. DESY TESTBEAM FEB 2014
4.4
28
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 damage1 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=0) and blue (DAC=15) distributions of threshold values. The narrower the
black peak, the better the equalisation. A unit of threshold corresponds to 10 electrons.
In a threshold scan, the 4 bit DAC of the individual pixels is set. First, it is set to its
minimum value, DAC=0, 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.
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 pixel1 .
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
CHAPTER 5. TOT-CHARGE CALIBRATION
5.1
30
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 1000
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 100 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 100 testpulses are
injected, the charge of the testpulse is raised and the same measurement is repeated. This
is done 200 times so that input charges between 0 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 403.2 mV. These were thus calculated from 100 testpulses per shutter. ToT
maps like these could be made for all input charges between 0 and 448 mV for every 2.24
mV (2 DAC steps).
CHAPTER 5. TOT-CHARGE CALIBRATION
31
Mean ToT distribution
hTOT3
Entries
Mean x
Mean y
RMS x
RMS y
1255368
129.3
128.2
73.31
73.55
ToT
50
250
45
40
200
35
30
150
25
Y
20
100
15
10
50
5
0
0
50
100
150
200
250
0
X
(a) Input charge 224 mV
hTOT3
Mean ToT distribution
Entries
Mean x
Mean y
RMS x
RMS y
2309113
129.7
128
73.35
73.57
ToT
50
250
45
40
200
35
30
150
25
Y
20
100
15
10
50
5
0
0
50
100
150
200
250
0
X
(b) Input charge 403.2 mV
Figure 5.1: (a) The mean ToT value per pixel from 100 injected testpulses of 224 mV.
(b) The mean ToT value per pixel from 100 injected testpulses of 403.2 mV. As can be
seen from both pictures there is an evident spread in ToT values.
CHAPTER 5. TOT-CHARGE CALIBRATION
5.2
32
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
(112,160) (lower graph) and (144,168) that were chosen at random. The error bars indicate
the rms error from 100 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]:
c
(5.1)
f (x) = ax + b −
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 (112,160)
0.0738 ± 0.0021 3.74 ± 1.07 96.9 ± 131 9.76 ± 38.1
pixel (144,168)
0.0864 ± 0.0016 4.15 ± 0.74 74.9 ± 71.2 12.2 ± 18.44
Table 5.1: The mean and rms values of the surrogate function fit parameters of pixels
(112,160) and (144,168).
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.
hB_pfx
fit parameter a
A per collie
Entries
Mean
Mean y
RMS
RMS y
Underflow
Overflow
Integral
Skewness
65536
127.5
0.08442
73.32
0.009576
0
0
21.44
0.04684
0.095
0.09
0.085
0.08
0.075
50
100
150
200
250
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”:
p
ta
+
T
oT
−
b
+
(b + ta − T oT )2 + 4ac
Qin (e− ) = 18.75 ×
(5.2)
2a
The factor 18.75 comes from the built-in capacitor of 3 fF in every Timepix3 pixel. Per
step voltage of 1 mV, the corresponding charge is 18.75 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.
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
CHAPTER 6. GRIDPIX CHARACTERISATION
6.1
35
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
16384 (214 ) and 16 (24 ) 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 [30]. The effect of this non-flatness
on time resolution is small.
counts
TOA distribution
hToA
Entries
Mean
RMS
1000000
8161
4717
7000
6000
5000
4000
3000
2000
1000
0
0
2000
4000
6000
8000
10000
12000
14000
16000
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. 340]
hFToA
counts
FTOA distribution
Entries
Mean
RMS
1000000
7.506
4.57
70000
60000
50000
40000
30000
20000
10000
0
0
2
4
6
8
10
12
14
16
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. 340]
CHAPTER 6. GRIDPIX CHARACTERISATION
6.2
36
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
(90/10). Figure 6.3 illustrates this difference by showing a typical event for each of these
gases at the same grid voltage, namely 340 V. In this case, the beam runs along the
x-direction, coming in from the left (x = 0).
hTOT2
Total (alles ToT waardes opgeteld) ToT distribution xy
Entries
Mean x
Mean y
RMS x
RMS y
Total (alles ToT waardes opgeteld) ToT distribution xy
6
57.5
2.337
22.51
1.238
hTOT2
Entries
Mean x
Mean y
RMS x
RMS y
ToT
10
1
48
159.8
3.485
35.6
1.957
ToT
10
9
0.9
9
8
0.8
8
7
0.7
7
6
0.6
6
24
22
20
18
Z [mm]
16
14
Z [mm]
5
0.5
5
12
4
0.4
4
10
3
0.3
3
2
0.2
2
1
0.1
1
0
0
0
8
6
0
0
50
100
150
X
200
250
4
2
50
100
X
(a)
200
250
0
(b)
hTOT
hTOT
Total (alles ToT waardes opgeteld) ToT distribution on grid (xy)
Entries
Mean x
Mean y
RMS x
RMS y
150
18
57.5
168.5
22.51
1.708
Total (alles ToT waardes opgeteld) ToT distribution on grid (xy)
Entries
Mean x
Mean y
RMS x
RMS y
ToT
1
250
144
159.8
116.8
35.6
4.303
ToT
18
250
0.9
16
0.8
200
200
14
0.7
12
0.6
150
Y
0.5
150
10
Y
8
0.4
100
100
6
0.3
0.2
50
4
50
2
0.1
0
0
50
100
150
200
X
(c) Event He/i C4 H10 340 V
250
0
0
0
50
100
150
200
250
0
X
(d) Event Ar/i C4 H10 340 V
Figure 6.3: Two typical events for a grid voltage of 340 V. For He/i C4 H10 (a)(c) the mean
number of hits per event is around 1.6, whereas for Ar/i C4 H10 (b)(d) it is 15.4. These
plots also show that the amplification in the argon-isobutane mixture is higher, apparent
from the higher ToT values. [HeIso I / ArIso, GridV. 340]
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
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 580 electrons.
