Characterisation of the Timepix Chip for the LHCb VELO Upgrade

Transcription

1 Particle and Astroparticle Physics Master Thesis Characterisation of the Timepix Chip for the LHCb VELO Upgrade Veerle Heijne Supervisor: Dr. Martin van Beuzekom Second reviewer: Dr. Auke-Pieter Colijn July 2010 Detector Research and Development, LHCb Nikhef Universiteit van Amsterdam

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3 Abstract Although the Large Hadron Collider has only recently started taking data, the plans for replacement of some of the detectors are already in progress. The silicon strip Vertex Locator (VELO) at the LHCb experiment should be replaced in order to process a higher luminosity and larger data rates. The Timepix chip is a suitable starting point for the VELO upgrade. This hybrid pixel chip consists of a 256x256 array of 50x50 micron pixels, and can be used to measure the charge deposit or the arrival time of high-energy particles. In order to investigate the suitability of this chip for the VELO upgrade, it has been characterised in a tracking telescope in the 120 GeV pion beam at CERN. The analysis and results of this beam test are discussed, in particular the spatial and timing resolution of the chip. The tracking telescope, which consisted of Medipix and Timepix devices, provided a track pointing resolution down to a few micrometers. Optimisation of the clustering, tracking and alignment revealed an optimal spatial resolution in the order of 5 micrometer at an angle of incidence of 8 degrees. Binary reconstruction reduces the data rate and the dead time in the chip. A 4 bit read out reduces the spatial resolution by at most one micron compared to a 14 bit readout. The timing resolution of the Timepix chip is not yet sufficient to cope with the 40 MHz beam interaction frequency, mainly due to the timewalk effect. The results of this research can be used to improve the design of a new VELO pixel chip. i

4 Contents 1 Introduction 1 2 LHCb Vertex Locator LHCb VELO Requirements for the VELO Upgrade Hybrid Pixel Detectors Energy Loss Diffusion and Angled Incidence Timepix Chip Time over Threshold Mode Time of Arrival Mode Readout and Data Acquisition Timepix for VELO Timepix Beam Test Telescope Energy Loss Distribution Analysis Software Clustering Alignment Tracking Spatial Resolution Binary Spatial Resolution Centre of Gravity Eta Correction Linear Gain Correction Timing Resolution Timewalk Timepix Beam Test Telescope First Results Conclusion and Outlook Resolution Timewalk Outlook ii

5 Bibliography 54 Summary of contribution made to the research 56 Samenvatting 57 iii

6 1 Introduction The field of high energy physics is currently going through a very exciting period, as the world s largest particle accelerator, the Large Hadron Collider in Geneva, is providing its first data. The behaviour of particles interacting at very high energies will provide fundamental information about the evolution of our universe. In order to study the products of the proton-proton interactions at the LHC, advanced detectors are needed to identify the particles and to determine their tracks and energies. One of those detectors is used at the Large Hadron Collider beauty experiment (LHCb). At LHCb, the interaction point of the particles can most accurately be determined in the Vertex Locator (VELO). This is a silicon strip detector which determines the position of vertices in the proton-proton interaction region. In a few years time, there will be a need for better performance and more statistics at the LHCb detector. One of the reasons to have an upgrade is to clarify discoveries in new physics which may be made after the first years of data taking. In order to get more statistics, the luminosity at the LHCb detector will be increased. This will increase the interaction rate, cause more radiation damage, and it will demand for a faster readout. Since the current VELO will not be able to cope with these issues, it will have to be replaced. For the upgrade of LHCb, the VELO group considers to replace the current strip detector with a pixel detector. One reason for this choice is that a pixel detector is more suitable for handling the high hit occupancies which will occur at a higher luminosity. The new detector will need to have a high spatial and timing resolution. The best starting point for the upgrade is the Timepix chip, which can be used for arrival time, charge deposit or photon counting measurements. An updated version of Timepix, the so-called Velopix, should be designed to meet the specific requirements of the VELO detector. The aim of this project is to characterise the Timepix chip in order to see if it provides a viable solution for the LHCb VELO upgrade. The method used to test the chip is to insert it into a tracking telescope in one of the particle beams at CERN. The main subject of this thesis is the analysis of beam test telescope data, in particular the spatial and timing resolution of the Timepix chip. Furthermore, additional tests have been performed in the laboratory, using for example radioactive sources and test pulses. The result of this project will be a better picture of the potentials and weaknesses of the Timepix chip, enabling a well-prepared design of the Velopix chip. This research has been performed with help of both the LHCb and the Detector Research and Development groups at Nikhef and CERN. The first chapter of this report describes the LHCb and VELO detectors in their current state, and the requirements for the upgrade. The second chapter introduces the concept of a hybrid pixel detector. Next, the Timepix chip and its readout system will be described. After a description of the set-up of the 2009 beam test, the main subject of the research will be discussed, namely the data analysis of this first beam test. The first chapter of this part of the report describes the software used for clustering, tracking and alignment. Next, the measurements in both spatial and 1

