Master Thesis
Going Three Dimensional
Characterisation of a 3D sensor on a Timepix3 ASIC
by
Peter Bosch
10741968
August 2019
60EC
20/08/2018 - 23/08/2019
Supervisor/Examiner:
dr. Niels van Bakel
Daily supervisor:
dr. Martin van Beuzekom
Examiner:
Prof. dr. Auke-Pieter Colijn
Nikhef National Institute for Subatomic Physics
Detector R&D department
line in the North Area of the SPS particle accelerator at CERN. A mixed hadron beam with mainly positively charged pions with an energy of 180 GeV was used in this study. With a telescope consisting 8 planar Timepix3 sensors, tracks can be reconstructed which gives the precise location where the particles went through the device under test. The di-mensions of the pillars in the 3D sensors are determined using two different methods. The pillar diameter is measured to be 18±3 µm and the pillar height 215+2
−6 µm. Also the
response time as function of position in the pixels and the dependence on the beam an-gle have been investigated for the 3D sensor, and are compared to a planar silicon sensor.
Abstract ii
Samenvatting vii
Summary viii
1 Introduction 1
2 Theory 3
2.1 Particles and their properties . . . 3
2.2 Semiconductor physics . . . 4 2.3 Pixel detectors . . . 7 3 Experimental setup 14 3.1 Sensors . . . 14 3.2 Lab measurements . . . 16 3.3 Testbeam measurements . . . 19 4 Track reconstruction 22 4.1 Decoding software: Kepler . . . 22
4.2 Clustering . . . 23
4.3 Spatial alignment of the telescope and DuT . . . 25
4.4 Track reconstruction . . . 27
4.5 DuT cluster association . . . 28
5 Data analysis 31 5.1 Pillar dimensions . . . 31 5.2 Timing of 3D sensor . . . 37 5.3 Cluster size . . . 39 5.4 Spatial resolution . . . 41 6 Conclusion 44
Appendix A Supplementary figures 46
Appendix B Error analysis 51
Bibliography 56
1.1 CERN accelerator complex . . . 2
2.1 Particles of the Standard Model . . . 4
2.2 Landau distribution . . . 5
2.3 Energy levels of crystal lattices . . . 6
2.4 Band structure of sodium . . . 6
2.5 Energy bands for several kinds of materials . . . 7
2.6 Doping . . . 8
2.7 Schematic view of a pixel in a pixel detector . . . 9
2.8 Simplified Timepix3 logic . . . 11
2.9 Electronic signals after hit . . . 13
3.1 Schematic layout of sensors . . . 15
3.2 Detailed view of Timepix3 sensor . . . 16
3.3 Determining depletion voltage . . . 17
3.4 Equalisation . . . 18
3.5 Example of surrogate function . . . 19
3.6 Photographs of the testbeam setup . . . 19
3.7 Testbeam set-up . . . 20
4.1 Hitmaps . . . 23
4.2 Clustering . . . 24
4.3 Cluster charge distribution of a telescope plane . . . 24
4.4 Cluster sizes of a telescope plane and a DuT . . . 25
4.5 Residuals of a telescope plane as function of position . . . 26
4.6 Alignment of the setup . . . 26
4.7 Two possibilities for the alignment of DuTs . . . 28
4.8 DuT cluster associating . . . 29
4.9 Residuals of a DuT . . . 29
4.10 Residuals of a DuT as function of position . . . 30
5.1 Charge distribution in particular region of pixels . . . 32
5.2 Intra-pixel charge map . . . 33
5.4 Grazing angle track . . . 34
5.5 Expected charge deposited for 3D sensor under grazing angles . . . 35
5.6 Charge deposition for grazing angles . . . 36
5.7 Determining height of field pillar using grazing angle tracks . . . 37 iv
5.11 Location of clusters with particular sizes in an overlaid pixel . . . 41 5.12 Intra-pixel location size-2 clusters under angles . . . 42 5.13 Spatial resolution as function of angle . . . 43
ALICE A Large Ion Collider Experiment ATLAS A Toroidal LHC ApparatuS
ASIC Application-Specific Integrated Circuit
CERN Conseil Européen pour la Recherche Nucléaire CMS Compact Muon Solenoid
CP Charge Parity DoF Degree of Freedom DuT Device under Test HEP High Energy Physics
HL-LHC High Luminosity Large Hadron Collider LHC Large Hadron Collider
LHCb Large Hadron Collider beauty LINAC LINear ACcelerator
MIP Minimum Ionising Particle MPV Most Probable Value
PS Proton Synchrotron SM Standard Model
SPIDR Speedy PIxel Detector Readout SPS Super Proton Synchrotron ToA Time of Arrival
ToT Time over Threshold VELO VErtex LOcator
D
e Large Hadron Collider (LHC) deeltjesversneller van CERN in Genève is ge-bouwd met als doel het doen van onderzoek aan subatomaire deeltjes. Hiervoor worden vier grote detectoren gebruikt: ALICE, ATLAS, CMS en LHCb. Op dit mo-ment wordt LHCb geüpgraded zodat er nog meer deeltjes versneld kunnen worden. Do-ordat er meer deeltjes versneld worden, vinden er ook meer botsingen plaats. Daardoor moeten de detectoren sneller de metingen doen om alle botsingen te kunnen zien. Om dit te kunnen, moeten alle componenten van de detectoren herontwikkeld worden. Voor-dat deze nieuwe componenten gebruikt kunnen worden, moeten ze eerst getest worden. Voor het karakteriseren van de silicium pixel sensoren van de Vertex Locator (VELO) van LHCb, wordt onder andere gebruik gemaakt van pixel detectoren met een Timepix3 uitleeschip.In dit onderzoek is een bepaald type sensor, een 3D sensor, gekarakteriseerd. Een 3D sensor is een plaat silicium met daarin pilaren die als uitleeselectrode dienen. Daardoor heeft dit type sensor meerdere voordelen ten opzichte van de reguliere sensoren die geen pilaren hebben. Zowel deze speciale sensor als reguliere sensoren zijn onderzocht met de SPS-deeltjesversneller van CERN.
Met de data genomen met de SPS zijn de afmetingen van de pilaren in de 3D sensor gemeten. De diameter is zoals verwacht, maar de gemeten hoogte van de pilaren is kleiner dan de ontworpen hoogte. Dit is op twee onafhankelijke manieren vastgesteld. Naast het onderzoek aan de pilaren, is ook de resolutie van de tijdsmeting van de 3D sensor en de hoekafhankelijkheid van zowel de 3D als van gewone sensoren onderzocht.
T
he Large Hadron Collider (LHC) particle accelerator made by CERN in Geneva is built to do research on subatomic particles. To do so, four large experiments are used: ALICE, ATLAS, CMS and LHCb. At this moment LHCb is being upgraded to be able to more particles. Therefore, the rate of collisions is higher and the detectors have to measure more quickly to be able to see all collisions. To do so, all components of the detectors should be redeveloped. Before these new components can be used in the experiments every component should be tested. To characterise the silicon pixel sensors of the Vertex Locator (VELO) of LHCb, pixel detectors with Timepix3 readout chips are used.In this research a 3D sensor is characterised. A 3D sensor distinguishes from regular, planar sensors by having insensitive readout pillars in the bulk of silicon. Therefore, the 3D sensor has multiple advantages over regular sensors. Both this special sensor as well as planar sensors are tested using the SPS particle accelerator of CERN.
