Testbeam investigations of a 50μm silicon pixel detector

(1)

R

EPORT

B

ACHELOR

P

ROJECT

P

HYSICS AND

A

STRONOMY

Spatial resolution and cluster sizes in a

50 µm silicon pixel detector

Author: M.L.E. Heidotting 10727213 Daily Supervisor: Dr. D. Hynds Supervisor: Dr. W.D. Hulsbergen Examiner: Prof. Dr. M.H.M. Merk

Conducted between 03-09-2018 and 14-08-2019 Size: 15 EC

Faculteit der Natuurwetenschappen, Wiskunde en Informatica Faculteit Exacte Wetenschappen

(2)

(3)

iii

Abstract

The LHC is currently in its second long shutdown. During this period an upgrade of the VErtex LOcator (VELO), which is based on a 200 µm silicon hybrid pixel de-tector, is being installed. There are plans for future increases in the luminosity of the LHC, which makes it desirable to improve the timing resolution of the VELO. The next upgrade of the VELO is expected to be installed around 2030. This creates the opportunity to improve the timing resolution. One of the ways to increase the tim-ing resolution is to decrease the thickness of the sensor. In this thesis a hybrid pixel detector with a 50 µm n-in-p silicon sensor and a Timepix3 readout ASIC, was char-acterised in terms of the cluster size behaviour and spatial resolution. Measurements were taken with a Timepix3 telescope at the beam facilities in the SPS North Area at CERN to provide tracking information. The data was taken at different angles and voltages. The lowest resolution of 5 µm was achieved at 50◦.

(4)

(5)

Populaire Nederlandse Samenvatting

Diep onder de grond in Genève ligt de LHC, een 27 kilometer lange deeltjesver-sneller. Protonen worden eerst in een serie van deeltjesversnellers versneld, totdat ze bijna met de lichtsnelheid gaan, waarna ze de grote LHC ring in worden ges-tuurd. De protonen in de ring gaan tegengestelde kanten op, daardoor kunnen ze tegen elkaar botsen. Bij deze botsingen komt zo veel energie vrij dat er nieuwe deelt-jes gevormd kunnen worden. Deze deeltdeelt-jes zijn nog kleiner dan protonen en bestaan vaak niet lang. Na een tijdje vervallen ze naar andere deeltjes. Deze deeltjes kun-nen worden gemeten met grote grote detectoren, die op verschillende punten in de LHC-ring staan. Een van die detectoren is de LHCb detector, die je hieronder kunt zien. Om de kleinste deeltjes te zien, heb je vaak de grootste detectoren nodig. Dat geldt ook voor de LHCb, die meer dan 20 meter lang is en bijna vijf meter hoog.

Het LHCb experiment met de VErtex Locater (VELO) als eerste detector aan de linkerkant.

Het LHCb experiment bestaat uit een verzameling van kleinere detectoren, die alle-maal verschillende taken hebben en zo samen kunnen bepalen welke deeltjes er doorheen gaan en hoe hun pad loopt. Een van de detectoren is de VErtex LOca-tor, die ook wel de VELO wordt genoemd. De taak van deze detector is te bepalen waar de deeltjes gevormd worden en waar ze vervallen. De deeltjes die door de detectoren gaan, hebben vaak hele hoge energiën, die er voor zorgen dat ze de de-tectoren langzaam beschadigen. Na een tijdje zullen de dede-tectoren dus vervangen moeten worden. Op dit moment wordt de eerste upgrade van de VELO detector geïnstalleerd. De volgende geplande update wordt waarschijnlijk rond 2030 geïn-stalleerd.

In de tweede upgrade van de VELO wordt de VELO helemaal opnieuw ontwor-pen. Dit biedt de mogelijkheid om de detector nog beter te maken. Er wordt nu gekeken naar de mogelijkheid om de tijdsmeting preciezer te maken. Dit zou bi-jvoorbeeld gedaan kunnen worden door het sensormateriaal van de detectordelen

(6)

vi

van de VELO dunner te maken.

In deze scriptie is er gekeken naar de resolutie van een detector(deel) met een dunne sensor, die slechts een twintigste van een millimeter dik was. Dit is maar een kwart van de dikte van de sensor in de huidige VELO. De detector was veel kleiner dan de hele VELO. Het sensordeel is een vierkant met zijden van ongeveer anderhalve centimeter. Hieronder zie je een foto van een detectordeel.

De detector met de sensor en bijbehorende printplaat.

De detector is onder verschillende spanningen en hoeken ten opzichte van de deelt-jes getest met een deeltdeelt-jesbundel bij CERN. Daaruit is gebleken dat de resolutie beter wordt bij grotere hoeken (in ieder geval tot 50◦). De detector gedraagt zich verder ook zoals er verwacht was. Dit biedt een mooi beginpunt bij de verkenning naar opties voor de tweede upgrade van de VELO.

(7)

vii

List of Figures

1.1 The accelerator complex at CERN. Figure taken from [11]. . . 2 1.2 The LHCb detector at CERN, showing the VErtex LOcator (VELO),

Ring Imaging CHerenkov detectors (RICH1 and RICH2), tracking sta-tions (TT, T1, T2, T3), the dipole magnet, muon stasta-tions (M1-M5) and the subdetectors providing energy information (SPD/PS, ECAL, HCAL). Figure taken from [7]. . . 2 2.1 Layout of strips and pixels in strip- and pixel detectors. The strips

and pixels are shown in grey. . . 3 2.2 Band diagrams of an insulator (characterised by a large band gap),

conductor (overlapping bands) and semiconductor (small band gap). . 4 2.3 Band diagrams of not-doped, n-doped and p-doped silicon. In the

n-doped silicon the dopant has added an energy level just below the conduction band and donated electrons into the conduction band. In the p-doped silicon the dopant has added an extra energy level just above the valence band into which electrons from the valence band can travel, creating an excess of holes in the valence band. . . 5 2.4 Depth of depletion in the sensor, assuming Na = 10−14 cm−3 and

Nd=5.5∗10−12cm−3. . . 6 2.5 Electric field inside a silicon sensor with Na = 10−14cm−3and Nd=

5.5∗10−12 cm−3 for 50 µm thickness 15V (black), 10V (red) and 5V (green). . . 7 2.6 Cross-section of a silicon hybrid pixel detector, showing a partially

depleted sensor that has been bump-bonded to a readout chip. Figure taken from Rossi et al. [15] . . . 8 2.7 Generic Landau distribution. . . 9 2.8 Diffusion parameter for 20V (red), 30V (green), 60V (blue) and 90V

(black). . . 10 2.9 Pixel logic in Timepix3. Shows the analogue and the digital sections.