Total (alles ToT waardes opgeteld) ToT distribution xy
Total (alles ToT waardes opgeteld) ToT distribution xy
hTOT2
Entries
Mean x
Mean y
RMS x
RMS y
hTOT2
12
191.6
2.111
19.98
1.098
Entries
Mean x
Mean y
RMS x
RMS y
ToT
10
16
15
140.6
5.468
50.14
2.757
ToT
10
22
9
9
14
8
20
8
18
7
16
6
14
12
7
10
6
Z [mm]
Z [mm]
5
8
4
12
5
10
4
6
8
3
3
6
4
2
2
2
1
0
0
50
100
150
X
200
250
4
1
0
0
0
2
50
100
150
X
(a)
200
250
0
(b)
hTOT
Total (alles ToT waardes opgeteld) ToT distribution on grid (xy)
Total (alles ToT waardes opgeteld) ToT distribution on grid (xy)
Entries
Mean x
Mean y
RMS x
RMS y
hTOT
Entries
Mean x
Mean y
RMS x
RMS y
36
191.6
126.9
19.98
12.5
ToT
ToT
16
250
45
140.6
115.4
50.14
1.327
250
22
14
200
20
200
12
18
16
10
150
Y
8
14
150
Y
12
10
100
6
100
8
6
4
50
50
4
2
0
0
50
100
150
200
250
0
2
0
0
X
(c) Event He/i C4 H10 370 V
50
100
150
200
250
0
X
(d) Event He/i C4 H10 390 V
Figure 6.4: Two typical events for He/i C4 H10 at different grid voltages. It shows that at
higher grid voltage the ToT values have increased. At 370 V (a)(c) the mean number of
hits is around 3.6, at 390 V (b)(d) it is around 4.8. [HeIso IV, GridV. 370 / 390]
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 30◦ , see Appendix B, Table B.4. The track in Figure 6.4(d) is not
angled since the detector was not tilted, roll 0◦ , when the measurement was performed.
6.2.1
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.
CHAPTER 6. GRIDPIX CHARACTERISATION
38
ToT as function of HV
mean ToT value [25 ns]
mean nhits
ArIso
5
4.5
4
3.5
3
11
10
9
8
2.5
7
2
6
1.5
340
350
360
370
380
390
340
350
360
370
grid voltage [V]
380
390
grid voltage [V]
(a) Mean number of hits helium-isobutane (95/5)
(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. 340 - 390]
ToT as function of HV
mean ToT value [25 ns]
mean nhits
ArIso
16
14
12
10
8
11
10
9
8
6
7
4
6
2
300
305
310
315
320
325
330
335
340
grid voltage [V]
(a) Mean number of hits argon-isobutane (90/10)
300
305
310
315
320
325
330
335
340
grid voltage [V]
(b) Mean ToT argon-isobutane (90/10)
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. 300 - 340]
6.2.2
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 340 V.
CHAPTER 6. GRIDPIX CHARACTERISATION
39
h21
Entries
Mean
RMS
2
χ / ndf
Prob
1000000
2276
1576
3.289e+05 / 94
0
2.421e+04± 3.564e+01
5.443 ± 0.006
2752 ± 2.2
Charge_distributions of all tracks Grid 340 V
counts x1000
N
m
meanG
×103
100
80
60
40
20
0
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Charge [electrons]
Figure 6.7: The charge distribution for 1M hits fitted with a Polýa function. [ArIso,
GridV. 340]
The data in Figure 6.7 is fitted by the Polýa function as described by Equation 3.13. The
measured fit parameters are N = 24210±36, m = 5.44±0.01 and G0 = 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 340 V.
hHITS
Entries
Mean x
Mean y
RMS x
RMS y
6.452732e+07
126.3
124.8
47.27
45.52
Hit distribution on grid (xy)
Mean ToT distribution on grid (xy) with Divide()
hTOT3
Entries
Mean x
Mean y
RMS x
RMS y
662461
124.3
125
49.3
49.23
nhits
ToT
17
9000
200
200
16
8000
180
180
15
160
14
140
13
7000
160
6000
140
5000
Y
Y
120
4000
100
3000
11
100
10
80
2000
80
60
1000
60
0
40
40
40
40
60
80
100
120
140
160
180
200
12
120
9
8
60
80
100
120
140
160
180
X
X
(a) Hit distribution on chip
(b) ToT distribution on chip
200
7
Figure 6.8: (a) The distribution of hits on the chip for 4139853 events (tracks), corresponding to a total of 6.45 · 107 hits. (b) The distribution of mean ToT values per hit on
the chip for the same events (tracks). [ArIso, GridV. 340]
CHAPTER 6. GRIDPIX CHARACTERISATION
40
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 (60 µm). This is a pattern of blobs that repeats itself every 12
(60/5) 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.
hCharge
hCharge
Entries
Mean x
Mean y
RMS x
RMS y
nan
122.6
125
49.93
49.22
Entries
Mean x
Mean y
RMS x
RMS y
Mean Charge distribution on grid (xy) with Divide()
nan
122.6
125
49.93
49.22
Mean Charge distribution on grid (xy) with Divide()
-
-
Charge [e ]
Charge [e ]
3000
200
200
2800
5000
180
160
4000
140
Y
3000
120
Y
180
2600
160
2400
140
2200
2000
120
1800
100
2000
80
100
1600
80
1400
1000
60
40
40
60
60
80
100
120
140
160
180
200
0
40
40
1200
60
80
100
120
140
160
180
X
X
(a) All charge
(b) Zoomed charge scale
200
1000
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. 340]
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 340 V is around 3000 ± 220 electrons per hit1 . This value is compared with
simulations [31]. These simulations give a value of 3500 electrons per hit at the centre of
the holes, however for an amplification gap of 75 µm with a voltage difference of 500 V.
The amplification gap in my experiment was 50 µm and had a voltage difference of 340 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
220 electrons corresponds on average to 1 ToT count.
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 6.10 shows that for a lower Ikrum (Ikrum1 > Ikrum2 ) 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 6.10: The shape of two signals with the same charge but different Ikrum setting.
With lower Ikrum (Ikrum1 > Ikrum2 ) 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 5
11
10
9
8
7
6
5
4
3
360
365
370
375
380
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. 360-380]
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 10 electrons. With
a high threshold setting there are less ToT counts than with a low threshold setting (see
Figure 6.10) 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 10 electrons is really marginal compared to a ToT count, which
corresponds to 220 electrons.
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 tw (lower line). High charge leads to many ToT counts
and short timewalk (upper line).
43
CHAPTER 7. TIMEWALK
7.1
44
ToT values
mean ToT value [25 ns]
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 (90/10) mixture.