With the data taken at the SPS the dimensions of the pillars in the 3D sensor are de-termined. The diameter is as expected, but the height is not. The pillars were smaller than the designed height. This is found using two independent studies. Besides the study of the pillar dimensions also the resolution of the time measurement of the 3D sensor and the dependence of the 3D sensor and planar sensors on the angle with the incoming beam is investigated.
1
Introduction
I
n 1954 the European Organisation for Nuclear Physics (CERN) was founded. Since then many big scientific breakthroughs were achieved at CERN: the discovery of the W±andZ0bosons [1, 2], the first observation of direct CP-violation [3], the discovery of the Higgs
boson [4, 5] and many more. For these discoveries particle accelerators were used in which accelerated particles collide into each other and create new particles. The currently largest and most powerful accelerator is the Large Hadron Collider (LHC) [6], which collides protons onto protons.
Before being injected into the LHC, the protons are accelerated in older accelerators up to an energy of 450 GeV (see Figure 1.1). Then two beams of particles are accelerated by the LHC up to 6.5 TeV (so in total 13 TeV). At four points along the LHC ring the particle beams are brought into collision. At each point experiments are being done with the ALICE, ATLAS, CMS and LHCb detectors.
To be able to measure potentially new physics the LHC and its experiments are continu-ously improving. Currently the LHC is in a long shutdown to improve both the LHC itself and the experiments (mainly LHCb and ALICE). For the upgrade of an experiment new de-tectors need to be developed, which must be characterised before they can be applied in large numbers in the experiments. Among others, also the Vertex Locator (VELO) prototype sen-sors of LHCb have been tested with charged particle beams. To test the semiconductor pixel detectors a so-called beam telescope, consisting of eight Timepix3 detectors, is used. This telescope needs to be state of the art to match the requirements of the VELO. For future up-grades of LHCb, sensors that can register the time of arrival of a particle with a much higher
Figure 1.1:Overview of the CERN accelerator complex. Protons are first accelerated by a linear accel-erator (LINAC 2). Then the protons are accelerated by respec vely the Booster, the PS and the SPS. The SPS injects the protons in the LHC where the protons are accelerated to their peak energy of 6.5 TeV. Figure from [7].
accuracy must be developed. One of the candidate sensors is a so-called 3D sensor where the read-out electrodes are pillars penetrating the bulk of silicon. In this thesis, this different kind of Timepix3 sensor is characterised and tested in a mixed hadron beam of the SPS particle accelerator.
Sir Ernest Rutherford
2
Theory
T
he theoretical background for this thesis is covered in this chapter. Section 2.1 intro-duces the properties of particles and their passage through matter. In Section 2.2 the physics behind semiconductors used in pixel detectors is explained. The last section of this chapter, Section 2.3, is about pixel detectors in general and about the pixel detectors used in this research specifically.2.1 Particles and their properties
The current day best theory which is consistent with measurements of particles and forces is the Standard Model (SM) [8]. In the SM 12 matter particles (fermions), 5 force carriers (bosons), and their antiparticles are known (see Figure 2.1). Combinations of quarks form bigger particles such as protons (up–up–down), neutrons (up–down–down) and pions (combinations of an (anti-)up and an (anti-)down).
When one of these particles such as the proton passes through matter it loses energy mainly due to its interaction with the atomic electrons. The distribution fLof the energy loss ∆ in a
layer of silicon of thickness x was first calculated by Landau [10] in 1944 and equals
fL(x, ∆) = 1 ξ 1 2πi ∫ σ+i∞ σ−i∞
exp (u ln u + λu)du, (2.1) where λ = 1
ξ
[
∆− ξ(ln[ϵξ′
]
+1− C)], C ≈ 0.5572 is the Euler–Mascheroni constant, 3
Figure 2.1:The par cles of the Standard Model. Figure from [9].
σis the cross section and for silicon ϵ′ ≈ 0.03 eV and ξ = 17.81 keV/mm × βx where β is
the velocity of the particle as fraction of the speed of light [11, 12]. The most probable value (MPV) of this energy loss distribution for highly energetic particles is
∆MPV ≈ βγ>100ξ [ ln ( 2mc2ξ ( ℏωp )2 ) +j ] , (2.2)
where m is the mass of the particle, ℏ is the reduced Planck constant, ωpis the plasma
fre-quency and j = 0.200. However, Landau neglected the binding of the atomic electrons, leading to an underestimating of the width of the distribution. To account for the binding the Landau distribution should be convoluted with a normal distribution. This normal dis-tribution also accounts for (electronic) noise in the measured disdis-tribution. An example of this distribution is given in Figure 2.2.
2.2 Semiconductor physics
The pixel detectors used in this research are semiconductor detectors. Before going into depth about the detectors, first a brief semiconductor physics background is given.
Figure 2.2:A Landau distribu on as given in Equa on 2.1 convoluted with a normal distribu on. The distribu on is normalised to a peak value of 1. For this distribu on the MPV is∆MPV =
10 ke−, the width of the Landauw = 4× ξis 1200 e−, the integral of the distribu on is 6.9 ke−and the standard devia on of the normal distribu on is 500 e−.
2.2.1 Models of atoms
In 1913 Niels Bohr came with a new model for atoms: a positively charged nucleus that has electrons around the nucleus in certain, fixed, shells [13]. It was the first model that used quantised energy levels. Later an updated quantum model was proposed, including the wave-matter duality [14], the Schrödinger equation [15] and the uncertainty principle [16].
In the latter models, the possible energy levels of an electron are restricted. Due to the Pauli exclusion principle [17], electrons cannot all have the same energy level. Hence, if the lowest energy level is occupied, remaining electrons must have a higher energy. When two atoms ap-proach each other and form a crystal lattice, the state (i.e. the energy levels) of the electrons split [18]. Therefore twice as much energy levels are possible (see Figure 2.3a). Similarly, when six atoms form a crystal lattice, each energy level splits into six (see Figure 2.3b). For larger crystal lattices the energy levels are so close to each other that they seem continuous (see Figure 2.3c). This is called an energy band. The distance between two bands is called the energy gap.
The energy levels in a crystal lattice will be filled with electrons from lowest to highest en-ergy level. So first the band with the lowest enen-ergy will be filled, then the bands with some-what higher energy level and so on until all electrons are placed. For e.g. sodium this is shown in Figure 2.4. Here the bands are completely filled up to and including the 2p band. The 3s band is only partially filled. A crystal lattice with the highest energy band only partially filled with electrons is called a conductor (see Figure 2.5a). Because the next energy level an electron
(a)Two atoms approaching. (b)Six atoms approaching. (c)Many atoms approaching.
Figure 2.3:When atoms approach each other energy levels split as described by the Pauli exclusion principle. Therefore new energy levels become available. If many atoms are close together, like a (larger) crystal la ce, the energy levels are so close that they become con nuous and are called energy bands. The difference in energy between bands is called the energy gap. Figure from [19].
Figure 2.4:Energy band structure for sodium. Because the3sband is only half filled, sodium is a conductor. Figure from [19].
can be excited to is almost the same as the energy the electron already has, the transition goes very easily and hence the electrons are very mobile. When all electrons fit precisely in the first N bands, the next energy level available is in the next energy band. Crystal lattices with this band structure are called insulators (see Figure 2.5b). The band which is completely filled and has the highest energy is called the valence band. The first free band is called the conduction band. Typically, the energy needed for an electron in an insulator to excite to the next avail-able energy level is Eg = 5 − 10 eV [19]. In comparison, the thermal energy of an electron
at room temperature is in the order of 0.04 eV. Hence electrons will never go into the con-duction band. Some materials, however, have a much lower energy gap (typically 1 eV, see Figure 2.5c). These materials are called semiconductors.