Figure taken from Hynds [10]. . . 11 2.10 Signal pulse showing the Time of Arrival (ToA) and Time over

Thresh-old (ToT). . . 12 3.1 Plot of the equalisation of the chip, showing the number of pixels that

fire for a given THL. The scan with mask (0000) is shown on the left in blue, the scan with mask (1111) is visible on the right in red and the scan after equalisation is shown in the middle in black. . . 14 3.2 Map of the hot pixels that were masked during the taking of data at

CERN testbeam. . . 14 3.3 IV curve for the detector under study . . . 15 3.4 Time over the threshold for charge at -20V with a90Sr source. . . 16

(10)

x

3.5 Image of the Timepix telescope. The Timepix3 telescope looks mostly the same, but the Timepix planes are now Timepix3 planes and there is no separate Timing Plane. The Timepix3 telescope has four planes up-stream of the Device Under Test (DUT) and four planes downup-stream of the DUT, as well as the two scintillators on either end of the tele-scope. The DUT is placed on a movable stage. (Image taken from Akiba et al. [3].) . . . 17 3.6 Small angle scan through which a shifted parabola has been fitted,

showing that the minimum cluster size and the angle that puts the detector perpendicular to the beam occur at−1.4◦. . . 18 3.7 Flowchart showing the software analysis process using Kepler. . . 20 4.1 Hitmap showing the number of hits on each pixel for a 50 µm thick

sensor at -90V. . . 21 4.2 Lateral distance . . . 22 4.3 Size of associated clusters at -90V and different angles: 0◦(black), 55◦

(red) and 80◦(green). . . 23 4.4 Size distributions of associated clusters at 0◦ and different voltages:

-15V (black), -30V (red), -60V (green) and -90V (blue). The lines for -60V and -90V mostly overlap. . . 24 4.5 The mean sizes (red circles), widths (blue triangles) and lengths (green

squares) of raw clusters as a function of angle at -90V. . . 25 4.6 Size distributions of associated (green), raw (black) and non-associated

(red) clusters at -90V at 0◦and 80◦. . . 26 4.7 Comparison of the mean sizes of raw (black triangle), associated (green

circles) and non-associated (red squares) clusters for different angles at -90V. . . 26 4.8 The fractions of associated clusters with sizes 1 (red circle), 2 (green

squares), 3 (blue triangle) and larger than 3 (inverted pink triangle) at -90V. . . 27 4.9 Distributions of the distance of clusters to the track they have been

associated with (residuals) in the x direction at -90V. . . 28 4.10 Resolution of the 50 µm silicon pixel detector at -15V (red circle), -30V

(green square), -60V (blue triangle) and -90V (pink inverted triangle). . 29 4.11 Time over threshold of associated clusters at -90V. . . 30 4.12 Intrapixel track intercepts for cluster sizes one, two, three and four at

(11)

xi

"I don’t know how to express happiness anymore."

-Second year PhD student

(12)

(13)

1

Chapter 1

Introduction

1.1 CERN

The European Organisation for Nuclear Research (CERN) is a research laboratory for particle physics and home to an extensive accelerator complex (see figure 1.1) [1]. It consists of a series of linear and circular accelerators that were previously used for distinct experiments. They now feed proton beams into the main accelerator ring, the 27 kilometer Large Hadron Collider (LHC) [1]. A variety of experiments are spread out along the LHC, the four main ones being ATLAS, CMS, ALICE and LHCb.

1.2 The LHCb experiment

The LHC Beauty experiment (LHCb) focuses on research into b-physics, looking at CP-violation and searching for new phyics among these and a variety of other anal-yses [8]. Figure 1.2 shows a cross section of the LHCb detector, detailing the different subdetectors which perform distinct functions. Tracking information is provided by the Tracking stations (TT, T1, T2 and T3); particle identification is done by the combi-nation of the Ring Imaging CHerenkov detectors (RICH1 and RICH2), the calorime-ters (ECAL and HCAL) and the muon stations (M1-M5). The focus of this report is the VErtex LOcater (VELO) subdetector, which is used to determine the production and decay vertices of beauty particles [8].

1.3 LHCb Upgrade

The LHC is currently in the second long shutdown (LS2), during which most parts of the detector are being replaced and updated [5]. During LS2 the VELO is being replaced entirely by an upgraded version that is based on a 200 µm silicon hybrid pixel detector (see chapter 2) and will be able to support a 40 MHz readout [5]. There are plans to further increase the luminosity of the LHC, which means the VELO will need a better timing resolution [14]. A possible way to achieve a better timing resolution could be to base the VELO on a detector with a thinner sensor, where they are currently 200 µm thick [5]. In this report the cluster sizes and spatial resolution of a 50 µm thick n-in-p silicon hybrid pixel detector will be discussed as part of the characterisation of this detector.

(14)

2 Chapter 1. Introduction

FIGURE 1.1: The accelerator complex at CERN. Figure taken from [11].

FIGURE1.2: The LHCb detector at CERN, showing the VErtex LOca-tor (VELO), Ring Imaging CHerenkov detecLOca-tors (RICH1 and RICH2), tracking stations (TT, T1, T2, T3), the dipole magnet, muon sta-tions (M1-M5) and the subdetectors providing energy information

(15)

3

Chapter 2

Detection of charged particles

2.1 Use of silicon in particle detection

At the start of the research into semiconductor materials, silicon was mostly used in the siliconcarbide (SiC) form, but around 1935 the research into making a purer version of silicon started [12]. This research led to the development of procedures to produce doped silicon (see section 2.3.1), which would eventually make it possible to produce silicon particle detectors [12]. The first silicon microstrip detectors were produced in the late 1970s at CERN, and consisted of 100 strips that were 140 µm wide [9]. Types of silicon strip detectors are still in use today. The original VELO in LHCb was based on a type of silicon strip detector [6]. A disadvantage to the strip detector is that it provides one-dimensional information, since all the deposited charge is measured at the end of a single rectangular strip (see figure 2.1a) [16]. In an effort to move away from the projected view that the strip detectors provided and instead provide more two-dimensional information, pixel detectors were developed [16]. Where strip detectors contain a row of strips that are read out at one side of the chip (see figure 2.1a), pixel detectors contain of a grid of pixels that are individually read out (see figure 2.1b). The VELO upgrade is based on a silicon pixel detector (see section 2.4) [5].