ToT as function of HV
11
10
9
8
7
6
300
305
310
315
320
325
330
335
340
grid voltage [V]
Figure 7.2: The relation between grid voltage and mean ToT value. [ArIso GridV. 300 340]
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
0 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 (tw = 0) to the timewalk value in the tail of the
distribution1 . 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.
CHAPTER 7. TIMEWALK
45
Graph
Timewalk [ns]
Timewalk [ns]
Graph
40
35
30
40
35
30
25
25
20
20
15
15
10
10
5
5
0
0
2
4
6
8
10
12
14
16
18
20
-
0
0
2
4
6
8
10
12
Charge [ke ]
(a) Measured timewalk-charge relation
14
16
18
20
-
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:
(
70 − 62 · Q,
if 0.7 < Q < 1 ke−
tw [ns] =
exp(3.37 − 1.01 · 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. 340 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 340 V, Figure D.7, is multiplied by the corresponding timewalk values:
CHAPTER 7. TIMEWALK
46
Timewalk [ns]
Timewalk as function of charge TPX3
100
90
80
70
60
50
40
30
20
10
0
0
10
20
30
40
50
60
ToT counts [25 ns]
Figure 7.4: The average relation between timewalk and ToT counts for Ikrum = 1.2 nA.
mean timewalk =
T oT
=50
X
fraction (ToT) · timewalk (ToT)
(7.2)
T oT =0
Using the above formula, a value of 40.5 ± 30 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 340 V demonstrates this.
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
CHAPTER 8. TRACK FITTING
8.1
48
From data to tracks
To convert the raw data into a usable format it is divided into tracks. A track is defined
as a group of hits with times of arrival close enough to have come from one and the same
particle travelling through the detector. In this case a period of 80 ToA counts is chosen,
corresponding to 2 microseconds. This choice is based on the average track rate, which
was a few kHz. Also, the maximum drift time within the detector, based on drift speed
and detector size, is about 1 µs. Taking a little more margin, a maximum track time is
chosen to be 2 µs.
Just as a reminder, the essential information to visualize a track is the number of hits
that make up the track and their properties. Each hit has an x-coordinate (Column),
y-coordinate (Row), time of arrival (ToA) and time over threshold (ToT).
From the above data the track can be reconstructed. However, a problem is that we did
not perform a t0 measurement, meaning we did not record the time an electron passed
through the detector2 . This implies that from the drift time only a difference in height
∆z can be calculated, and not an absolute position. However, the mean distance between
hits in a track indicate where the grid is. The grid will not be
far away from the position of ionisation of the last hit. Also, for
long drift time, the particle has travelled through all of the gas volume and therefore the z-coordinate is related to the x-coordinate.
Since the track angle is known, ∆x always provides an independent
cross check of the height information, because ∆x is related to ∆z.
A track with an angle of 45 degrees angled in the x,z-plane has
∆x = ∆z.
Figure 8.2 shows an example of a track. A ROOT GUI (graphical user-interface) was built
to produce the event display. The data was organized in a so-called Tree, with branches
called Column, Row, ToA and ToT for example. The computing language that was used
is C++ in combination with CERN’s data analysis program ROOT [36]. For quick track
information the GUI was used, furthermore York’s method was used for track fitting.
The x,y-plots on the left side of the figure seem to show a δ-ray, the circled region. This
is an electron which has high enough energy to escape from the original track and cause
some further ionisations. It is expected to see this in the x,z-plane as well. However, the
numbered hits (corresponding hits) do not show the same pattern.
8.2
York’s method
In the analysis of this study York’s method [37] is used to fit tracks. To reconstruct 3
dimensional particle trajectories, tracks are fitted in the x,y-plane, as well as in the x,z
and y,z-planes. York’s method is an iterative method and is chosen because it can take
uncertainties in both directions of the fit into account.
2
The reason we did not perform a t0 measurement is that a connection to the scintillator was not yet
implemented on the SPIDR board by the time the measurement was performed. However, today it is.
CHAPTER 8. TRACK FITTING
49
Figure 8.2: An example of a track showing hits on the chip’s plane, Row versus Column
(left) and ToA [s] versus Row and Column (right). [ArIso GridV. 340]
York’s method works as follows. The uncertainties are assigned to the data points as
weights, calculated by: wi = σ12 . In the following text, the two variables in the data are
i
called x and y, but remember that these could be replaced by x and z or y and z.
The goal is to find the solution in the form of a straight line y = mx + b, i.e. to find the
best fit values for slope m and intercept b [38]. Initially, approximate values for these are
chosen. Also the weights for x and y are determined 3 , see above. Then the iteration loop
starts. In every iteration there are a few steps, namely:
Iteration:
wxi wyi
1. Calculate for each point (i) Wi = wxi +m
2w
yi
P
P
P
P
2. From this, calculate x̄ = Wi xi / Wi and ȳ =
Wi yi / Wi
3. Calculate the observed points Ui = xi − x̄, Vi = yi − ȳ and βi = Wi
h
Ui
wyi
+
mVi
wxi
4. With these an improved estimate of the slope and intercept are calculated:
mimp =
3
P
P Wi βi Vi
Wi βi Ui
and bimp = ȳ − mx̄
Weights are assumed to be uncorrelated, which is appropriate for this study.
i
CHAPTER 8. TRACK FITTING
50
The improved estimates, mimp and bimp , are the starting values for the next iteration. The
iteration loop is exited when changes in m are small. In this study m − mimp < e−10 is
chosen. Uncertainties in the calculated fit parameters are given by:
1
2
+ (x̄ + β̄)2 σm
σb2 = P
Wi
(8.1)
and
2
σm
=P
1
Wi (βi − β̄)2
(8.2)
Figure 8.3 shows tracks fitted with York’s method.