2.2.2 Semiconductors
An electron in a semiconductor can jump over the energy gap due to thermal energy or due to the interaction with a particle with enough energy (for instance a Minimum Ionising
Par-(a)Conductor (b)Insulator (c)Semiconductor (d)Semiconductor with a few electron-hole pairs
Figure 2.5:Highest occupied energy bands for several kinds of materials. When the band is only par ally filled like in (a), the material is called a conductor. If the highest occupied energy band is totally filled and the energy gap is rela vely large(Eg=5−10 eV
)
like in (b), it is called an insulator. When the energy gap is low (typically 1 eV) the material is considered to be a semiconductor (c). In (d) a semiconductor is given where a few electrons are excited from the valence band to the conduc on band. Figure from [19].
ticle, MIP). When this happens, the electron will leave a place for another electron in the va-lence band (see Figure 2.5d). This empty place is called a hole. To increase the production of electron-hole pairs, one uses a process called doping [19]. A way to do this, is by replacing a small fraction of the semiconductor atoms by another atom with an extra electron (n-type doping) or hole (i.e. an electron less, p-type doping) in the outer shell, see the upper part of Figure 2.6. Or, in the terminology of energy levels, adding an extra permitted energy level just above the conduction band or just below the valence band (see the bottom part of Figure 2.6). Because the small energy difference between the normal band and the extra level, electrons will need much less energy to jump to the next energy level. Hence, the material is conduc-tive.
When a p-type and an n-type doped semiconductor are put in contact with each other, currents can only flow one way. This is called a p-n junction diode and is used in many elec-tronics like chips, solar cells and LEDs.
For more details on semiconductor physics, see e.g. [20], [21] or [22].
2.3 Pixel detectors
Nowadays all mobile phones have one or more digital cameras built-in. These cameras can all be categorised as pixel detectors: the sensor of the camera is divided into small pixels and detects incoming photons. This is an everyday example of a pixel detector. In high energy physics pixel detectors are also widely used [23]. For example, all large LHC experiments (AL-ICE, ATLAS, CMS and LHCb) use pixel detectors. Although the cameras and high energy physics (HEP) detectors are both pixel detectors, there are some differences. In comparison with the non-scientific cameras, the scientific pixel detectors can, among others, efficiently detect high energy particles and measure much faster. Also not all pixels have a signal in
scien-(a)N-type doping (b)P-type doping
Figure 2.6:Representa on of n-type (a) and p-type (b) doping. N-type doping is adding an atom to the crystal la ce with an extra electron. This causes an extra allowed energy level just below the conduc on band called the donor level (as is donates the extra electron). With p-type doping on the other hand an atom is added with an electron less (so an extra hole) in the outer shell. This also causes an extra energy level (the acceptor level), but now just above the valence band. Figure from [19].
tific detectors while in cameras all pixels measure the incoming light. In the remaining part of this section scientific pixel detectors will be discussed.
2.3.1 Detection of charged particles
A hybrid pixel detector exists of two main parts: a sensor made of a doped semiconductor (mostly silicon) and a chip with electronics [23]. These parts are produced separately us-ing different technologies and are therefore attached to each other with solder bumps. Each pixel has its own electronics and bump. In Figure 2.7 a schematic drawing of a typical pixel is given. The sensor is segmented into pixels because doped implants are placed in the silicon layer. The type of doping depends on the doping of the silicon. The implant is doped with the opposite type than the silicon. The type of doping also indicates whether the electrons or the holes are collected at the implant.
Before the measurements start all free electrons and holes in the sensor must be removed. This is done by applying an external voltage V on one side of the sensor. The voltage will re-move free carriers in the sensor up to
W≈
√ 2ϵ0ϵSi
Figure 2.7:When a par cle goes through a sensor it creates electron-hole pairs. If the electron-hole pairs are inside the deple on zone, electrons dri to the top and holes to the bo om of the sensor (or other way around, depending on the type of sensor) due to the electric field set by the bias voltage. Via the implant and the bump the electrons/holes are collected by an amplifier in the readout chip. From there the signal is further processed. Figure from [23].
where W is the width of the depletion zone, ϵ0is the permittivity of the vacuum, ϵSiis the
permittivity of silicon, e is the electron charge and NDis doping concentration of the
sil-icon [23]. If the depletion zone reaches over the whole sensor, it is fully depleted. When a particle goes through the sensor and creates electron-hole pairs, these will be the only free charge carriers present. They will drift towards the implants of the sensors by the electrical field caused by the applied voltage. The velocity at which the electrons drift is
v = µ× E
= qτ
mn
E (2.4)
mnis the effective electron mass and E is the electrical field. As the number of collisions per
second increases with increasing velocity, and therefore the electrons lose kinetic energy, the velocity will saturate at
vs≈ 1.53 × 109cm/s × T−0.87 (2.5)
where T is the temperature [24].
When the electron-hole pairs are created, a current is generated following the Shockley-Ramo theorem: the current I generated by a moving charge q equals
I = q (v · E) (2.6)
where v is the velocity of the electron (or hole) and E is the electrical field [25, 26]. Via the bump the current will enter the electronics where the signal is amplified, processed and sent to a computer.
2.3.2 Timepix
The process as described above is the general working process of a semiconductor detector. The detectors used in this research are sensors made of silicon (see Section 3.1) connected to a Timepix3 readout chip. Timepix3 is part of the Medipix ASIC family. Medipix is a collab-oration of a group of institutes and universities which has developed several readout chips. In 1998 the first detector came from this collaboration: the Medipix chip [27]. Medipix has 64×64 pixels of each 170×170 µm2and can count the number of photons going through
the sensor. A few years later (in 2002) the Medipix2 chip was developed [28]. Like Medipix also Medipix2 could do photon counting, but now with 256×256 pixels of each 55×55 µm2.
The collaboration also developed a chip which was capable of measuring the Time of Ar-rival (time of detection, ToA) or Time over Threshold (charge liberated by a passing particle, ToT): Timepix [29].
The development of these chips continued, resulting in the Medipix3 [30] and Timepix3 chips [31] (key properties of Timepix3 in Table 2.1). Contrary to its predecessor, Medipix3 has no dead time between detections and because it has multiple thresholds, it can resolve x-ray photons with different energies (often called colour imaging). Timepix3 can do si-multaneous ToA and ToT measurements, which Timepix cannot do. Also, Timepix3 has a better time resolution, 1.56 ns for Timepix3 versus 10 ns for Timepix. For the readout of both Timepix3 and Medipix3 the Speedy PIxel Detector Readout (SPIDR) has been devel-oped [32].
Table 2.1:Key proper es of Timepix3 [31].
Number of pixels 256×256 Pixel size 55 µm×55 µm Time resolution 1.5625 ns
ToA Acquisition modes ToA + ToT
Counting and total charge Logic in Timepix3
The drifting electrons/holes in the sensor create a current which is integrated by the pre-amplifier and digitised by a discriminator (see Figure 2.8). The threshold of the
discrimina-Figure 2.8:Front-end part of Timepix3. The input signal from the sensor (or, to calibrate the response of the front-end, test pulses with a computer-controlled known charge (see Sec on 3.2.3)) is amplified and digi sed by a discriminator with tuneable threshold. If the pixel is not masked, it is further processed (adding mestamps, ToT informa on, etc.).
tor can be set per pixel. If the pixel is not masked (pixels can be masked to exclude noisy pix-els), the signal will be further processed. The main feature of Timepix3 is that it can measure ToA and ToT simultaneously. The ToA is measured with two clocks (oscillators, for details see [31]). One of the clocks has a frequency of 40 MHz and is continuously ticking and is common for the whole chip. The 40 MHz is also used for the ToT measurement. The other clock has a frequency of 640 MHz and is shared by a group of 4 × 2 pixels called a superpixel. The 640 MHz clock is only running when needed. It is started when one of the pixels in the superpixel crosses threshold.