7 timing resolution will be covered, as well as the improvements made in the reconstruction. The final part of this thesis focusses on the preparation of the 2010 beam test, including a short overview of the first results. 2

8 2 LHCb Vertex Locator 2.1 LHCb The world s largest high-energy physics facility is situated near Geneva, at the European Organization for Nuclear Research (CERN). It consists of a circular particle accelerator, the Large Hadron Collider (LHC), and four large experiments, as can be seen in Figure 2.1. The LHC is stationed in a 27 km long tunnel about 100 meter underground, in which protons are accelerated in opposite directions. The two proton beams collide at four interaction points where the detectors are located. The proton bunches have a ns bunch spacing, and the peak luminosity of LHC is cm 2 s 1. Currently the accelerated protons collide at a centre-of-mass energy of 7 TeV, which will eventually be increased to 14 TeV. Figure 2.1: Schematic overview of the Large Hadron Collider at CERN. The detector of interest to this research is the LHCb detector [18], at the Large Hadron Collider beauty experiment. The purpose of LHCb is to search for physics beyond the Standard Model and to find differences between matter and anti-matter, by studying CP-violation and rare decays. In order to do this, LHCb analyses the behaviour of B-mesons that are produced in the proton-proton collision. Mesons are hadrons consisting of a quark-antiquark pair, and B-mesons in particular contain either a b or b quark. The way in which these B-mesons decay can indicate CPviolation. The design of the LHCb detector differs from the other large detectors at the LHC. Instead of being symmetric around the interaction point, it covers only the 3

9 forward direction (Figure 2.2). The reason for this specific layout is that the angular distribution of b and b peaks at the angles θ = 0 and θ = π. Since the partons inside the colliding protons usually have unequal momenta, the B-meson interaction is boosted in the direction of the beam. Figure 2.2: Schematic overview of the LHCb Detector. Whereas the design luminosity of LHC is cm 2 s 1, LHCb will only use a luminosity of cm 2 s 1, which is achieved by defocussing the beams. At this lower luminosity, the number of inelastic interactions per bunch crossing is on average 0.7. The advantage of a low luminosity is that the probability to have more than one interaction per bunch crossing (pile-up) decreases. Having only a single interaction facilitates the identification of B-mesons. To ease the reconstruction process even further, a pile-up veto detector has been installed in the Vertex Locator (VELO) which discards bunch crossings with multiple interactions. Another benefit of low luminosity is that the radiation dose is reduced, which is favourable to detectors close to the beam. As can be seen in Figure 2.2, the LHCb detector consists of different subdetectors. The proton-proton collisions take place at the left side of this picture, where the VELO is located. The Vertex Locator is part of the tracking system, together with the Tracker Turicensis (TT) and the tracking stations T1-T3. This tracking system is used to reconstruct primary and secondary vertices in the B-interactions. Furthermore a magnetic field enables the determination of the momenta of the particles by measuring their track curvature. Besides a tracking system there is also a particle identification 4