Track == 77
track
10
250
York's Method Fit
9
York's Method Fit
8
200
7
6
150
Z [mm]
Y
5
4
100
3
2
50
1
0
0
50
100
150
200
250
X
(a) York’s method fit x,y
0
0
2
4
6
8
10
12
14
X [mm]
(b) York’s method fit x,z
Figure 8.3: (a) A track with 22 hits fitted with York’s method. The error bars depend
on diffusion and thus on drift time. Hits at large x-coordinate originate from closer to
the grid and therefore are less diffused from the track than hits at low x-coordinate. (b)
A track with 10 hits fitted with York’s method. The error bars depend on diffusion and
timewalk. Timewalk delays a hit which makes it seem to originate from higher than it
actually does. Therefore, the error bars on z are asymmetric. [ArIso, GridV. 340]
8.2.1
Errors
To determine the most plausible track fit the errors in the data points need to be well
known. For the gridpix detector, the errors in the measured points (xi ,yi ,zi ), are [39]:
d2p
(8.3)
σx2i = σyi2 =
+ DT2 zi + ∆d2c
12
σzi2 =
(Tc · vd )2
+ DL2 zi + (σtw · vd )2 + ∆d2c
12
(8.4)
Here, dp is the pixel pitch (55 µm), DT the diffusion constant in the transverse direction,
DL the diffusion constant in the longitudinal direction, ∆dc the rms range of a primary
ionisation electron w.r.t. the electron trajectory (12 µm), Tc the precision of the TDC
(25/16 ns), vd the drift velocity of the electrons inside the gas and σtw the error on the
time measurement due to timewalk. Note that σtw is not Gaussian and very asymmetric.
CHAPTER 8. TRACK FITTING
51
The error due to timewalk only spans one direction since timewalk always delays a hit.
This is clear from the residual distribution in Section 8.3.2.
The errors in x and y originate from three different aspects. First, there is an uncertainty
in the position of a hit within a pixel, defined by the pixel pitch: 55 µm. Second, there is
an error due to diffusion. After diffusing in the transverse direction, the hit on the pixel
will not end up exactly beneath its starting point. Last there is an uncertainty in the
position of the ionisation which does not happen exactly at the trajectory of the original
electron.
The error in z comes first from the time the electron needs to drift and the resolution of
the TDC. This is a systematic error with Tc · vd the resolution of the TDC. Second, there
is an error due to diffusion in the longitudinal direction. Third, there is a delay in the
signal due to its rise time, timewalk. Finally, the ionisation position is uncertain in all
three spatial directions, which leads to an error in z as well.
Values for the diffusion parameters and drift velocity from simulations can be found in
Appendix A. To provide an indication, for a drift field of 400 V/cm, in the argon-isobutane
mixture DT = 36 µm/mm, DL = 21 µm/mm and vd = 46 µm/ns. For the same drift field,
in the helium-isobutane mixture, DT = 28 µm/mm, DL = 21 µm/mm and vd = 14 µm/ns.
8.3
Residuals
One of the key characteristics of a tracking detector is its spatial resolution. This is
obtained from a residual measurement. A residual is the distance from a measurement
point to the fitted track. It can be defined in different ways, in this case:
resy = yfit − yhit
(8.5)
Here, y can be replaced by x or z.
Residuals here are treated biased as well as unbiased. Biased means that the point of
which the residual is calculated was also used as a data point for the fit. In other words,
yfit is influenced by yhit . Unbiased residuals are calculated for data points that are not
used in the fit. Therefore, these provide more reliable information. However, when calculating unbiased residuals, one track has to be fitted many times. For example, a track
of 10 hits has to be fitted 10 times, each time leaving out 1 of the hits. Because the use
of unbiased residuals did not improve the results significantly, the results shown below
are based on biased residuals. Here, York’s method is used to fit the data with errors as
described in Section 8.2.1.
Residuals contain information on for example the diffusion inside the gas and timewalk.
These two properties are treated in the following sections.
CHAPTER 8. TRACK FITTING
8.3.1
52
Diffusion
residuals in y z<1
residuals in y 8<z<9
hresY1
Entries
Mean
RMS
10880
0.002018
0.2882
χ / ndf
Prob
Constant
Mean
Sigma
hresY9
0.08049 / 73
1
0.08706 ± 0.14528
-0.002014 ± 0.217916
0.2069 ± 0.2632
Entries
Mean
RMS
8583
0.00245
0.3734
χ / ndf
Prob
Constant
Mean
Sigma
2
fraction
fraction
2
0.1
0.0845 / 75
1
0.06633 ± 0.10765
-0.0009635 ± 0.2855881
0.2699 ± 0.3257
0.08
0.07
0.08
0.06
0.05
0.06
0.04
0.04
0.03
0.02
0.02
0.01
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0
-2
2
residualininyy[mm]
[mm]
residual
-1.5
-1
-0.5
0
0.5
1
1.5
2
residual
in yy[mm]
[mm]
residual in
(a) Residual distribution for a drift distance of 1 mm (b) Residual distribution for a drift distance of 8 mm
Figure 8.4: Residuals for different drift distances. From the σ of the normal distribution,
0.211 ± 0.002 for 1 mm drift and 0.270 ± 0.004 for 8 mm drift, it is clear that residuals
depend on height and thus are due to diffusion. Because of the uncertainty in z the
distributions here are actually a sum of many Gaussians. That is the reason the peak at
0 is high. [HeIso IV, GridV. 390]
residuals in y z<1
residuals in y 8<z<9
hresY1
13306
-0.002928
0.2405
0.04434 / 68
hresY9
Entries
Mean
RMS
2
χ / ndf
Prob
Constant
Mean
Sigma
1
0.09739 ± 0.14449
-0.004599 ± 0.199638
0.1941 ± 0.2049
fraction
fraction
Entries
Mean
RMS
2
χ / ndf
Prob
Constant
Mean
Sigma
0.1
36628
0.002972
0.3165
0.01221 / 75
1
0.06599 ± 0.08587
0.00216 ± 0.29960
0.2969 ± 0.2408
0.07
0.06
0.08
0.05
0.06
0.04
0.03
0.04
0.02
0.02
0
-2
0.01
-1.5
-1
-0.5
0
0.5
1
1.5
2
residual in y [mm]
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
residual in y [mm]
(a) Residual distribution for a drift distance of 1 mm (b) Residual distribution for a drift distance of 8 mm
Figure 8.5: Residuals for different drift distances. From the σ of the normal distribution,
0.194 ± 0.004 for 1 mm drift and 0.297 ± 0.002 for 8 mm drift, it is clear that residuals
depend on height and thus are due to diffusion. Because of the uncertainty in z the
distributions here are actually a sum of many Gaussians. That is the reason the peak at
0 is high. [ArIso, GridV. 340]
The residuals in the x,y-plane are mostly affected by diffusion, since timewalk does not
play a role here. Therefore, by looking at the distribution of residuals at different ionisations heights, one can extract the transverse diffusion parameter. Figure 8.4 shows the
distribution of residuals in y from tracks fitted in the x,y-plane for the helium-isobutane
mixture. Figure 8.5 shows the same for the argon-isobutane mixture. In both figures, for
(a) only hits with a z-value of about 1 mm are selected, for (b) only hits with z is about
8 mm. This is done in two different ways to minimize the error. First, there is made a
selection on x, because the track angle is known and therefore from the x-position of a hit
the z-position can be extracted. To do so only long tracks are selected, tracks that have
ionisation points through the whole height of the drift volume. Since the height of the
drift volume is 9.2 ± 0.5 mm, this corresponds to tracks with a difference in x-coordinates
CHAPTER 8. TRACK FITTING
53
of 9.2 mm/55 µm ≈ 167 columns. Second, there is made a selection on z by transforming
drift time into drift height using the drift speed. However, the exact drift time, and thus
drift height, is not known because there was no exact t0 . The total error on the height of
the selected hits is estimated to be 1 mm, and eventually z = 1±1 and z = 8±1 are the selected heights. The width (σ) of these distributions quantifies the transverse diffusion [15].