When a particle liberates charge in the sensor, which is integrated by the pre-amplifier, and the accompanying signal goes over threshold, the 640 MHz clock starts ticking (see Fig-ure 2.9). This clock stops ticking on the first rising edge of the 40 MHz clock after the hit. The ToA can be calculated using
where N40 MHzis the number of ticks of the 40 MHz clock since the last reset of the 40 MHz
counter and N640 MHzis the number of ticks of the 640 MHz clock. The number of “fast”
clock ticks and the time of the 40 MHz clock are saved and give the ToA up to a precision of 1
640 MHz ≈1.56 ns. (2.8)
The signal of a particle with high energy deposition stays longer over threshold because the amplifier is discharged with a constant current. Hence larger signals will need more time to discharge. As long as a signal is over threshold, the number of rising edges of the 40 MHz clock is counted. This is defined as the ToT and is a measure for the number of electron-hole pairs created in the sensor.
As can be seen in Figure 2.9 the hit with high energy deposition is detected earlier than a hit with low energy deposition that arrived at the same time. This time difference is called
timewalk. To overcome this effect one could do a per pixel and per ToT correction on the
Figure 2.9:The electronic signals for two hits in a Timepix3 detector. When a par cle goes through the sensor it deposits charge in a certain (fixed) amount of me. When all charge is de-posited, the charge is reduced with a fixed slope. So the signal of a par cle which deposits much charge (like the signal in green) will be longer than the signal of a par cle which de-posits less charge (like the signal in blue). The red line is the set threshold for the hit signal. If the signal goes over threshold the discriminator turns from a logic zero to one. At that
me a 640 MHz clock starts cking. It con nues cking un l the first rise of the con n-uously cking 40 MHz clock, shown in black. The number of rising edges of the 40 MHz clock while the signal is over threshold is counted; this gives the ToT. The ToA is deter-mined with the number of cks of the 640 MHz clock and the ming of the first ck of the 40 MHz clock (determined with the 40 MHz counter).
Max Planck
3
Experimental setup
T
his chapter discusses the design of the sensors in Section 3.1, the lab measurements in Section 3.2 and the setup and measurements done at the SPS testbeam in Section 3.3.3.1 Sensors
In this research several types of sensors bump bounded to a Timepix3 ASIC were used. The main focus was on characterising a 3D sensor, see Section 3.1.1. However, as comparison also two planar sensors were measured. The planar sensors consist of a bulk of silicon (see Figure 3.1a) lightly doped with boron (p-type doping) and pixel implants which are heavily doped with phosphorus (n-type). The backside of the sensor is heavily p-type doped. The thicknesses of these sensors are 50 µm and 200 µm. A photograph of a sensor on a Timepix3 chip mounted on a read-out board is given in Figure 3.2.
3.1.1 3D sensor
The design of the 3D sensor is different from the planar sensors. First the silicon in the 3D sensors is doped with phosphorous (n-type doping) and not with boron. Also, there are p-and n-type pillars in the bulk silicon from both the front- p-and the backside of the sensor (see Figure 3.1b and 3.1c). To make these pillars, first gaps are etched in the silicon. Then the p-and n-type implants are created using diffusion. A potential is applied between the front p-and
(a)Planar sensor (b)3D sensor
(c)Top view of 3D sensor
Figure 3.1:Side view of a schema c layout of (a) a planar sensor and (b) a 3D sensor. In (c) the top view of a 3D sensor is illustrated. In the planar sensor electrons created by a MIP dri “up” towards the bump and the chip. The holes go down to the backside of the sensor. In the 3D sensor it is the other way around: holes are collected and dri via the read-out pillar (red) to the chip while the electrons go via the field pillars (green) to the backside.
back pillars. The holes are driven towards the read-out pillars where the holes are collected for further processing.
The sensor is 285 µm thick with pillars of length 250 µm and a diameter of 10 µm [33]. Around the pillars there is a region of 2.9 µm on all sides which is highly doped. Hence, this part of the sensor is not depleted, but conductive. Therefore this part of the sensor is “dead”. So the total diameter of the region from which no charge is collected is 15.8 µm. For a particle that crosses the sensor at normal incidence, holes have to travel only an average distance of
1 2× √( 55 2 )2 + ( 55 2 )2 ≈ 20 µm (3.1) to reach the read-out pillar. In comparison the average travel distances for the planar sensors are 1
2 × 50 µm = 25 µm for the 50 µm sensor and 1
2 × 200 µm = 100 µm for the 200 µm
Figure 3.2:Close-up photo of a sensor on a Timepix3 ASIC.
drift time in the 3D sensor is shorter for the same electrical field. Also, the voltage needed to fully deplete the sensor is lower, the radiation tolerance is improved and the charge sharing between pixels is less [34]. The last is beneficial for timing properties as it reduces timewalk effects.
3.2 Lab measurements
In addition to the testbeam measurements, which are described in Section 3.3, lab measure-ments were performed. The lab measuremeasure-ments provide complementary information for the testbeam measurements.
3.2.1 Bias voltage
As stated in Section 2.3.1 a sensor only gives a detectable current when an external bias volt-age is applied. The bias voltvolt-age needed to fully deplete the sensor depends on the thickness and doping level of the sensor. Because a too high voltage could damage the sensor, an IV-curve is made (see Figure 3.3a). With this IV-curve it can be checked that the breakdown voltage, which is defined as the voltage at which there is a strong increase of current, is not yet reached. To make sure that the sensor does not get damaged, the current is required to stay below ap-proximately 10 µA. For the 3D sensor this is around 60 V (see Figure 3.3a). Note that at 60 V the sensor does not show signs of breakdown.
(a) (b)
Figure 3.3:To determine the deple on voltage two measurements are done. An IV-curve is done in
(a)to determine that the sensor is not operated beyond its breakdown voltage. Also the voltage at which the sensor is completely depleted is determined. This is defined as the voltage at which the ToT in (b) does not increase anymore with a higher voltage. For the 3D sensor (given in this figure) the deple on voltage is approximately 30 V and the safe opera ng voltage approximately 60 V.
of the ToT as function of the bias voltage is made, see Figure 3.3b. To make a detectable sig-nal electrons from a strontium-90 radioactive source are used. Before full depletion is reached not all charge is collected. Hence, the ToT should rise with increasing bias voltage until the full depletion voltage is reached. Once full depleted the ToT becomes constant because all charge is collected. From Figure 3.3b it can be concluded that the full depletion voltage of this sensor is about 25 V. There is chosen to overdeplete the sensor a bit and use as standard operation voltage 30 V.
3.2.2 Threshold equalisation
During the fabrication process of the chips small fluctuations in the process parameters can appear. This leads to variations both between different chips and between different pixels within a chip. As result of these variations each pixel needs a slightly different threshold volt-age for its discriminator.