(A) Layout of strips. (B) Layout of pixels.

FIGURE2.1: Layout of strips and pixels in strip- and pixel detectors. The strips and pixels are shown in grey.

(16)

4 Chapter 2. Detection of charged particles

2.2 Electronic band structure

When atoms are placed into an infinite crystal lattice, the behaviour they show can be used to describe their electrical properties. Electrons in atoms can have different discrete energies, and can be thought of as occupying different bands around the nucleus, determined by their energy. The band of energies containing the highest energy that is still tightly bound to the nucleus, is the valence band. The band that is one energy step higher than the valence band is the conduction band. The conduc-tion bands of neighbouring atoms overlap, which allows electrons to travel between atoms.

Using band structure, materials can be divided into three different categories: con-ductors, in which the conduction band and the valence band overlap; insulators, in which the gap between the bands is very large; and semiconductors, which have a small gap between the two bands (see figure 2.2). This means that electrons in metals can travel between the conduction and valence bands easily. The energy gap in insulators is a lot larger than the energy that thermally excited electrons can ac-quire. In contrast the energy gap between the valence band and the conduction band in semiconductors is such that it can be crossed by thermally excited electrons and thus there will be electrons in the valence band as well as thermally excited electrons in the conduction band.

FIGURE2.2: Band diagrams of an insulator (characterised by a large band gap), conductor (overlapping bands) and semiconductor (small

band gap).

2.3 Silicon as a semiconductor

2.3.1 Doping

Silicon is a semiconductor and thus always contains a certain amount of thermally-excited electrons in the conduction band. There is a considerable concentration of these free carriers, meaning that any signal generated by an ionizing particle will be indistinguishable from the background [15]. The doping of silicon is the first step towards reducing the concentrations of free carriers. Silicon is doped by replacing a portion of silicon atoms in the crystal structure with a dopant, in the case of silicon this is an atom from group III (such as boron) or V (such as phosphorus). If silicon is doped with an element from group III, the dopant will add an extra energy level just above the valence band. The dopant in this case has one less valence electron

(17)

2.3. Silicon as a semiconductor 5

and thermally excited electrons can usually travel to the newly introduced energy level, which will introduce an extra hole in the valence band of silicon (see figure 2.3). This type of silicon is p-doped and acts as an acceptor. To create an n-doped material, silicon is doped with an element from group V. This will add an energy level just under the conduction band. These atoms have one more valence electron, which can usually travel to the conduction band of silicon and creates an excess of electrons (see figure 2.3). This material therefore acts as an electron donor.

FIGURE2.3: Band diagrams of not-doped, n-doped and p-doped

sil-icon. In the n-doped silicon the dopant has added an energy level just below the conduction band and donated electrons into the con-duction band. In the p-doped silicon the dopant has added an extra energy level just above the valence band into which electrons from the valence band can travel, creating an excess of holes in the valence

band.

2.3.2 PN-junctions and depletion

Silicon detectors make use of the two types of doped silicon to create PN-junctions. A piece of p-doped silicon is placed against a piece of n-doped silicon. This results in the electrons in the n-doped region and the holes in the p-doped region combining, which leaves the region around the junction/boundary between the p- and n-doped parts without free carriers and with an electric field. The region without free charge carriers is now considered to be depleted.

This built-in depletion region does not cover the entire sensor. The depletion region can be extended or narrowed by applying an external electric field (bias voltage) to the sensor. In a forward biasing scheme a negative charge is applied to the n-doped side and a positive charge to the p-doped side. This will work against the built-in depletion and allow free carriers to flow in a larger section of the sensor, eventually resulting in large currents over the detector. In a reverse biasing scheme, a nega-tive voltage is applied to the p-doped side and a posinega-tive voltage is applied to the n-doped side. The applied electric field will be in the same direction as the internal electric field, leading to a widening of the depleted region. When the entire region of the sensor is depleted, there will only be some thermally generated free charge carriers in the sensor, generating a current that is referred to as the leakage current. The leakage current is proportional to the depleted volume. Equation 2.1 shows the width of depletion (xd) for a sensor with internal bias Vbi, applied bias V, permit-tivity of the material (in this case silicon) e, and dopant concentrations Na and Nd,

(18)

where the voltage is positive for reverse bias and negative for forward bias [15].

x2_d = 2e(Vbi+V) q 1 Na + 1 Nd (2.1) From equation 2.1 a plot of the depletion depth can be constructed. Figure 2.4 shows the depletion depth for a silicon sensor with dopant concentrations of 10−14 cm−3 and 5.5∗10−12cm−3for holes and electrons respectively. These dopant concentra-tions are not the ones of the device under testing (DUT), since those concentraconcentra-tions are not known. They were chosen, because they generate a result where the depth of depletion is 50 µm at 10V, which is comparable to the depletion voltage of the DUT (see section 3.2).

FIGURE 2.4: Depth of depletion in the sensor, assuming

(19)

2.3. Silicon as a semiconductor 7

Figure 2.5 shows the electric field for a sensor with the same doping concentrations for three different applied biases. The maximum of the electric field occurs at the boundary between the p-doped and the n-doped material, after which it linearly declines to the the edge of the depleted area, where the electric field is zero.

FIGURE 2.5: Electric field inside a silicon sensor with Na = 10−14 cm−3and Nd = 5.5∗10−12cm−3 for 50 µm thickness

(20)

2.4 Hybrid pixel detectors

A popular category of particle detectors is the category of hybrid pixel detectors, in which the chip is separated into different pixels. These pixels are individually read out by an ASIC that is separate from the sensor. Small drops of conducting metal that are placed on all individual pixels connect the sensor material to the readout chip (bump-bonding). The pixels are not physically separated. Instead every pixel has a separate dopant implant in a much larger bulk. Figure 2.6 shows a cross section of one such pixel. When free charge carriers are in the depletion zone, the electric field will cause them to drift in opposite directions. Depending on the the way the bulk and implant are doped, the signal will be formed from either electrons or holes that are collected through the bump. This report concerns a detector with n-doped implants placed in p-doped bulk material.