Diffusion^2 as function of drift length HeIso
0.12
σ2 [mm2]
σ [mm]
Diffusion as function of drift length HeIso
0.35
0.3
0.25
0.0095Ldrift + 0.0094
0.1
0.08
0.2
0.06
0.15
0.04
0.1
0.02
0.05
0
1
2
3
4
5
6
0
7
8
9
drift length [mm]
1
2
3
4
5
6
7
8
9
drift length [mm]
(b) σ 2 as a function of drift length
(a) Diffusion (σ) as a function of drift length
Figure 8.6: Diffusion versus drift length. The fit function in the right figure is σ 2 =
0.0095Ldrif t + 0.0094. [HeIso IV, GridV. 390]
Diffusion as function of drift length ArIso
Diffusion^2 as function of drift length ArIso
0.12
σ2 [mm2]
σ [mm]
0.35
0.3
0.25
0.0088Ldrift + 0.017
0.1
0.08
0.2
0.06
0.15
0.04
0.1
0.02
0.05
0
1
2
3
4
5
6
7
8
9
drift length [mm]
(a) Diffusion (σ) as a function of drift length
0
1
2
3
4
5
6
7
8
9
drift length [mm]
(b) σ 2 as a function of drift length
Figure 8.7: Diffusion versus drift length. The fit function in the right figure is σ 2 =
0.0088Ldrif t + 0.017. [ArIso, GridV. 340]
In Figures 8.6 and 8.7 the diffusion factor at different drift lengths is plotted. From these
figures the diffusion for the selected√drift field can be extracted. For the helium-isobutane
4
mixture a diffusion of 323 ± 16 µm/ cm is measured
√ for a drift field of 424 V/cm . From
simulations this is expected to be about 280 µm/ cm, see Appendix A. Note that the
fit in Figure 8.4(b) does not describe the data properly. However, from omitting the
√last
two points from the fit, the measured diffusion would even be higher, 346 ± 18 µm/ cm,
which agrees even less with the expected value.
√ Including only the first and last point in
the fit, the diffusion would be 286 ± 11 µm/ cm. This agrees, within the error, with the
expected value from simulations. However, there is not a properly understood reason to
explain whether this is the true value.
4
The drift field of 424 V/cm is calculated form the drift field inside the gas, 390 V, for 9.2 mm.
CHAPTER 8. TRACK FITTING
54
√
For the argon-isobutane mixture a diffusion of 324 ± 14 µm/ cm is measured for a√drift
field of 434 V/cm. According to simulations this is expected to be about 350 µm/ cm,
see Appendix A. The fit in Figure 8.5(b) does agree with the measured points, therefore
the deviation between measurement and expectation can not be explained fitting the same
points differently.
The relation between σ 2 and drift length is expected to be linear. This shows nicely in Figure 8.7 for the argon-isobutane mixture. However, in Figure 8.6 for the helium-isobutane
mixture this is not the case. The reason for the decreasing diffusion factor is not known.
Different ideas are tried. For example, only hits with very high ToT values, and therefore
low timewalk, are taken into account. Also, only tracks with many hits (20 or more)
are selected. This was done to minimize the error that occurs from calculating biased
residuals. To completely eliminate this error residuals are calculated unbiased instead of
biased. However, even this did not change the result. Other data is used, data with a
different grid voltage, which resulted in the same effect. It must be noted that there is
an uncertainty in drift distance (no t0 ) as well as in the height of the gas chamber. These
two uncertainties might have led to the fact that diffusion does not act linear with respect
to the calculated drift height, which has large uncertainty.
8.3.2
Timewalk
The residuals in the x,z-plane are not only affected by diffusion, but also by timewalk.
Therefore, the distribution of residuals contains information about the factor of longitudinal diffusion as well as the factor of timewalk. Figure 8.8 shows the distribution of
residuals in z from tracks fitted in the x,z-plane.
Figure 8.8: Residual of 83708 hits. z is measured in ns, and not transformed into mm, to
be able to extract the factor of timewalk in ns as well. [ArIso, GridV. 340]
CHAPTER 8. TRACK FITTING
55
The distribution is fitted with an exponentially modified Gaussian function. It is a convolution of the normal probability density function with an exponential probability density
function:
λ λ (2µ+λσ2 −2x)
µ + λσ 2 − x
√
(8.6)
f (x) = e 2
erfc
2
2σ
The parameters in this equation, µ, σ and λ correspond respectively to the mean of the
Gaussian component, the variance of the Gaussian component and the rate of the exponential component.
The fitted parameters in Figure 8.8 are: µ = −18.89 ± 0.12, σ = 12.85 ± 0.11 and
λ = 0.04812 ± 0.00038. The parameter of λ corresponds to 1/tw . The measured value
for timewalk (tw ) in this case is thus 20.78 ± 0.17 ns. This is a promising result. It
matches the result of the mean timewalk calculated in Section 7.3 within the error bar.
The timewalk for Timepix1 was estimated to be 110 ns [40]. It can be concluded that
Timepix3 is improved with respect to Timepix1 on this aspect of time resolution.
Chapter 9
Conclusion
The goal of this research was to characterize the Timepix3 chip and the gaseous micromegas detector that was constructed with it. In this chapter the findings of the research as well as some ideas for improvements of the measurements are given. It ends with
a short outlook on the development and implementation of Timepix3 based detectors in
the coming years.