To overcome these per pixel variations a threshold equalisation procedure is performed. This procedure makes use of 4 adjustment bits to tune the threshold per pixel in addition to the global (per-chip) threshold. First a binary adjustment value of 0000 is set for each pixel. The global threshold is scanned which gives noise hits when the threshold reaches the base-line voltage of the amplifier. For each pixel this gives a normal distribution which is fitted. From the mean value of this normal distribution for each pixel, the blue distribution in Fig-ure 3.4 is made. The same is done with an adjustment value of 1111 (red line in FigFig-ure 3.4). Next, for each pixel an adjustment value is chosen such that the threshold is as close as pos-sible to the midpoint between the blue and red distributions (resulting in the black line in Figure 3.4). This is done by assuming a linear relation between the two settings. This will lead
Figure 3.4:Equalisa on of a Timepix3 chip. The mean of the distribu on of noise hits of the pixels with a 0000 adjustment bit is plo ed in blue and an 1111 adjustment bit in red. Assuming a linear rela on the op mal adjustment in the middle of the blue and red distribu on is found (black).
to a narrower distribution of the threshold of the pixels. Hence, all pixels have about the same threshold.
3.2.3 Charge calibration
Timepix3 measures the time over threshold and not directly the deposited charge in the sen-sor. Test pulses are used to determine the conversion between ToT and the number of elec-trons. A known charge is injected via a capacitor into the electronics of a pixel (see Figure 2.8) and the corresponding ToT is measured. This is done for each pixel, and for several charges. The measured ToTs are fitted per pixel with the surrogate function [35]
ToT = p0+p1 × q −
c
q− t, (3.2)
where p0, p1, c and t are the fit parameters and q the charge in electrons (see Figure 3.5 for an
example). Parameters p0and p1define respectively the intercept and slope of the linear part
well above threshold (high charge), while c and t define the non-linearity around threshold (low charge). Using these parameters and the inverse function of Equation 3.2, the charge induced by a MIP can be calculated from the ToT. Comparison with X-rays from a syn-chrotron showed that an accuracy of 4 % can be achieved [36, 37]. The charge can be con-verted to energy as the creation of an electron-hole pair costs, on average, about 3.6 eV [38].
Figure 3.5:The result of a charge calibra on of a single pixel. A known charge is injected in the elec-tronics of a pixel using test pulses. The ToT is measured and a fit with the func on from Equa on 3.2 is performed. Using the fit results, the ToT measured in the testbeam can be converted to collected charge.
3.3 Testbeam measurements
The data taking was done at the H8 beamline in the North Area of the SPS. A secondary mixed hadron beam with mainly pions with an energy of 180 GeV induced by the SPS were used. These particles come in spills of about 4.5 seconds with about 2 × 106particles. A
per-manently installed Timepix3 telescope [36] is used as reference for precise spatial and timing information for the DuT (see Figures 3.6 and 3.7). The telescope has a pointing resolution
(a) (b)
Figure 3.6:Photographs of the testbeam setup. The two telescope arms are visible in (a) with a DuT in the middle. In (b) a close-up of the downstream telescope arm is shown.
of 1.6 µm at the DuT position and a timing resolution of 350 ps [36]. It consists of eight Timepix3 chips with 300 µm thick planar sensors. The telescope planes are divided into two arms of each four planes. Both arms have two SPIDRs for the read-out of the planes. More-over, all planes are rotated 9◦around the x- and y-axis to give optimal spatial resolution. An
Figure 3.7:The Timepix3 telescope installed in the H8 beamline at the North Area of SPS, CERN. The beam goes from le to right and crosses eight telescope planes divided into two arms. A DuT can be placed on a rota on stage in the middle of the telescope (blue part in the figure). Figure from [36].
external bias voltage of 200 V is applied on the telescope planes. Also the coincidence of two scintillators (one upstream and one downstream of the telescope) provides an additional track timestamp.
The DuT is placed in the centre of the telescope. A rotation stage is placed at this position which allows rotation of the DuT around the y-axis. The DuT can also be displaced in x and
y. Furthermore, the whole telescope table can also be adjusted in x and y to align the whole
telescope with respect to the beam. Additionally, the distance between the telescope arms can be reduced or enlarged to accommodate for the size of different DuTs.
3.3.1 Measurement scans
The data taking was split into multiple series of measurements each performed for other pur-poses. For example scans where the bias voltage applied on the DuT was changed are per-formed to do timing studies. Also angle scans were done where the angle between the DuT and the particle beam is changed. This is done for close to perpendicular and for angles then the DuT is almost parallel to the beam (grazing angles). These scans can be used for e.g. spa-tial resolution studies. To calibrate the zero angle setting of the rotation stage a small angle scan is done. For each angle the average cluster size on the DuT is determined. As the cluster size is at a minimum for a zero degrees angle, the angle of the rotation stage can be calibrated using these measurements. A list of all scans used in the analysis described in this report, and accompanying parameters, is given in Table 3.1.
Table 3.1:The condi ons of the measurements done for each sensor and each study. E.g. [0, 45, 3] should be read as all integers between 0 and 45 with steps of 3.
Sensor Scan Bias voltage [V] Angle [◦] Spills Used for
study of
3D
2D 20, 40, 65 [0, 45, 3] 5 Pillar dimensions Angle 60 [0, 20, 2] 10 Cluster size
Bias 2.5, 5, [10, 60, 10] 0 10 Timing Grazing 60 87.5 5 Pillar dimensions 50 µm 2D -90 [0, 80, 5] 10 Cluster size
4
Track reconstruction
I
n this chapter the track reconstruction steps are discussed. First the data is decoded, then clusters are formed, the setup is aligned, tracks are formed and the cluster on the DuT are associated with the tracks.4.1 Decoding software: Kepler
The data from the Timepix3 detectors has to be decoded before further analysis can be done. A dedicated software package called Kepler [39] is used, which is based on the GAUDI frame-work [40, 41]. Kepler decodes the raw hit data that is coming from Timepix3 and sort the hits by time. With the decoded data hitmaps like the ones in Figure 4.1 can be made which give a first indication on the quality of the data and about the alignment of the telescope and DuT with respect to the beam. Using these plots it can be concluded that the beam has a Gaussian profile with a width of σx = 4.3 mm in x and σy = 3.8 mm in y. Hence, about 82 % of the
beam particles traverse the telescope. Besides the decoding Kepler also prepares the data for the analysis: individual hits are clustered; the telescope planes and DuT are aligned; telescope tracks are reconstructed; and clusters on the DuT are associated with the tracks. These steps are described in the following sections.
Figure 4.1:Hitmaps for a run with a 50 µm thick planar sensor as DuT. The first four planes (W0002_J06 ll W0002_D05) form the upstream telescope arm, the middle plane (W0039_I11) is the DuT and the last four planes (W0002_G05 ll W0002_I03) form the downstream telescope arm. The beam is clearly visible in all planes.
4.2 Clustering
When a particle goes through the sensor near the edge of a pixel, it is likely that some of the charge will diffuse to a neighbouring pixel. Also when the sensor is under an angle multiple pixels will be hit by the same particle. These hits are grouped together into clusters. All hits in adjacent pixels (also diagonally) within a time range of 100 ns are assumed to belong to a sin-gle cluster. In Figure 4.2 an example is given of a possible outcome of the clustering algorithm for all hits within a time range of 100 ns. The charge calculated from the ToT information of each individual hit in a cluster is summed to form the cluster charge. This cluster charge fol-lows a Landau distribution convoluted with a normal distribution as described in Section 2.1. In Figure 4.3 an example is given of a distribution of the cluster charge of a telescope plane.
Figure 4.2:Part of the sensor where some pixels are hit (red) and some not (grey). All pixels that are hit within 100 ns and touch each other (including diagonally) are considered to be a single cluster.