FIGURE2.6: Cross-section of a silicon hybrid pixel detector, showing

a partially depleted sensor that has been bump-bonded to a readout chip. Figure taken from Rossi et al. [15]

(21)

2.5. Interaction of ionising particles with matter 9

2.5 Interaction of ionising particles with matter

For a charged particle in the energy range 0.1< βγ<104the mean energy loss as it

moves through matter can approximately be described by the Bethe-Bloch formula [4]. A part of the mean energy loss originates from very rare high energy interac-tions. Since there is a lower number of interactions in thin materials, these collisions skew the mean energy loss towards a higher energy than is experimentally mea-sured [4]. The energy loss distribution for thin sensors is approximately given by a Landau distribution convoluted with a Gaussian distribution [4]. Figure 2.7 shows an example of a Landau distribution. In thin materials the rare high energy collisions cause the mean to shift towards the tail of the Landau-Gaussian distribution, so in-stead of using the mean it is more effective to use the Most Probable Value (MPV) of the energy loss distribution [4].

FIGURE2.7: Generic Landau distribution.

One phenomenon that contributes to the background in a detector is the occurence of delta-rays or δ-electrons, electrons that have acquired so much energy in the ioni-sation process that they can ionise particles themselves [4]. These ionising particles will travel in a different direction from the main source of ionising particles and will therefore spend more time in the detector and deposit more energy than particles originating from the beam.

(22)

2.5.1 Lateral diffusion

As an ionizing particle travels through the detector it will create electron-hole pairs along its path. Under the influence of the electric field these electrons will travel to one side of the detector. However, they will also diffuse from areas with higher concentrations to areas with lower concentrations, which will result in a cone of charge. This cone does not always hit just one pixel; an amount of charge sharing between pixels is a common occurrence. The relation between the sharing of charge and the position between the pixels is often approximated to be linear, while it is in fact more complicated, leading to an error on the position. Without taking charge sharing into account, the error for the lateral charge drift is described for a front-depleted detector by equation 2.2 with d0defined in equation 2.3, kbthe Boltzmann constant, ρ the resistance of silicon, µ_bthe mobility of the bulk material, N the dopant concentration, d the thickness of the material, z the depth in the material and Vdep the depletion voltage [10]. Figure 2.8 shows the diffusion parameter for 15V, 20V, 50V and 90V for a 50 µm thick sensor.

σdiffusion= s 2kbT q eρµbln d+d0 d+d0−z (2.2) d0 = e(V−V_dep) qNd (2.3)

FIGURE 2.8: Diffusion parameter for 20V (red), 30V (green), 60V (blue) and 90V (black).

(23)

2.6. Timepix3 11

2.6 Timepix3

The readout of the signal from the detector is performed by the Timepix3 Appli-cation Specific Integrated Circuit (ASIC), connected to a SPIDR readout system [17]. The Timepix3 chip contains 256x256 channels with a 55 µm squared pixel width [13]. Figure 2.9 shows the internal pixel logic of a Timepix3 pixel for both the analogue and the digital parts. A 4-bit adjustment is applied to the energy threshold (see sec-tion 3.1), in such a way that all pixels provide the same informasec-tion for the charge deposited in a pixel. The analogue part also includes a tuneable discharge current Ikrum[13].

FIGURE 2.9: Pixel logic in Timepix3. Shows the analogue and the digital sections. Figure taken from Hynds [10].

A signal is constantly transmitted to the Timepix3 chip, but it is only registered when it crosses the threshold for current, this moment in time is registered as the Time of Arrival (ToA) (see figure 2.10). This starts a clock that counts until the signal drops below the threshold value, the measured time is registered as the Time over Thresh-old (ToT) (see figure 2.10). The ToT is a measurement of charge, because the amount of time a pixel spends above the threshold for current is proportional to the amount of charge that has been deposited in that pixel. The Timepix3 can measure the ToA and ToT simultaneously, which means it can provide both timing information (ToA) and information on the charge that was deposited in the detector (ToT) [13].

(24)

FIGURE 2.10: Signal pulse showing the Time of Arrival (ToA) and Time over Threshold (ToT).

(25)

13

Chapter 3

Methods

3.1 Equalisation

The first step required to operate the Timepix3 chip is the equalisation. The chip has a global energy threshold (THL) for the number of electrons required to reg-ister a hit. Due to engineering tolerances in the manufacturing process, interpixel variations arise. These variations include transistor size and doping concentration, both resulting in interpixel gain and noise baseline variation. Part of the method to compensate for this is an adjustment of the threshold using 4 bits, where the scale goes from no correction (0000), to the maximal correction (1111). In the process of equalising the chip, the optimal adjustment bit per pixel is determined. Equalisation consists of three threshold scans of noise. The first scan is taken without any ad-justment (mask (0000)), the second one has the maximum correction (mask (1111)). From the first two scans, the average value per scan that the pixels fire at is deter-mined. For the third scan, the optimum adjustment value per pixel is calculated so that the pixels fire as close as possible to the the average of the scans (see figure 3.1). Higher accuracy can be achieved with more adjustment bits, however this is fixed during the design of the chip given the requirements and space available.

When looking at the number of hits over the chip some pixels show a dispropor-tional amount of hits. These are referred to as hot pixels and are masked, meaning their data is not taken into account in the analysis of the data. Figure 3.2 shows a map of the masked pixels for the device under study.

(26)

14 Chapter 3. Methods

FIGURE3.1: Plot of the equalisation of the chip, showing the number of pixels that fire for a given THL. The scan with mask (0000) is shown on the left in blue, the scan with mask (1111) is visible on the right in red and the scan after equalisation is shown in the middle in black.

FIGURE3.2: Map of the hot pixels that were masked during the tak-ing of data at CERN testbeam.

(27)

3.2. Laboratory measurements 15

3.2 Laboratory measurements

After the detector has been equalised, the next step in the operation of a pixel de-tector is determining the depletion voltage of the dede-tector. Figure 3.3 shows the current for different operation voltages of the detector. The DUT has negative po-larity, which means a negative voltage needs to be applied to the sensor backside to deplete the sensor. Since the leakage current is proportional to the depleted vol-ume, the leakage current will increase until the entire sensor volume is depleted, after which the leakage current stabilizes (see section 2.3.2). This continues until the created electron-hole pairs have such energies that they themselves create new electron-hole pairs, which ultimately leads to avalanche breakdown [4]. In this fig-ure the breakdown and the depletion voltages are easily recognizable, with the de-pletion voltage occurring around -10V and the breakdown voltage occurring after -160V.