56
CHAPTER 9. CONCLUSION
9.1
57
Summary and Conclusions
Testbeam measurements
The measurements that were performed at the DESY testbeam lead to a large amount
of data. Two different gases were tested as well as different settings for grid voltage,
threshold and Ikrum. Measurements were performed at different angles with respect to
the beam line. All of these different measurements were of great use in the analysis of the
Timepix3 chip and the micromegas detector.
Calibration
The ToT-charge calibration was performed at Nikhef. The relation between ToT and
charge could be described by the appropriate surrogate function. Normally this relation
would be implemented on each pixel individually. However, since the calibration measurement was performed using a different Timepix3 chip than the one used at the testbeam
this was not possible. Therefore it was chosen to implement the mean ToT-charge relation
for each column instead. Since a clear column to column variation exists, which is almost
the same for different Timepix3 chips, this gives a first order calibration.
Grid voltage
For both gas mixtures the number of hits as well as the mean ToT values per hit are
shown to increase with increasing grid voltage. This was expected, since a higher grid
voltage causes higher charge in the avalanches that are formed in the amplification region. Because of the higher charge in an avalanche, more hits are measured because more
avalanches will have enough charge to pass the threshold. The gas gain at the centre of
the holes for the argon-isobutane mixture at a grid voltage of 340 V was determined to
be around 3000 ± 220 electrons per hit. This was about 500 electrons less than expected
from simulations. The charge distribution of the hits was measured to follow the expected
Polýa distribution.
Micromegas
As discussed in Chapter 3, the amplification grid that was used in this research was a
micromegas foil. It is a 5 µm thick copper foil with a hole every 60 µm. Because of
the difference in pitch with respect to the Timepix3 chip, 55 µm, a Moiré pattern arises.
This is not ideal, but it did not pose a big problem in the analysis since the pattern is
predictable. Even though the Moiré pattern reduces the hit detection efficiency, there
were enough events with a sufficiently large number of hits to make tracking possible.
Tracking
The gaseous detector that was constructed on the Timepix3 chip was characterised by
fitting tracks using York’s method. From these track fits, residual distributions were obtained, from which diffusion and timewalk parameters were extracted. The transverse
diffusion in the two different gas mixtures was determined. However, it was difficult to
compare these with the expected value from simulations due to the large uncertainty in
the height measurement. This was caused by different aspects, namely: the absence of
CHAPTER 9. CONCLUSION
58
an exact track time, see below, the uncertainty in the height of the drift chamber, the
presence of timewalk and the impossibility of measuring the longitudinal diffusion parameter. It was impossible to extract the latter from the residual distribution, since that is
dominated by timewalk. However, from the residual distribution in the drift direction the
mean timewalk parameter for measurements with the argon-isobutane mixture at a grid
voltage of 340 V was calculated to be 20.8 ± 0.17 ns. This is significantly better than the
timewalk for Timepix1, which is around 110 ns [40]. Note that 20 ns already satisfies the
required maximum of 25 ns for VeloPix.
The measurement of the drift time is used to calculate the drift height (z-coordinate),
using drift velocity. Actually, the drift time indicates a difference in height, not an exact
position. A track time or t0 measurement can be performed to measure the exact time
of ionisation. In that case, the drift time is the difference between t0 and the time of
arrival of a hit on the chip. Unfortunately, my experiment did not include a t0 measurement. However, for long tracks, tracks with ionisations across the total height of the drift
volume, this is not necessary since the height of the drift volume is known. Therefore,
mostly long tracks are used in the analysis. For shorter tracks, the position of ionisation
inside the drift volume can be restrained by looking at the mean number of ionisations
per track length. This can be used to determine restrictions on the position of the grid.
ToA and ToT
With respect to Timepix1, a great advantage of Timepix3 is the possibility of using the
combined ToA&ToT mode. It makes 3D tracking possible since ToA information (necessary to determine the z-coordinate of a hit) could be combined with ToT information
(necessary to determine the error in this height).
9.2
Improvements
The measurement described in this thesis induced the first results obtained with a micromegas on a Timepix3 chip. At the time of the experiment the readout was still not
fully developed. However, it was important that useful first measurements could be done,
even though not everything was ready. When this measurement would be redone in the
future, some improvements to the setup could be made.
Protection layer
The relatively low grid voltage that could be applied, to prevent damage to the chip due
to sparks, was the reason that a low number of ToT counts were measured. The low ToT
counts led to a significant timewalk in the data and thus to a low resolution in the height
measurement. Also, if it would have been possible to apply a higher grid voltage, the
number of detected hits per track would have been higher. This would further improve
the spatial resolution. Higher voltages could be applied when the Timepix3 chip would
be protected against sparks. For this purpose, silicon rich nitride (SiRN), which consists
of silicon nitride (Si3 N4 ) with extra silicon, could be used. Silicon rich nitride is highly
resistive and therefore well suited to be used as protection layer. It has already been
CHAPTER 9. CONCLUSION
59
implemented on Timepix1 in 2008, where it was deposited on the chip in different thicknesses [41]. Currently, the first Timepix3 chips are covered with this protection layer and
thus Timepix3 can now be tested at higher grid voltages. This will improve the spatial
resolution measurements
Track time measurement
A t0 measurement could for instance be performed by using a trigger from a coincidence
of two scintillators. A measurement of the arrival time of a track strongly reduces the
uncertainty of the height measurement. However, at the time my experiment was performed, the TDC that is needed to trigger the signal was not yet implemented on the
SPIDR board. This functionality has been added recently.
Ingrid
To avoid the Moiré pattern that arises because of the difference in pitch between the chip
and the micromegas, the use of an aluminium Ingrid would be the solution. The holes in
the grid would be manufactured to have the same pitch as the Timepix3 chip. The Ingrid
was not yet available for Timepix3 when my measurement was performed. At the time
of writing, the production of an aluminium Ingrid is ongoing.
9.3
Outlook
My experiment was the very first test of Timepix3 as particle detector using a beam of
electrons in our research group. Different people in the group are now testing Timepix3
in other experiments. The SPIDR board is adapted so that it can be used for triggering
the events. Also a protection layer is now applied on some of the chips.