The MPV of the fit is 26 ke−, which matches the energy loss of a MIP traversing a 300 µm
silicon sensor (80 e−1/µm ∗ 300 µm ≈ 24 ke).
Figure 4.3:The distribu on of the cluster charge for a telescope plane. The distribu on is fi ed with a Landau distribu on convoluted with a normal distribu on. The MPV is about 26 ke−, which matches the energy loss of a MIP traversing a 300 µm silicon sensor.
Clustering also improves the spatial resolution. For a single pixel hit the spatial resolution is
δx = √1
12 ∗ 55 µm ≈ 16 µm (4.1) as this is the standard deviation of a uniform distribution of width x = 55 µm. For a clus-ter the position is defined as the charge weighted centre of gravity of the hits in the clusclus-ter. This gives a much better resolution (up to a few microns). For the best spatial resolution, one should aim for clusters covering two rows and two columns. In that way the position can still be determined from the centre of gravity and the timing resolution is only slightly reduced
due to a smaller deposited charge. The angle of the telescope planes is therefore optimised to get mostly cluster sizes of 3 pixels (see Figure 4.4). The optimal angle for a 300 µm thick sensor and a 55 µm pitch sensor is
α =tan−1 ( 55 µm 300 µm ) ≈ 10◦. (4.2) The angle used for the telescope is 9◦to account for charge spread due to the diffusion of the
charge carriers while drifting to the read-out electrodes [36].
Figure 4.4:The number of hits in a cluster (the cluster size) of (a) a telescope plane and (b) a 50 µm planar sensor. The telescope plane is rotated by 9◦around thexandyaxis to get maxi-mum number of size-3 clusters. The 50 µm sensor is not rotated, resul ng in mostly size-1 clusters.
4.3 Spatial alignment of the telescope and DuT
So far only clusters on individual planes are known. To reconstruct tracks from these clusters, the precise location of the planes is needed. As the alignment of the mechanics is not suffi-cient enough, a software alignment procedure is needed. During the alignment procedure tracks are formed using six alignment parameter per plane which are adjusted after each step (for the track fitting procedure, see Section 4.4). The correctness of the alignment is judged from the χ2distribution of a set of 10 000 tracks. By minimising the χ2of the tracks a new,
The alignment procedure is divided in several steps. First a general alignment is performed with the so-called TbAlignmentMinuit0 tool in Kepler. In this tool the manually set align-ment parameters are varied and the tracks are refitted. For all the tracks the χ2is summed.
The summed χ2is minimised to get a reasonably good first alignment.
When a reasonable starting point is provided by TbAlignmentMinuit0, the main telescope alignment starts. The Kepler tool TbMillepede [42] simultaneously fits the track constants and the alignment parameters of the telescope planes. After doing this several times for a
col-(a)x-residuals (b)y-residuals
Figure 4.5:The residuals of a telescope plane as func on of posi on in the sensor. This indicates the correctness of the alignment of the telescope. If the residuals are at each loca on in the sensor a Gaussian with the same mean, the alignment is correct.
lection of 104tracks, gradually tightening the constrains, TbMillepede finds an alignment for
the telescope with minimised χ2. To see if the alignment process worked fine, one can look
at the residuals, which are defined as the difference between the measured location and the
Figure 4.6:Example of an aligned run. The coordinates of clusters on each individual sensors on the Timepix3 planes are indicated.
location predicted by the track. The distribution of these residuals (see Figure 4.5) should be a Gaussian with a constant mean at each location in the sensor. If there is a dependence of the x- or y-residual as function of the global x- or y-coordinate, the alignment is sub-optimal.
In the TbMillepede alignment the DuT is not included to get tracks independent of the clusters on the DuT. To get the spatial alignment of the DuT a TbAlignmentMinuit2 align-ment is executed. It is specially designed to do an alignalign-ment of a single plane, such as the DuT. This alignment is also done multiple times while the parameters of the DuT are gradu-ally tightened and the parameters of the telescope are kept fixed. After successful completion of the DuT and telescope alignment, the tracks can be reconstructed. In Figure 4.6 an exam-ple is given of an aligned run.
In the alignment process initially something strange appeared in the plot of the residuals as function of (x,y). There was a (large) slope although the location of the sensors seemed fine (see Figure 4.7). The slope disappeared when a term in the χ2of the tracks was added,
but then the DuT z-position moved by 20 cm in the upstream direction. A small variation in the z-position can be explained because it is a weak mode in the alignment procedure, but a displacement of 20 cm is considered too large. When the z-positions were fixed to the centre of the telescope, the slope in the residual plots appeared again. It is unclear why this happens. Because the residual plots are correct when using the strange placement, the alignment with correction is used.
4.4 Track reconstruction
In the tracking process a cluster on the first telescope plane is used as basis. Next a cluster on the second plane is searched within a time window of 10 ns, which is much less than the av-erage time between hits (O (few µs)). If a second cluster is found, the two clusters form a potential track. The track is extrapolated to the third plane. On this plane a cluster is searched within the 10 ns time window and within a spatial range of θ × δz where θ = 0.01 rad and
δzis the distance between the planes. If this cluster is found the track parameters are updated
and a cluster in the fourth plane is searched in the same time and spatial frame. This process is repeated for all 8 telescope planes. The reconstructed track is defined as a straight line fit through the clusters on the telescope planes. The time of the track is determined as the aver-age of all individual cluster times of the eight telescope planes where the cluster rime is that of the fasted hit in the cluster. About 75 % of the clusters on the planes can be associated to tracks. The DuT is not used in the tracking to avoid biasing of results.
(a)Posi ons (b)Residuals
Figure 4.7:The posi ons of the DuT w.r.t. the telescope and the accompanying residuals. When no extra term is added to theχ֜of the tracks to correct for the slope in the residuals plot, the
posi on of the DuT was correct but the residuals were not (top plots). If this extra term is added the DuT shi ed towards the upstream telescope arm (bo om plots). The residuals are now correct, but the loca on is not. Restric ng the posi on of the DuT to the correct posi on and keeping the term for the slope did not reduce the slope (leading to the top plots again).
4.5 DuT cluster association
To associate the DuT clusters with the tracks an association procedure is performed. This procedure looks for clusters on the DuT within 100 ns of the track time and 1 mm of the lo-cation predicted by the telescope (see Figure 4.8). When at least one pixel of a cluster is inside the search window, the whole cluster is associated. With the associated clusters the alignment of the DuT can be checked. At zero degrees beam angle the residuals (see Figure 4.9) should give a uniform distribution around zero with a width equal to the pixel pitch [43]. If not, the alignment is not good. Also the residuals as function of x and y of the sensor should remain constant (see Figure 4.10).
Figure 4.8:Associa ng principle of the DuT clusters (not to scale). The telescope predicts the impact loca on of the par cle on the DuT (black dot). If the centre of at least one pixel in a cluster is within 1 mm inxandyof the impact loca on, the whole cluster is associated to the track.
(a)x-residual distribu on (b)y-residual distribu on
Figure 4.9:The unbiased residuals of a run with the 50 µm thick planar sensor at zero degree beam angle. As expected, the residuals form a uniform distribu on with a width equal to the pixel pitch.
(a) (b)
Figure 4.10:The unbiased residuals as func on of posi on of a run with the 50 µm sensor are shown in (a). In (b) the mean of the residuals in (a) are shown. The residuals are constant over the whole sensor. This indicates a good alignment of the telescope and DuT.