10 system. The Ring Imaging Cherenkov (RICH) detectors identify charged particles by measuring Cherenkov radiation. Following the RICH2 detector, there are several calorimeter layers. The SPD calorimeter determines whether particles are neutral or charged, and the PS identifies the electromagnetic properties of the particles. The ECAL is used to measure the energy of photons and electrons, whereas the HCAL measures the energy of heavier particles like protons, pions and neutrons. Lastly, muons are identified by five stations of muon chambers. In order to reduce the data rate, several trigger levels are applied. First, the L0 hardware trigger reduces the event rate from 40 MHz to 1 MHz, using information from the muon chambers, the calorimeters and the pile-up system in the VELO. Currently bunch crossings with at least one proton-proton interaction occur at a rate of about 10 MHz, whereas the total bunch crossing rate is 40 MHz. The pile-up veto triggers on those single-interaction events. Additional information on the energy and momentum is used to further reduce the rate from 10 to 1 MHz, thereby reducing the load on the CPU farm. A second level in the trigger, the High Level Trigger, uses the full event data to further reduce the event rate from 1 MHz to 2 khz. This is the event rate that is eventually used in the off-line analysis. 2.2 VELO The focus of this chapter will be on the Vertex Locator [18], which is closest to the proton-proton collision region. The VELO is a silicon micro-strip detector, used for tracking and vertex reconstruction. Since the VELO is placed closely to the beam, it is integrated with the LHC vacuum, thereby serving as a part of the LHC beampipe. As can be seen in Figure 2.3, it consists of 21 planes perpendicular to the beam direction. The distance from the first to the last VELO station along the beam axis is cm. Each of these 21 stations consists of two halves (modules), which contain two sensors each. One of the VELO modules, consisting of a silicon sensor surrounded by readout electronics, is shown in Figure 2.4. The active area of the modules starts at 8.2 mm, and ends at 42 mm from the beam axis. Half of the sensors (one on each module) has a geometry of strips positioned radially, whereas the other half is oriented in the azimuthal direction. This enables us to reconstruct both the r and φ coordinates of the hits. The three-dimensional position is obtained by using the position of the detector plane in z as the third coordinate. The innermost strip, being so close to the beam, is exposed to up to n eq cm 2 per year at the lowest LHCb luminosity. To protect the detector from radiation damage during injection and ramping of the beams, the detector modules can be mechanically pulled away from the beam to a safe distance of 30 mm. The first two stations in the VELO, which form the pile-up veto detector, reject bunch crossings in which multiple interactions take place. The pile-up veto detector is part of the L0 trigger. The other 21 modules are used for the two main VELO functions. Firstly, the VELO is part of the LHCb tracking system, which reconstructs the paths of particles through the complete detector. Secondly, it selects events that 5

11 Figure 2.3: Schematic overview of the VELO Detector. On the left, one half of all modules is shown, including the pile-up veto. The right shows a cross section of one detector plane, consisting of two halves. are of interest to the LHCb experiment, i.e. those including a B-meson. There are two properties of B-interactions which enable us to distinguish them from other events. Firstly, the decay particles of a B-meson have a higher transverse momentum than other particles produced in proton-proton collisions. Secondly, travelling at almost the speed of light, the B-mesons have a decay length of a few mm, depending on their energy. Therefore the B-events have a secondary vertex which is displaced from the proton collision point (the primary vertex). In order to reconstruct those vertices, a spatial resolution of a few micron is needed. Figure 2.4: VELO module showing the sensitive area and the readout electronics. A beam test experiment showed that the single hit resolution of the current VELO at perpendicular incidence is µm for a strip pitch varying from 38 to 92 µm [14]. The front-end electronics currently used for the VELO read-out, the BEETLE chip, can accept trigger rates of 1.1 MHz, corresponding to a read-out time of 900 ns [7]. During the first LHC run at the end of 2008, the VELO detector has not been 6