Telescope
To determine the resolution, Timepix3 is now tested using a so-called telescope. This is
a collection of, in this case, eight detectors in a row. The Timepix3 based detector under
test (DUT) is placed in between the detectors. The exact coordinates of tracks inside the
DUT can thus be obtained, once it is aligned with the telescope. Such a telescope using
silicon sensors has been developed by Nikhef for use with the LHCb VELO group.
LHCb VELO
The Vertex Locator (VELO) detector is one of the detectors of the LHCb experiment
(LHC, CERN) [42]. For the VELO detector the VeloPix is developed, which is derived
from Timepix3. It is planned to be installed at the LHCb detector in 2019. VELO is
specialized in measuring B mesons which have a lifetime of only 1.5 × 10−12 seconds. To
reconstruct displaced vertices, only 1 mm from the primary vertex, very sensitive and accurate sensors are needed. This is what VeloPix is used for. Currently researches on the
characteristics of the Timepix3 chip are performed at Nikhef and CERN for this purpose.
Appendix A
Properties of gas mixtures
In this appendix some properties of the gas mixtures that are used in this thesis can be
found. It contains graphs of the drift and diffusion properties of the gases He/i C4 H10
in a ratio of 95/5 and Ar/i C4 H10 in a ratio of 90/10. The graphs are the outcomes of
simulations with MAGBOLTZ performed by S. Tsigaridas and W. Koppert.
60
APPENDIX A. PROPERTIES OF GAS MIXTURES
A.1
61
He/i C4H10 95/5
Figure A.1: MAGBOLTZ simulation of the electron drift velocity as a function of the
drift field in He/i C4 H10 .
APPENDIX A. PROPERTIES OF GAS MIXTURES
62
Figure A.2: MAGBOLTZ simulation of the diffusion as a function of the drift field in
He/i C4 H10 . Longitudinal diffusion (yellow line) is the diffusion in the drift direction,
whereas transverse diffusion (green line) is the diffusion perpendicular to the drift direction.
APPENDIX A. PROPERTIES OF GAS MIXTURES
A.2
63
Ar/i C4H10 90/10
Figure A.3: MAGBOLTZ simulation of the electron drift velocity as a function of the
drift field in Ar/i C4 H10 .
APPENDIX A. PROPERTIES OF GAS MIXTURES
64
Figure A.4: MAGBOLTZ simulation of the diffusion as a function of the drift field in
Ar/i C4 H10 . Longitudinal diffusion (yellow line) is the diffusion in the drift direction,
whereas transverse diffusion (green line) is the diffusion perpendicular to the drift direction.
Appendix B
Testbeam data
This appendix gives an overview of the data that was taken. It is grouped into measurements having the same settings for threshold and Ikrum. Also, most measurements in a
set have the same orientation (yaw, roll) with respect to the beam line. (It is indicated
behind the measurement if different.)
Each data set consists of files with different grid and cathode voltage (GridV. and CathV.),
sometimes changing the potential difference (V. diff.) inside the drift region. The names
of the data sets are used as reference throughout the thesis.
The threshold setting consists of two parts. The first is the zero threshold which is the
offset of the baseline. The second corresponds to the actual threshold for which the number should be multiplied by ten to get the number of electrons. For example, in Table
B.1 the baseline is at 262, whereas the threshold is about 400 electrons above this baseline.
The Ikrum value indicates the number of steps. Each step corresponds to 240 pA. Thus,
Ikrum: 5 corresponds to 1.2 nA and Ikrum: 15 to 3.6 nA.
The number of files corresponds to the time of data taking. Each run took 10 seconds.
So, multiplying the number of files by 10 gives the time in seconds data was taken with
the corresponding settings.
65
APPENDIX B. TESTBEAM DATA
B.1
66
He/i C4H10 data
Data taken with the He/iC4 H10 (ratio 95/5) mixture:
HeIso I
settings:
threshold: 262 + 40
Ikrum: 5
yaw: 45
roll: 0
Measurements
GridV. CathV. V. diff. number of files
320
690
370
168
330
700
370
77
340
710
370
277
340
700
360
286 (roll: 15)
Table B.1: HeIso I
HeIso II
settings:
threshold: 262 + 45
Ikrum: 5
yaw: 45
roll: 30
Measurements
GridV. CathV. V. diff. number of files
340
710
370
69
350
720
370
98
Table B.2: HeIso II
HeIso III
settings:
threshold: 262 + 57
Ikrum: 15
yaw: 45
roll: 30
Measurements
GridV. CathV. V. diff. number of files
350
700
350
90
360
750
390
189
370
760
390
176
380
770
390
157
380
770
390
Table B.3: HeIso III
158 (roll: 0)
APPENDIX B. TESTBEAM DATA
HeIso IV
settings:
threshold: 262 + 58
Ikrum: 5
yaw: 45
roll: 30
67
Measurements
GridV. CathV. V. diff. number of files
360
750
390
92
370
760
390
106
380
770
390
171
390
780
390
234
380
390
770
780
390
390
154 (yaw,roll: 0)
363 (roll: 0)
Table B.4: HeIso IV
B.2
Ar/i C4H10 data
Data taken with the Ar/i C4 H10 (ratio 90/10) mixture:
ArIso
settings:
threshold: 269 + 58
Ikrum: 5
yaw: 45
roll: 0
GridV.
300
310
320
330
340
Measurements
CathV. V. diff. number of files
700
400
75
710
400
102
720
400
99
730
400
96
740
400
161
340
740
400
Table B.5: ArIso
144 (roll: 30)
Appendix C
DAC scan
This Appendix contains the results form the DAC scan measurement, which was performed to do the calibration.
The relation between mV and electrons is determined by the built-in capacitor of a
Timepix3 pixel. This capacitor has a value of 3 fF. The charge per mV is then given
by the following Formula:
Q = C · V = 3 · 10−15 · 10−3 = 3 · 10−18 Coulomb.
Since the charge of an electron is −1.602 · 10−19 Coulomb, 1 mV corresponds to
3 · 10−18 /1.602 · 10−19 = 18.75 electrons.
68
(C.1)
69
-
1200
22000
20000
1000
18000
testpulse e
testpulse mV
APPENDIX C. DAC SCAN
16000
800
14000
12000
600
10000
8000
400
6000
4000
200
2000
0
0
50
100
150
200
250
300
350
400
0
450
500
testpulse step
50
2.5
e- / step
mV / step
Figure C.1: The absolute testpulse charge [mV and electrons] for each testpulse step.