5
Data analysis
W
ith the tracks reconstructed by Kepler further analyses are done on the 3D sensor: a study is done to determine the pillar dimensions (Section 5.1), the timing variations as function of the position within the pixel of the 3D sensor are investigated (Section 5.2), the cluster sizes of the 3D sensor are compared with that of the planar sensors (Section 5.3), and finally, the spatial resolution of all sensors are investigated (Section 5.4).5.1 Pillar dimensions
The pillar dimensions of the 3D sensor designed by Pellegrini et al. [33] are determined and checked against the design value. Both the pillar diameter and the pillar length are determined by looking at the deposited charge. If a particle crosses the sensor between the pillars for a sensor oriented perpendicular to the beam, charge is deposited in the whole thickness of the sensor. When a particle traverses a pillar only a fraction of the charge will be measured as the pillars are dead material. Hence, the measured charge will be less in the pillars. This effect can be used to determine the diameter of the pillars. As the charge is deposited more or less linear with the thickness of the sensitive layer, the deposited charge can also give an indication of the pillar length.
The tracks reconstructed by Kepler give the location of the MIP on the DuT with a preci-sion of 1.6 µm. Information about the DuT is extracted from the clusters that are associated
to the track. By doing so, the deposited charge in each region of a pixel can be determined. By plotting the charge as function of position within the pixel the pillars become visible because in the pillar regions only charge deposited above or below the pillar is measured.
In this study regions of 1 µm×1 µm are chosen. This leads to 55×55 regions per pixel. All pixels are assumed to be the same. Hence, data from all pixels are overlaid in intra-pixel plots and form an overlaid pixel. From all tracks going through a region of the pixels a distribution of the cluster charge of the DuT is made (see Figure 5.1). Fitting these distributions with a
(a)Non-pillar (b)Pillar (c)Edge of pillar
Figure 5.1:The charge distribu on in three regions: (a) regions away from the pillar, (b) regions inside the pillar and (c) at the edge of the pillar. At the edge both pillar and non-pillar distribu ons arise due to the uncertainty in posi on by the telescope. Also, the region of the distri-bu on might cross the edge of the pillar and hence, be partly a pillar region and partly a non-pillar region. Furthermore, the individual par cles in the beam might be under an angle. This leads to par cles going only partly through the pillar.
Landau convoluted with a normal distribution gives the MPV of the distribution and hence, the deposited charge in that region.
There are two possibilities for a particle to go through the sensor: it hits the pillar or it does not1. As stated earlier, the energy deposited in a pillar does not give a detectable signal. So
the collected charge in these regions only comes from the depleted region above or below the pillar. Therefore, the MPV in a pillar region (Figure 5.1b) is much lower than in a non-pillar region (Figure 5.1a). For regions near the edge of the non-pillar the charge distribution has two peaks (see Figure 5.1c): one for tracks traversing the pillar and one for tracks not travers-ing the pillar. This is due to the uncertainty on the track position predicted by the telescope. Also, the regions might cross the edge of the pillar. In that case it will be partially a pillar re-gion and partially a non-pillar rere-gion. The two distributions are both fitted with a Landau convoluted with a normal distribution. The MPV of the distribution with most entries is used for further analysis. Plotting the MPVs of all regions gives the intra-pixel map of the deposited charge as shown in Figure 5.2. With this map the radius of the pillars can be deter-mined.
The cross section of this map for x = 30 µm and the cross section for y = 30 µm are fitted
1For a very small fraction of the tracks the particle might traverse the pillar partially. Because of scattering the direction of the track can change and hence move from pillar to non-pillar region.
Figure 5.2:Map of the deposited charge as func on of posi on in the pixel overlaid for all pixels of the 3D sensor. The field pillars are clearly visible in the corners and the read-out pillar in the centre of the pixel. The DuT was placed at a 0◦angle and a bias voltage of 40 V was applied.
with the function
Q = p0+p1 × [ erf ( x− p2− 12× p3 √ 2× p4 ) − erf ( x− p2+ 12× p3 √ 2× p5 )] , (5.1)
where Q is the charge, x is the x-location in the pixel and piare the fit parameters. In this
func-tion fit parameter p3is the diameter of the read-out pillar. For the DuT at 0◦the diameter is
determined to be 18±3 µm in both directions (see Figure 5.3). This is consistent with the ex-pected diameter of 15.8 µm [33]. The error in the diameter consist partially of the error on the location predicted by the telescope which has a pointing resolution of 1.6 µm [36] and partially the error on the angle under which the DuT is placed2.
From the proportion of charge collected from the silicon above the read-out pillar, Qpillar,
and besides the pillar, Qnon-pillar, the height of the pillar is calculated with
hpillar = ( 1− Qpillar Qnon-pillar ) × hsensor, (5.2)
(a) (b)
Figure 5.3:The cross sec on of the map in Figure 5.2 fory = 30 µm in (a) andx = 30 µm in (b) is used to determine the pillar diameter. The cross sec on is fi ed with Equa on 5.1 which gives the diameter. This is determined to be 18±3 µm in both direc ons.
where hsensoris the thickness of the sensor, according to Pellegrini et al. [33]. The height is
found to be 217±12 µm3. This does not correspond to the 250 µm which was expected from
the design. Therefore an independent cross-check is done with tracks under a grazing angle.
5.1.1 Cross-check of pillar height using grazing angles
As a check of the measured pillar height derived from the charge deposition ratio for perpen-dicular tracks, tracks under a grazing angle are used to investigate the pillar height. Grazing angles are very large angles (around 90◦) between the incoming beam and the normal vector
(a)Top view (b)Side view
Figure 5.4:Example of the working principle determining the height of the pillars using tracks at grazing angles. In (a) the top view of two tracks traversing a 3D sensor under grazing angles is given. The red one goes though the read-out pillars while the green track does not. This will broaden the charge distribu on. When looking to the red track from the side, one gets Figure (b). In (b) a par cle goes through the pillars un l at a certain point it enters the layer where there are no more read-out pillars. There the deposited charge will increase suddenly. This can be used to determine the pillar height. N.B. the shown angle of the track in (b) is not near grazing, but chosen to improve the visibility of the figure. Furthermore, (a) is not to scale and only read-out pillars are given.
of the DuT plane. This will lead to long clusters in the DuT running along the row direction (see Figure 5.4). The alignment for grazing angles is not working (there is not a well defined starting point). To still be able to select the tracks that traverse the read-out pillars, only tracks that give hits in a single row are used. Hence, the tracks cross the sensor close to the centre of the pixels and thus mostly through the read-out pillar. Tracks crossing the field pillars are not selected as they produce two row clusters.
The MIP enters the DuT e.g. in the bottom of the sensor under a small angle. While going upwards in the sensor, the particle traverses the read-out pillars. At a certain point in the sen-sor the MIP will stop penetrating the read-out pillars. This will lead to a sudden increase in collected charge (see Figure 5.5). From the step in the distribution the height of the pillar can
Figure 5.5:The expected charge deposited for the 3D sensor under grazing angles. The numbers in this figure are arbitrarily chosen. The frac on of the charge reduced depends on the di-am̃eter of the pillar and is not covered in this study. The loca on of the step in the charge is used to determine the height of the pillar. In the first pixels the MIP does not penetrate the pillar: it goes above the pillar. At a certain point in the sensor the MIP will start pene-tra ng the pillars. From then on there will be less charge deposited as the pillars are dead. So, this sudden step in the charge can be used to determine the height of the pillar.
be calculated using
hpillar= Np
N × hsensor (5.3)
where hpillaris the pillar height, hsensoris the sensor thickness (here 285 µm), Npis the number
of pixels with a lower charge and N is the total number of pixels.