(28)

In section 2.5 it was stated that the energy loss distribution of charged particles in silicon can be described by a Landau distribution (as seen in figure 2.7), convoluted with a Gaussian distribution. As a part of the detector characterisation a ToT mea-surement was performed with a90_{Sr source, while the detector was being operated} at -20V. Figure 3.4 shows the result of the ToT measurement, on which a Landau-Gaussian distribution can be fitted.

FIGURE3.4: Time over the threshold for charge at -20V with a90Sr source.

(29)

3.3. Data collection at the testbeam 17

3.3 Data collection at the testbeam

In order to be able to determine the tracking performance of the chip, the circum-stances during testing should be the same as the circumcircum-stances under which the chip will be used in future applications. This means that high energy circumstances and additional planes for track reconstruction are needed. After the first determina-tions of depletion voltage, the time over threshold behaviour and the equalisation process the detector was taken to the beam facilities in the SPS North Area at CERN. The beam consists mostly of positively charged pions, containing a few protons and kaons. The testbeam coming from the SPS usually has about two spills every 30 seconds, where a typical spill lasts ~10 seconds and contains ~1-2 million particles. A Timepix3 telescope has been placed in the beam. A DUT can be placed in the center of the telescope on a stage that can be moved rotationally and translation-ally. On both the upstream and the downstream sides of the DUT four Timepix3 planes are placed on an arm, angled to 9◦ in the vertical and horizontal directions. The Timepix3 planes have 300 µm thick sensors. Additional timing information and possibilities to use triggers on the DUT are provided by two scintillators placed at either end of the telescope. Figure 3.5 shows the layout of the older Timepix tele-scope, the Timepix3 telescope looks the same, except that the Timing Plane has been removed and the Timepix planes have been replaced by Timepix3 planes.

FIGURE3.5: Image of the Timepix telescope. The Timepix3 telescope looks mostly the same, but the Timepix planes are now Timepix3 planes and there is no separate Timing Plane. The Timepix3 telescope has four planes upstream of the Device Under Test (DUT) and four planes downstream of the DUT, as well as the two scintillators on either end of the telescope. The DUT is placed on a movable stage.

(30)

After the DUT is placed in the telescope as shown in figure 3.5, the DUT is aligned by eye to be perpendicular to the beam. After this a small angle scan is performed to get the real zero, where the DUT is perpendicular to the beam. For the small angle scan the bias voltage of the DUT is set to -90V, while the THL is set to 1000 electrons and data is taken for one spill. The mean cluster size is determined for a few angles between−13◦ and 13◦. If the DUT is perpendicular to the beam, the cluster size is at its minimum, because there would be no lateral distance through the sensor. A shifted parabola fit was applied to the data points from the small angle scan (see fig-ure 3.6). It was determined from the fit that the minimum mean cluster size would occur at−1.4◦. From now on 0◦ refers to the real zero angle.

FIGURE3.6: Small angle scan through which a shifted parabola has been fitted, showing that the minimum cluster size and the angle that

puts the detector perpendicular to the beam occur at−1.4◦.

For the analysis that will be discussed in this report a data set was taken with the THL set to 700 electrons and for every measurement data was taken for 5 spills. A 2D scan was performed with bias voltages of -15V, -30V, -60V and -90V and all angles from 0◦to 80◦in steps of 5◦.

(31)

3.4. Method of data analysis 19

3.4 Method of data analysis

To analyse the data, the Kepler framework for offline analysis of Timepix3 test beam data was used [2]. This framework considers the data in separate algorithms (see figure 3.7). It first looks at the individual hits on the detector, after which it com-bines these hits into clusters. The clustering is performed by starting with a seed pixel and adding hits that occur within a certain time window on the same plane and are next to the seed pixel or other hits already added to the cluster.

In order to be able to know if a cluster on the DUT is a noise hit or caused by an ionising particle from the beam, the tracks through the telescope are reconstructed with the tracking algorithm. The track reconstruction is initialised by looking at a cluster on the first telescope plane, after which a cluster is sought on the next tele-scope plane, that occurs within a certain temporal and spatial window. Clusters that contain too many pixels are skipped, because it is likely, that they have been caused by delta-rays. Clusters with a time over threshold that is considered too low are also not considered in the track reconstruction. Clusters caused by ionising parti-cles from the beam, would have deposited more energy in the sensor and would therefore have a larger ToT. After the clusters are grouped together and form sets of potential tracks, a straight line is fitted through the potential tracks that have clus-ters on all telescope planes. As a final cut in the track reconstruction the tracks with a χ2that is considered too large are cut to improve the resolution.

As mentioned in section 3.3, the telescope and the DUT are aligned by eye, but a soft-ware alignment is also performed. The alignment algorithm uses the tracks from the tracking algorithm and starts by setting one plane as a reference and subsequently slightly moving the other planes, fitting a straight line again and looking for combi-nation of alignment values that result in the tracks with the smallest χ2_{. This process} is repeated until sufficient alignment is reached. Figure 3.7 represents the software analysis process.

(32)

FIGURE3.7: Flowchart showing the software analysis process using Kepler.

(33)

21

Chapter 4

Analysis of testbeam data

4.1 Hitmaps

After analysis of the data from testbeam, the most basic information available after the data taking are the hitmaps of pixel hits. These hitmaps display the number of hits on each pixel. Figure 4.1a shows the hitmap for 0◦ and -90V; the beamspot can be clearly seen here. As the detector is rotated around the y-axis, the lateral dis-tance of particles in the detector increases. For example, at 0◦ the lateral distance is 0 and only one pixel will be hit; while with a lateral distance of one pixel, the particle will always travel through two pixels and generate clusters containing two pixels. Figure 4.2 shows the relation between angle and lateral distance through the detector. Since the lateral distance increases as the angle increases, higher angles will lead to a longer lateral distance and longer clusters, which will make it look like the beamspot is spread out over the detector at higher angles. Figure 4.1b shows this for 80◦at -90V. Since the detector only rotates around the y-axis, the lateral distance only increases in one dimension. Since the lateral distance in the stationary dimen-sion stays the same, the height of the beamspot also stays the same.