40
2
30
1.5
1
20
0.5
10
0
0
-0.5
-1
0
-10
50
100
150
200
250
300
350
400
450
500
testpulse step
Figure C.2: The increase in testpulse charge [mV and electrons] per testpulse step.
Appendix D
Hit and ToT distributions
In this Appendix relevant hit and ToT distributions can be found.
70
APPENDIX D. HIT AND TOT DISTRIBUTIONS
D.1
71
Distributions of number of hits
The figures below show the distribution of number of hits per event corresponding to the
events shown in Figures 6.3 and 6.4.
Fraction of events
Number of hits per track
h
Entries
1619437
Mean
RMS
1.639
1.616
Underflow
Overflow
0
5.557e-06
Integral
Skewness
0.999
5.105
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
Number of hits per event
Figure D.1: Distribution of the number of hits per event. The mean number of hits is
1.663. [HeIso GridV. 340]
Fraction of events
Number of hits per track
Entries
h
Mean
RMS
9003
3.287
4.028
Underflow
Overflow
0
0
Integral
Skewness
0.9993
5.553
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
10
20
30
40
50
60
Number of hits per event
Figure D.2: Distribution of the number of hits per event. The mean number of hits is
3.587. [HeIso GridV. 370]
APPENDIX D. HIT AND TOT DISTRIBUTIONS
72
Fraction of events
Number of hits per track
h
Entries
4289620
Mean
RMS
4.607
5.474
Underflow
Overflow
0
2.215e-05
Integral
Skewness
0.9982
5.012
0.22
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
10
20
30
40
50
60
70
Number of hits per event
Figure D.3: Distribution of the number of hits per event. The mean number of hits is
4.766. [HeIso GridV. 390]
Fraction of events
Number of hits per track
h
Entries
2525035
Mean
RMS
15.35
17.18
Underflow
Overflow
Integral
Skewness
0
0.001131
0.9984
3.391
0.1
0.08
0.06
0.04
0.02
0
0
20
40
60
80
100
120
140
160
180
Number of hits per event
Figure D.4: Distribution of the number of hits per event. The mean number of hits is
15.43. [ArIso, GridV. 340]
APPENDIX D. HIT AND TOT DISTRIBUTIONS
D.2
73
Distributions of ToT values
The distribution of ToT values of many hits is important in the estimation of timewalk.
The Figures below show the ToT distribution for data taken with the argon-isobutane
mixture at different voltages. It is evident that an increase of the grid voltage and thereby
gain means a decrease in hits with ToT values of 0 and 1. The rest of the distribution is
shifted towards higher ToT counts.
ToT gridv 380 ikrum 15
h20
fraction
Entries
Mean
RMS
500000
5.658
5.222
0.25
0.2
0.15
0.1
0.05
0
0
5
10
15
20
25
30
ToT counts [25 ns]
Figure D.5: Distribution of the ToT values of many hits. [ArIso GridV. 300]
ToT gridv 380 ikrum 15
h20
fraction
Entries
Mean
RMS
500000
7.562
6.209
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
5
10
15
20
25
30
35
40
ToT counts [25 ns]
Figure D.6: Distribution of the ToT values of many hits. [ArIso GridV. 320]
APPENDIX D. HIT AND TOT DISTRIBUTIONS
74
ToT gridv 380 ikrum 15
h20
fraction
Entries
Mean
RMS
500000
10.48
7.838
0.12
0.1
0.08
0.06
0.04
0.02
0
0
10
20
30
40
50
ToT counts [25 ns]
Figure D.7: Distribution of the ToT values of many hits. [ArIso GridV. 340]
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Samenvatting
Het onderwerp van studie in deze masterscriptie is de Timepix3-chip. Dit is een pixelchip
van 256 bij 256 pixels van 55 x 55 µm, die wordt gebruikt voor het uitlezen van data. De
chip is nog in ontwikkeling en moet eerst worden gekarakteriseerd voordat hij kan worden
toegepast in grote detectoren. De chip kan breed toegepast worden, en zal bijvoorbeeld
worden gebruikt in de LHCb-VELO-detector bij het LHC-experiment op CERN. Daarvoor wordt de VeloPix-chip ontwikkeld, die gebaseerd is op Timepix3.
In dit onderzoek is de Timepix3-chip verwerkt in een gasdetector. De detector is getest
met behulp van een testbundel, bestaande uit elektronen van 6 GeV, op DESY, Hamburg. Verschillende aspecten van de detector zijn getest, vooral door gebruik te maken
van gereconstrueerde tracks. Als een elektron door het gas vliegt, worden de gasmoleculen
geı̈oniseerd. Door een spanning over het gasmengsel te zetten worden de elektronen naar
de chip geleid. De pixel die ze daar raken wordt bepaald door de positie van ionisatie. De
hoogte van ionisatie wordt gemeten aan de hand van de aankomsttijd van deeltjes op de
chip.
De vernieuwing van Timepix3 met betrekking tot zijn voorganger Timepix1 is dat de
aankomsttijd en de lading van een deeltje op de chip tegelijk gemeten kunnen worden.
De lading wordt gebruikt om de fout in de meting te bepalen. De resolutie van de chip
is bepaald door te kijken naar de distributie van residuals, afwijkingen tussen meting en
track fit. Een belangrijk resultaat hiervan is de bepaling van de timewalk : een effect dat de
aankomsttijd van een deeltje op de chip vertraagt. De vertraging is bepaald op ongeveer
20 nanoseconden, een verbetering ten opzichte van Timepix1, waarbij de vertraging 110
nanoseconden was.
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Acknowledgements
I would like to thank the following persons for making this master’s thesis possible. My
daily supervisor Martin van Beuzekom for his great help during the whole period of this
research project. My examiners Els Koffeman and Ivo van Vulpen for willing to read
and review this thesis. All members of the R&D group for creating the nice atmosphere
and being always prepared to help. Especially Panagiotis Tsopelas for taking the time
to discuss and figure out things with me and for organizing the very useful Pixel and
Tracking meetings. Furthermore, I would like to thank the institute Nikhef for being able
to execute my master’s thesis here. The research leading to these results has been carried
out at the Testbeam Facility at DESY, a member of the Helmholtz Association (HGF).
A very special thanks to my parents for supporting me throughout all of my study years
and proofreading parts of this thesis. And finally to my lovely boyfriend and sister for
making the stressful times of writing a thesis a bit less stressful.
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