Besides the restriction on the width of the clusters as described above, also the length is restricted. To be sure the MIP went through the whole thickness of the sensor, only clusters of length
l = tan (90hsensor◦
are selected in which α is the angle between the beam and the normal vector of the DuT plane. This length is then converted to the number of pixels using the pixel size (55 µm) and rounded to the nearest integer. Furthermore, clusters that start or end at the edge of the sen-sor are excluded.
The pillar height is determined for tracks under an angle of 87.5◦. For each pixel in the
cluster a distribution of the charge is made and fitted with a Landau convoluted with a nor-mal distribution. The height found using this method is 213±4 µm (see Figure 5.6 and Equa-tion 5.3)4. Hence, also the height found using the grazing angle method is smaller than
ex-pected. Combining the results of both methods gives a pillar height of 215+2
−6µm.
Figure 5.6:The charge deposited in the pixels by grazing angle tracks in the 3D sensor. The DuT was placed under 87.5◦and a bias voltage of 60 V was applied. For the first 33 pixels, the MIP goes through the layer of silicon above the pillar and therefore should give a charge equivalent to the energy loss in 55 µm of silicon (80 e−1/µm∗55 µm ≈ 4.4 ke). So the found charge does not correspond to the expecta on. A er passing 33 pixels the MIP starts penetra ng the pillar. From there on the MIP will deposit less charge because the pillars are insensi ve. As this step in the charge gives the frac on of the thickness of the sensor where the pillars are, the height of the pillars can be determined with Equa on 5.3.
As well as the height of the read-out pillars, also the height of the field pillars are investi-gated. This is done by selecting the tracks with hits in two rows. This resulted in the plot in Figure 5.7. Here only the sudden step produced by the read-out pillar is visible, the field pil-lar is not. To make the field pilpil-lar visible, one could in future studies only look to the charge deposited right before and after the crossing of the rows.
The measured height of the pillars, 215+2
−6µm, does not correspond to the expected 250
µm. Since two independent techniques give the same result, the pillars are probably physically smaller. The shorter than expected length might be due to fluctuations during the etching
Figure 5.7:Same as Figure 5.6 but now the DuT was placed under 85◦and tracks with two rows are selected. This should make it possible to determine the height of the field pillar in the same way as is done for the read-out pillar. In the first 1̃5 pixels in the clusters one can see the contribu on of the read-out pillars while in the last pixels the contribu on of the field pillars should be visible. It is unclear why this happens.
process in the fabrication of the sensors. In the etching procedure the pillars are etched for a certain time to reach the designed depth. If for instance the temperature is lower, the pro-cess might become slower and hence yield shorter pillars. This could be checked by dicing the sensor and measure the physical length of the pillars directly. However, since this is a destruc-tive measurement, this is postponed until all data is analysed and the sensor is not needed for further studies.
5.2 Timing of 3D sensor
Having a good timing measurement will become important for the High Luminosity LHC (HL-LHC) [44]. The number of collisions per bunch crossing will increase drastically (up to 55 proton-proton collisions per bunch crossing [45]). This will decrease the efficiency of the VELO [46]. By measuring the hit times accurately, the separation of different interactions in the same bunch crossing is enhanced. To accurately measure the time of arrival, a large signal from the sensor is needed, while also a short drift distance improves the time accuracy. In 3D sensors the drift distance is decoupled from the length of the track segment in the sensor, which determines the amount of charge deposited by the track. Therefore the timing of the 3D sensor is investigated. This is done by looking at the time of arrival as function of intra-pixel position using perpendicular tracks.
each 1 µm × 1 µm region. The distributions are filled with the time difference between the cluster time of the DuT and the track time. The cluster time is the time measurement of the earliest pixel in the cluster and the track time is the mean of all cluster times of the track. The latter predicts the arrival time of the MIP at the DuT. The distributions are fitted with a nor-mal distribution and give the time needed to detect the MIP.
The time between the MIP going through the sensor and the measurement of the MIP depends on the location in the pixel. In Figure 5.8 the delay of the measurement of the DuT
(a)20 V (b)40 V (c)60 V
Figure 5.8:The (rela ve) delay of the measurement for several bias voltages as func on of the loca-on in an overlaid pixel of the 3D sensor. The absolute values for the delay are chosen arbitrary. Theχ֜per DoF of the fit is restricted to be below 2 5 and the width of the Gaussian fit used to calculate the delay below 1.35 ns. This causes the regions with no data around the pillars. For lower voltages, the delay is rapidly increasing. Especially at the edge of the pixel this is happening, because here the deple on region is withdrawn there first.
is presented as function of position in the pixel. A cut on both the fit χ2per DoF of 2.5 and
the resolution (width parameter of the Gaussian fit) of 1.35 ns is applied. This gives rise to several regions with no data
The delay can only be measured relative to each other as there might be delays over the whole sensor due to for example different clock cable lengths in the telescope or DuT. This will lead to a constant delay which is not due to the sensor. An arbitrary offset has been sub-tracted in Figure 5.8. The edge of the pixel is slower because the electrical field is lower at in-creasing distance from the pillars. This is because the hit charge5in these regions are less due
to charge sharing. As can be seen in Figure 2.9 the timewalk of these low charge hits could delay the signal.
Especially for a voltage of 20 V the sensor is much slower at the edge of the pixel. At this voltage the sensor is not fully depleted (see Figure 3.3). Therefore, the holes drift slower to the read-out pillar and will arrive later.
In Figure 5.8 an asymmetry appears in the y-location in the pixel. This could be explained by an alignment issue, but as all voltages (which are aligned separately) have the same asymme-try, this is unlikely.
The Gaussian fit also gives the time resolutions6of all locations in the overlaid pixel. In
Fig-ure 5.9 these resolutions are given. A time resolution of 987 ps is obtained in one 1 µm×1 µm
(a)20 V (b)40 V (c)60 V
Figure 5.9:For several voltages the me resolu on as func on of the loca on in an overlaid pixel of the 3D sensor is shown. The best resolu on is found to be near the centre of the pixel. If a voltage of 60 V is applied, the me resolu on gets down to 987 ps. For 40 V this is 986 ps. For a voltage of 20 V a resolu on of 1.02 ns is obtained.
region for the 3D sensor if a voltage of 60 V is applied. For a voltage of 40 V the time resolu-tion goes down to 986 ps and for 20 V this is 1.02 ns. The plots show the same structure as in Figure 5.8: better resolution near the centre of the pixel which is getting worse when going to the edge of the pixel. The reason for this is also timewalk. Even when the division of the charge between the pixel and its neighbour is only a bit different, the timewalk effect can be-come large [47]. To optimise the time resolution in a future study one could do a timewalk correction. This correction can be done by making a distribution of the delay as function of the deposited charge. Fitting this distribution can give a correction on the ToA which will overcome the decline of the time resolution.
5.3 Cluster size
To optimise the telescope for spatial resolution, the telescope planes are rotated by 9◦around
the x- and y-axis (see Section 3.3). A naive estimate of the optimal angle with the best resolu-tion can be made by looking at the cluster size. The optimal angle is reached when the cluster is two pixels wide and long. The angle at which this happens depends on the thickness of the sensor. For the DuTs the optimal angle is different as the telescope sensors are 300 µm thick and the DuTs are 50 µm, 200 µm and 285 µm thick. Both the total cluster size, as well as the cluster width in the row and column direction are investigated as function of the angle of the tracks.
The distributions of the cluster width in the direction of the rotation of the DuT are given for all sensors and for several angles in Figure 5.10. Because the DuT is only rotated around