12 moved to its position closest to the beam, in order to prevent radiative damage from the beam during injection. However, after the first 7 TeV collisions in March 2010, the VELO has been closed and it is providing data. 2.3 Requirements for the VELO Upgrade After about three years of data taking, radiation damage will deteriorate the current VELO detector to a level where its performance affects the spatial resolution. At this moment, a replacement VELO will be installed which has the same design as the current detector. When this replacement has also reached its lifetime of three years, an entirely new design will be installed. The upgrade of LHCb is planned for 2016, and in particular the VELO detector will undergo some radical changes. Besides the radiation damage, there are also physics motivations for an upgrade. The following paragraphs will explain the reasons for the changes, and the requirements for the upgrade detector. In the first five years of data taking at LHCb, hints of new physics might be found. However, in order to make significant discoveries and to clarify those discoveries, a large amount of data should be collected. The precision of measurements is always limited by a statistical error which depends on the amount of data collected. Whereas the current luminosity in LHCb will provide a data set of 10 fb 1 in five years, the upgrade will enable us to accumulate a factor 10 more over the next five years. Mere observations made in the initial run will have to be confirmed by the increased statistics from the upgrade. The increase in statistics of LHCb will be achieved by expanding the LHCb luminosity to cm 2 s 1, which is one order of magnitude larger than the current intensity [13], [2]. A higher luminosity increases the average number of interactions per beam crossing from less than one to four. Therefore it demands a stronger method to separate the B-events from the minimum bias events, and to untangle several interactions within one collision. A disadvantage of strip detectors is that a higher number of events increases the occurrence of ghost hits. Figure 2.5 shows how a hit in a strip detector is read out. The two-dimensional hit position can be determined by combining the information of strips in different directions. In the figure, the strips are in the x- and y-direction, in the VELO this would be r and φ. Ghost hits occur when two particles hit the detector simultaneously. Figure 2.5 shows on the left side one hit in the strip detector, and on the right side two hits. For one hit the position can be reconstructed unambiguously, but for two hits this is not the case. The number of ghost hits increases with the square of the number of real hits per plane. At high occupancies, the vertex reconstruction in a strip detector deteriorates. To avoid this problem, it is desirable to switch to a pixel detector in the upgrade. As explained before, a displaced secondary vertex indicates a B-interaction. The vertex positions of both primary and secondary vertices must be determined very accurately to select those B-interactions and therefore the spatial resolution of the upgrade detector needs to be at least as good as the strip detector resolution [2]. 7

13 (a) (b) Figure 2.5: Ghost hits in strip detector. The red dots represent real hits, the white dots represent ghost hits. Currently the L0 hardware trigger reduces the event rate to 1 MHz. However, high luminosity will deteriorate the efficiency and increase the occupancy in the downstream detectors at LHCb. The hardware latency is insufficient to implement the trigger decisions throughout the entire detector [6]. Since the efficiency of the current hardware trigger reduces too much with increasing luminosity, all detectors will be read out at 40 MHz. In order to select B-events, the vertex information from the VELO detector will be used in a software trigger. This makes it possible to benefit optimally from the high luminosity, by including bunch crossings with multiple interactions. Therefore the readout rate of the entire detector will have to be increased from 1 to 40 MHz. An advantage of implementing the trigger in software instead of in the hardware is that it can more easily be adapted to certain physics cases. However, the data rates will be very large, because the trigger will use all the information coming from the VELO to reconstruct all the primary vertices. In particular in the area closest to the beam axis, an estimated data rate of 10 Gbits s 1 cm 2 will be needed to transport all data from the sensors to the CPU farm. Another requirement for the upgrade is the limit on the amount of material which the particles traverse. In order to prevent multiple scattering, the material layers per module should be as thin as possible. Reduction of material thickness is in particular important for the VELO, which is close to the interaction point. Small deflections in the tracks in the VELO can have a large influence on the down-stream reconstruction. This has an impact on the geometry of the modules, the types of material used, the cooling system, and the number of modules. Finally, the current VELO detector will probably stand the radiation dose until it has collected 6 to 8 fb 1 of luminosity. Even after the replacement, this is not enough to survive the luminosity conditions in the upgrade. A better radiation hardness is needed, since the sensor in the inner part of the detector should be able to survive up to n eq cm 2 and the electronics should survive 400 MRad [13]. The detector which will be able to meet the VELO upgrade requirements most easily is a hybrid pixel detector. Section 4.4 will describe in detail why this type of detector, and in particular the Timepix chip, is a good starting point for the upgrade. First, the characteristics of hybrid pixel detectors will be discussed. 8