4.2 Association of clusters

To determine which clusters were caused by charged particles from the beam, the clusters need to be associated to tracks through the telescope. In the track recon-struction as described in section 3.4 a few cuts were applied to the data. Telescope

(A) Hitmap at 0◦ (B) Hitmap at 80◦ FIGURE4.1: Hitmap showing the number of hits on each pixel for a

(34)

22 Chapter 4. Analysis of testbeam data

FIGURE4.2: Lateral distance

tracks need to have associated clusters on all planes of the telescope and these clus-ters can be no more than 10 ns apart from one plane to the next. In the association of clusters on the DUT to the telescope tracks, clusters containing more than 10 pixels, and clusters wider than three pixels were excluded from association. After the com-plete reconstruction, all tracks with a χ2over number of degrees of freedom greater than 10 were cut.

For angles higher than 55◦the alignment did not converge sufficiently to be able to say something about the resolution. This was partly due to time constraints, and the starting position that was provided (0◦ was used as a standard starting point). The result was a partial alignment where the certainty of the track intercepts was not as optimal as it could be, meaning that it is not possible to say something about the resolution that can be achieved at higher angles. However, the certainty that was achieved is still a fraction of the size of a pixel, so it is still possible to associate the clusters to tracks.

(35)

4.3. Cluster sizes 23

FIGURE4.3: Size of associated clusters at -90V and different angles: 0◦(black), 55◦(red) and 80◦(green).

4.3 Cluster sizes

As the particles traverse more of the detector, the size of the clusters produced in-creases. This can be seen in the cluster size distributions in figure 4.3. At 0◦ the lateral distance is zero and as can be seen in figure 4.3, most of the clusters contain a single pixel. At 55◦ the lateral distance has increased to more than one pixel and most of the clusters now contain two pixels. After this the lateral distance increases more quickly and at 55◦ the lateral distance has increased to about 5.5 pixels (see figure 4.2), the most common cluster size has now also increased to six pixels. At testbeam the chip was operated at four different voltages: -15V, -30V, -60V and -90V. From measurements in the laboratory the depletion voltage of the detector was determined to be about -10V (see section 3.2). Figure 4.4 shows the distributions of cluster sizes for these four different voltages at 0◦. The overall shape of the distri-butions is the same for each voltage with in all cases the most common cluster size being 1 pixel. However, the specific values -15V and -30V are different from each other and from the values at -60V and -90V. At -60V and -90V the distributions of cluster size overlap, which means that running the detector at -60V and -90V will give the same results. This is most likely a result of the shape of the charge cloud. Even though the detector is fully depleted at all of the applied voltages, the electric field (section 2.3.2) and diffusion parameter (see section 2.5.1) still change, which leads to a narrower charge cloud at the higher voltages.

Detectors in experiments are operated under a variety of different angles and parti-cles hitting the detector can have a variety of incident angles, this makes it important to understand the cluster size behaviour under different angles. A rotation around one axis should in principle only cause a change in one direction, since the lateral

(36)

FIGURE4.4: Size distributions of associated clusters at 0◦and differ-ent voltages: -15V (black), -30V (red), -60V (green) and -90V (blue).

The lines for -60V and -90V mostly overlap.

distance only changes in one direction (figure 4.2). Figure 4.5 shows the mean sizes, widths and lengths of the raw clusters and shows that the mean length of the clus-ters increases only slightly, while the cluster width is the main contributor to the increase in the size of the cluster. The overall shape of the cluster widths also looks to have the same shape as the plot for the lateral distance (figure 4.2).

The data so far has been mainly for clusters that have been associated with a track. There are differences between raw, non-associated and associated clusters in terms of size. Figure 4.6 shows the distributions of cluster sizes for raw, associated and non-associated clusters. At 0◦the fraction of clusters with size one is higher for asso-ciated clusters than for raw and non-assoasso-ciated clusters, while the fraction of clusters with size two is lower for associated clusters. This can be explained by looking at the lateral distance, which is zero at this angle, which means that most particles from the beam will create clusters containing a single pixel. In the cluster size distribution for 80◦ (figure 4.6b) relatively less of the associated clusters have sizes smaller than seven, while raw and non-associated clusters have relatively more of these smaller clusters. At 80◦ the lateral distance through the detector is about 5.2 pixels, which means that particles originating from the beam travel this distance through the de-tector in the x-direction, if the clusters create a signal in each pixel they go through, this would mean the cluster could have a size of 6 or 7 (depending on how close to the edge of the first pixel they hit). In the 80◦plot, there is also a significant amount of clusters with smaller sizes. These clusters were most likely formed by particles that travelled near masked pixels (figure 3.2) or the edges of the sensor. Overall the non-associated and associated cluster distributions follow a similar shape, this is caused by clusters that have not been associated with a track, but were in fact caused by particles from the beam.

(37)

FIGURE4.5: The mean sizes (red circles), widths (blue triangles) and lengths (green squares) of raw clusters as a function of angle at -90V.

Figure 4.7 shows the means of cluster size distributions for raw, associated and non-associated cluster sizes. For angles of 60◦and lower, the mean size of the associated clusters stays lower than the size of the raw and non-associated clusters. One pos-sible reason for this is the cut on the cluster size during the association process (see section 4.2), which means that clusters with a size larger than 10 will never be asso-ciated to a track. In addition the lateral distance of the particle through the detector is not yet very large at this point (1.6 pixels at 60◦), so the associated clusters will usually have a size of two or three, depending on where on the pixel they hit. For angles of 65◦and higher the size of the associated clusters increases, because the size of clusters caused by ionizing particles from the beam increases, while the fraction of very large clusters is caused by other effects such as delta rays (see section 2.5). As a result the size of non-associated and raw clusters is lower for these higher angles. The mean cluster size can also be deconstructed into the fractions of each cluster size, shown in figure 4.8. In this figure the fractions of associated clusters with sizes one, two, three and larger than three pixels are displayed. At 0◦the fraction of clus-ters with size one is about 0.9, while most of the other clusclus-ters have size two. As the angle increases, the lateral distance of a particle through the detector increases (see figure 4.2), which leads the fraction of clusters with size one to decrease and clusters with size two to increase until 55◦. At 55◦ the lateral distance has increased to more than one pixel, meaning that a particle will always pass through at least two pixels and also makes it possible for a particle to go through three pixels. After 55◦ the fraction of clusters with size one stays smaller than 0.05, and the fraction of clusters with size two starts to drop, until it also stays smaller than 0.05 from 70◦. At the same time the fraction of clusters with size three and size larger than three increases until 70◦, where the lateral distance has increased to three pixels. As expected from

(38)

(A) Cluster sizes for 0◦. (B) Cluster sizes for 80◦. FIGURE4.6: Size distributions of associated (green), raw (black) and

non-associated (red) clusters at -90V at 0◦and 80◦.

FIGURE4.7: Comparison of the mean sizes of raw (black triangle), associated (green circles) and non-associated (red squares) clusters for

(39)

FIGURE4.8: The fractions of associated clusters with sizes 1 (red cir-cle), 2 (green squares), 3 (blue triangle) and larger than 3 (inverted

pink triangle) at -90V.

the previous behaviour, the fraction of clusters with size 3 drops to a fraction smaller than 0.05 again and just the clusters larger than three keep increasing.

(40)

(A) X residuals at 0◦ (B) X residuals at 55◦ FIGURE4.9: Distributions of the distance of clusters to the track they

have been associated with (residuals) in the x direction at -90V.

Residuals and resolution

4.4 Residual distributions and resolution

After looking at clusters, the next step is to look at the spatial precision of the DUT. Each associated cluster has a distance to the track it has been associated with, which is called the residual distance. As mentioned in paragraph 4.2, the alignment for angles over 55◦ was not performed well enough to be able to look at the residuals or resolution for these angles. In the 0◦ case, the only information that is available is that a particle hit in a certain pixel. This particle is equally likely to hit at any dis-tance from the center, meaning that the expected shape of the residual distribution looks like a tophat. As the lateral distance of particles through the sensor increases and the particle passes through multiple pixels, charges is also deposited in multiple pixels. Since the amount of charge that is deposited in a pixel is dependent on the time that a particle has spent in that pixel, this allows for a more specific location of the track to be determined. The shape that is expected for these higher angles is narrower and looks more like a Gaussian. Figure 4.9a shows the residual distribu-tion for 0◦, which indeed looks like a tophat shape. The shapes at the sides are a consequence of the track resolution and represent two error functions. Figure 4.9b shows that the distribution does get narrower at higher angles.

For each of the residual distributions a Gaussian distribution can be fitted to get the standard deviation. This standard deviation gives a measure for the certainty of the position of the clusters and is the spatial resolution of the detector. Figure 4.10 shows the resolution at -15V, -30V, -60V and -90V as a function of the angle, where it can be seen that the resolution is slightly worse for -15V, but the resolutions follow the same shape, where it improves as the angle gets larger with the best resolution of about 5 µm at 50◦ and 55◦.

(41)

4.5. Charge deposition and track intercepts 29

FIGURE4.10: Resolution of the 50 µm silicon pixel detector at -15V (red circle), -30V (green square), -60V (blue triangle) and -90V (pink

inverted triangle).

4.5 Charge deposition and track intercepts

As particles go through the detector material, they deposit charge by generating electron-hole pairs along their path. As these electrons and holes drift to either end of the sensor material, lateral diffusion causes them to form cones of charge. When the angle increases, the ionizing particle has a longer path through the detector and through the pixel, which leads the particle to deposit more charge in the pixel and cluster. The time a pixel spends over the threshold for charge gives a measure for how much charge has been deposited by the ionizing particle. Figure 4.11a shows the time over threshold at 0◦ and -90V, where the peak for the ToT is at around 50. For 55◦ (figure 4.11b) the peak has moved to about 250 and the distribution has broadened.

(42)

(A) Time over threshold at 0◦ (B) Time over threshold at 80◦ FIGURE4.11: Time over threshold of associated clusters at -90V.

The conical shape of charge deposition can lead to charge sharing between multiple pixels, which means that the location where a track goes through a pixel (track in-tercept) influences the cluster size. When a particle passes near the edge of a pixel for example, the cone of charge can extend to the neighbouring pixel and lead that pixel to also register a signal. When the same thing happens in a corner, this can even mean that the cone of charge extends to two or three other pixels, generating even larger clusters. The size of a cluster therefore depends on the track intercept. Clusters containing only one pixel, are mostly fordmed by particles that go through the middle of the pixel (see figure 4.12a), while relatively less clusters of this size are formed on the edges and in the corners. For clusters with two pixels, figure 4.12b shows that most of these clusters were formed along the edges of pixels. Figures 4.12c and 4.12d visualize the track intercepts for clusters containing three and four pixels respectively, for both of which the track intercepts mainly occur in the four corners of the pixels.

Plots 4.12a and 4.12b show that there is an effect where the left and the right side look different from the top and bottom, while you would expect them to look the same. This might be caused by a column effect or a light rotation along the y-axis.

(43)

4.5. Charge deposition and track intercepts 31

(A) Track intercept for clusters with one pixel

(B) Track intercept for clusters with two pixel

(C) Track intercept for clusters with three pixel

(D) Track intercept for clusters with four pixel

FIGURE 4.12: Intrapixel track intercepts for cluster sizes one, two, three and four at 0◦and -90V.

(44)

(45)

33

Chapter 5

Discussion and Conclusion

A 50 µm placed on a Timepix3 chip was succesfully characterised in terms of its clus-ter sizes, spatial residuals and resolutions.

Overall the cluster sizes as displayed in figure 4.5 agree with the cluster sizes that were predicted by the lateral distance as seen in figure 4.2. When the detector is rotated around one axis, only the width of the clusters increases, while the length of the cluster stays similar over all angles. However, the distribution of cluster sizes for higher angles (such as 80◦, see figure 4.6b) shows behaviour that deviates from the cluster sizes predicted by the lateral distance. A fraction of the associated clus-ters have a smaller cluster size than expected. There are multiple possible causes for these smaller clusters, they may have been caused by beam particles that hit near edges and/or masked pixels (see figure 3.2 for a map of masked pixels). These loca-tions of hits would have led to clusters that are smaller than they would otherwise have been. Other possible causes are that the clusters may have other sources than beam particles and they could also have been caused by either noise or noisy pix-els. Additionally figure 4.11b shows that even though the general trend of the ToT moves towards larger values, a smaller fraction of the values stays smaller. Clusters that are caused by particles from the beam typically have a larger ToT, because these particles are more energetic and deposit more energy in the silicon. So by looking at the sizes of the clusters that have a smaller ToT the cause for the clusters with smaller sizes could be determined.