14 3 Hybrid Pixel Detectors A hybrid pixel detector consists of a sensor (e.g. silicon) which is bump-bonded to an electronics read-out chip. A schematic lay-out is shown in Figure 3.1. The pixels are close to ground potential, and a bias voltage is applied on the backside plane in order to fully deplete the sensor. When a particle passes through the sensor, it releases charges (electrons and holes) along its track in the depletion zone, as can be seen in Figure 3.2. The depletion zone is the part of the sensor in which an electric field is applied, and its thickness depends on the bias voltage and the resistivity of the sensor. A higher bias voltage reduces the capacitance of the sensor and increases the thickness of the depletion zone and therefore results in a higher signal-to-noise ratio. A fully depleted sensor has an electric field applied over the entire sensor thickness. The thickness of the depleted region is given by: W = 0.5 ρ(v + V built in ) (3.1) Where V built in is typically 0.5 V, and ρ is the resistivity of silicon, typically several kωcm [1]. A 300 µm thick silicon sensor fully depletes at about 80 V bias voltage. The signal-to-noise ratio increases with bias voltage until it reaches a limit at about 2 to 3 times the full depletion voltage. In a silicon sensor, one electron hole pair is liberated per 3.6 ev energy deposit. The released charges (electrons or holes, depending on the polarity of the field) subsequently drift towards the electronics chip. The drifting charges induce a signal in the pixels which can be read out per pixel. Figure 3.1: Hybrid pixel detector lay-out [17]. Since most of the tests in this research have been performed with a 300 µm thick p-on-n silicon sensor, the following characteristics hold for this type of sensor. 3.1 Energy Loss The energy loss in matter of relativistic charged particles heavier than electrons is caused mainly by ionisation and atomic excitation. The mean rate of energy loss is 9

15 Figure 3.2: Particle passing through a hybrid pixel detector [17]. described by the Bethe-Bloch equation [1]: de dx = Z [ 1 1 Kz2 A β 2 2 ln2m ec 2 β 2 γ 2 T max β 2 δ(βγ) ] I 2 2 (3.2) Given in MeV g 1 cm 2, with the following variables[17]: K = 4πN Av r 2 em 2 c 2 = 0.307MeV cm 2 A atomic mass of absorber (28 for Si) Z atomic number of absorber (14 for Si) ze charge of incident particle (-1 for electron) β velocity of particle in units of speed of light γ = 1 β 1 Lorentz factor 2 m e c 2 = 0.511MeV electron rest energy 2m T max = ec 2 β 2 γ 2 1+2γm e/m+(m e/m), the maximum kinetic energy which can be transferred 2 to a free electron with a single collision, by a particle with mass M. For heavy particles, the linear and quadratic term in the denominator can be neglected. I mean excitation energy in ev (173 ev for Si) δ(βγ) density effect correction to the ionisation energy loss 10

16 Figure 3.3: Bethe-Bloch equation solved for different materials. Figure 3.3 shows the Bethe-Bloch equation solved for different absorption materials. The 1 term in 3.2 is dominant for low particle energies, so the energy loss β 2 decreases with increasing energy. A minimum is reached at βγ 3, or a particle velocity β = 0.96c. A particle with an energy loss in this minimum is called a minimum ionising particle (MIP). At higher energies, the energy loss rises due to the logarithmic term, but the density correction term eventually flattens the energy loss. For a MIP, the minimum ionization energy amounts to 1.7 MeVg 1 cm 2 = 3.9 MeVcm 1. To characterise the sensor of a pixel detector, the number of electron-hole pairs liberated by a relativistic minimum ionising particle should be known. This can be calculated using the energy needed for ionisation of one electron-hole pair, which is 3.6 ev for silicon. Dividing the energy deposit by the ionisation energy gives the number of e-h pairs, which for a fully depleted 300µm thick silicon sensor amounts 11