Figure 4.12 shows where on a pixel tracks intercept it. However, there seems to be an effect where tracks that generate clusters with sizes one (figure 4.12a) and two (figure 4.12b) have less intercepts along the vertical edges than along the horizontal edges. This suggests that there might be a column effect or a slight misalignment and requires further research.

The Timepix3 detector in this configuration with a 50 µm thick silicon sensor can reach a spatial resolution of about 5 µm at angles of 50◦and 55◦. Figure 4.10 shows that for the measured voltages of -15V, -30V, -60V and -90V there is little difference in terms of resolution between the different voltages, except that -15V deviates slightly. This slight increase is consistent with the depletion voltage of -10V, as determined in section 3.2. Moreover, the lateral diffusion in thin sensors is limited, because of there is limited drift. This means that the voltage will not influence the cluster sizes a lot. The research that has been done in this report indicates that a timepix3 based thin silicon detector is a good starting point for further research into detectors for fu-ture VELO upgrades. Further research into the temporal resolution needs to be per-formed, bu considering the thinness of the sensor, this is expected to yield good

(46)

34 Chapter 5. Discussion and Conclusion

(47)

35

Bibliography

[1] http://cern.ch.

[2] https://lbtwiki.cern.ch/bin/view/VELO/Tpx3TestbeamSoftware.

[3] Kazuyoshi Akiba et al. “The Timepix telescope for high performance particle tracking”. In: Nuclear Instruments and Methods in Physics Research Section A: Ac-celerators, Spectrometers, Detectors and Associated Equipment 723 (2013), pp. 47– 54.

[4] M. Tanabashi et al. “Review of Particle Physics”. In: Phys. Rev. D 98 (3 Aug. 2018), p. 030001. DOI: 10.1103/PhysRevD.98.030001. URL: https://link. aps.org/doi/10.1103/PhysRevD.98.030001.

[5] LHCb Collaboration. LHCb VELO Upgrade Technical Design Report. Tech. rep. CERN-LHCC-2013-021. LHCB-TDR-013. Nov. 2013.URL: http://cds.cern. ch/record/1624070.

[6] LHCb Collaboration. LHCb VELO (VErtex LOcator): Technical Design Report. Technical Design Report LHCb. Geneva: CERN, 2001.URL: http://cds.cern. ch/record/504321.

[7] LHCb Collaboration et al. LHCb: Technical Proposal. CERN, Geneva, 1998. Tech. rep. CERN-LHCC-98-004.

[8] LHCb Collaboration et al. “The LHCb detector at the LHC”. In: Journal of in-strumentation 3.08 (2008), S08005.

[9] Erik HM Heijne et al. “A silicon surface barrier microstrip detector designed for high energy physics”. In: Nuclear Instruments and Methods 178.2-3 (1980), pp. 331–343.

[10] Daniel Peter McFarlane Hynds. “Resolution studies and performance evalua-tion of the LHCb VELO upgrade”. PhD thesis. Glasgow U., 2015.

[11] Esma Mobs. “The CERN accelerator complex - August 2018. Complexe des ac-célérateurs du CERN - Août 2018”. In: (Aug. 2018). General Photo.URL: https: //cds.cern.ch/record/2636343.

[12] G. L. Pearson and W. H. Brattain. “History of Semiconductor Research”. In: Proceedings of the IRE 43.12 (Dec. 1955), pp. 1794–1806. ISSN: 0096-8390.DOI: 10.1109/JRPROC.1955.278042.

[13] T Poikela et al. “Timepix3: a 65K channel hybrid pixel readout chip with si-multaneous ToA/ToT and sparse readout”. In: Journal of instrumentation 9.05 (2014), p. C05013.

[14] L Rossi and O Brüning. High Luminosity Large Hadron Collider: A description for the European Strategy Preparatory Group. Tech. rep. CERN-ATS-2012-236. Geneva: CERN, Aug. 2012.URL: http://cds.cern.ch/record/1471000.

[15] Leonardo Rossi et al. Pixel detectors: From fundamentals to applications. Springer Science & Business Media, 2006.

(48)

36 BIBLIOGRAPHY

[16] M Turala. “Silicon tracking detectors—historical overview”. In: Nuclear Instru-ments and Methods in Physics Research Section A: Accelerators, Spectrometers, De-tectors and Associated Equipment 541.1-2 (2005), pp. 1–14. URL: https://doi. org/10.1016/j.nima.2005.01.032.

[17] J Visser et al. “SPIDR: a read-out system for Medipix3 & Timepix3”. In: Journal of Instrumentation 10.12 (2015), p. C12028.

(49)

37

Acknowledgements

Finally, at the end of my thesis, I would like to thank all of the people who helped me during my time at Nikhef. First of all of course my supervisor Daniel Hynds and the rest of the fast timing group: Martin van Beuzekom, Hella Snoek and Kazu Akiba, as well as the master students Robbert and Peter. Thanks to PhD student Kevin for providing me with the quote I used in the beginning of my thesis. Thanks as well to Navrit Bal.

At the request of my friend Floor, I will dedicate this entire paragraph to her and my brother Sebastiaan to thank them for proofreading and nitpicking my popular Dutch summary.

I would also like to thank everyone in the LHCb hallway, and especially Elena Dall’Occo for helping me during my first week at Nikhef. And lastly, thanks to Daniel (yes, he deserves the double thank you), Wouter and Marcel for being my supervisors and examiner.

Testbeam investigations of a 50μm silicon pixel detector

R

B

P

P

A

Spatial resolution and cluster sizes in a

50 µm silicon pixel detector

Abstract

Populaire Nederlandse Samenvatting

Contents

List of Figures

"I don’t know how to express happiness anymore."

-Second year PhD student

Chapter 1

Introduction

1.1

CERN

1.2

The LHCb experiment

1.3

LHCb Upgrade

Chapter 2

Detection of charged particles

2.1

Use of silicon in particle detection

2.2

Electronic band structure

2.3

Silicon as a semiconductor

2.4

Hybrid pixel detectors

2.5

Interaction of ionising particles with matter

2.6

Timepix3

Chapter 3

Methods

3.1

Equalisation

3.2

Laboratory measurements

3.3

Data collection at the testbeam

3.4

Method of data analysis

Chapter 4

Analysis of testbeam data

4.1

Hitmaps

4.2

Association of clusters

4.3

Cluster sizes

4.4

Residual distributions and resolution

4.5

Charge deposition and track intercepts

Chapter 5

Discussion and Conclusion

Bibliography

Acknowledgements