17 to 24000, or 80 pairs per micrometer [17]. Since the Bethe-Bloch equation only gives the mean of the energy loss in matter, it is worthwhile to look at the energy loss distribution, also called the Landau distribution. An example of a Landau distribution of the beam test data is shown in 5.3. The average value of the Landau is higher than the most probable value, due to the tail. The most important cause for Landau fluctuations is the presence of δ-rays, which are electrons that have sufficient energy to become ionising particles. δ-rays degrade the spatial resolution of the detector. Another effect which deteriorates the resolution is multiple scattering. This is the deflection of a charged particle due to Coulomb interactions with the nuclei in the absorption material. This is of importance for low particle energies and thick material layers. Since the beam test experiment does not suffer from multiple scattering due to the high energies of the particles, this effect will not be considered any further. Most of the electron-hole pairs are liberated up to a few micrometers around the particle track. Subsequently, either the electrons or the holes (depending on the polarity of the field) will start drifting toward the readout chip. The speed at which they travel depends on the bias voltage. For a bias voltage of 100 Volts across a 300 µm sensor, the electrons will be collected in less than 10 ns, whereas the holes take approximately three times longer. 3.2 Diffusion and Angled Incidence A single particle can lead to a signal in multiple pixels due to diffusion and due to the incidence angle of the particle. These processes will prove to be very important to understand the results of resolution studies. Due to random thermal motion, diffusion takes place during the drift of the liberated electrons or holes towards the electronics readout chip. The spread in position due to diffusion is a Gaussian distribution with standard deviation [17]: σ = 2Dt = 2 35 cm2 s s 3µm (3.3) where D is the electron diffusion constant and t is the drift time. The distance over which diffusion takes place is equal to about 3 times this standard deviation, so 3µm 3 9µm. If a hit occurs at the edge of a pixel (within those 9µm), a cluster of hits can be formed due to diffusion. Using Figure 7. 2(b) the region of diffusion in a chip with a 300 µm thick silicon sensor can be determined for the beam test experiment. Hits which occur up to about 12µm from the edge of the pixel still result 2-pixel clusters. The position of the clusters in Figure 7. 2(b) is determined by the track through the telescope. The error on this value caused by the uncertainty in track position is about 2.3µm. The diffusion width agrees with to the predicted value. A different effect takes place if a particle enters the detector under an angle. In this case, multiple pixels are hit directly, and a cluster is formed. The number of 12

18 pixels that are hit depends on the angle of the particle trajectory and on the sensor thickness. The angle which provides the best resolution depends on the thickness of the silicon sensor and on the pixel pitch as follows: pitch optimalangle = arctan[ thickness ] (3.4) For a 300 µm thick sensor and 55 µm pitch this results in a 10.4 degree angle. This is the angle at which the particle traverses the pixel from one corner to the other in a diagonal way. In theory this means that all the clusters will consist of 2 pixels. However, diffusion must also be taken into account. Hence the optimal angle will be smaller, since two-pixel clusters will be formed at a smaller angle of incidence due to the spread of the diffused charges. 13

19 4 Timepix Chip Currently the most promising technology for the VELO upgrade is a hybrid pixel detector, using front end electronics similar to that of the Timepix chip which is developed by the Medipix collaboration [12], [11]. Timepix is a pixel detector readout chip with a dimension of 14 x 14 mm. It consists of 256 x 256 square pixels of 55 µm, and can be bump-bonded to several types of sensors (e.g. silicon or diamond). Every pixel in the Timepix chip can be configured in one of three operation modes. These are the time over threshold (ToT), time of arrival (ToA) and counting mode. The latter is a single photon counting mode, which increments a 14-bit counter by one for each hit above a certain threshold. The counting mode will not be discussed any further, because it will not be used for the VELO upgrade. For the two other modes, the time is measured by a reference counting clock which is generated by an external clock. This reference clock is distributed within 50 ns throughout the pixel matrix in an alternating phase between columns. It can be set to various frequencies up to 100 MHz. Figure 4.1: Timepix chip board with silicon sensor. The Timepix chip contains an analogue and a digital part, which have a power consumption of respectively 440 mw and 450 mw, for a reference clock frequency of 80 MHz. To facilitate tiling the chip, the circuit is placed at one side of the chip, leaving three sides which have less than 50 µm non-sensitive distance between the pixels and the physical edge of the chip. The digital part contains wire-bonding pads and the control logic for input and output. The analogue part of the chip has 13 global digital to analog converters (DAC), of which eight are 8-bit current DACs, and four are 8-bit voltage DACs. A summary of some of the DACs and the corresponding current or voltage range is shown in Table 4.1. There is a linear voltage DAC which sets the threshold (THL) using 14 bits. This DAC is split in an overall threshold setting of 10-bit, and 4-bit for adjustments of the threshold for each individual pixel. In this way, variations between pixels can be equalised [10]. 14

20 DAC Range Bits Ikrum 0-40nA 8 Disc µA 8 Preamp 0-2µA 8 THL V 10+4 Table 4.1: Summary of the digital to analogue converters of the Timepix chip All individual pixels are also divided into an analogue and a digital area. Figure 4.2 shows the block diagram of a Timepix pixel cell. The analogue part contains a preamplifier, discriminator and the 4-bit threshold adjustment. The digital side of the pixel consists of the counting logic, synchronisation logic for the reference clock, overflow control logic, a buffer and a pixel configuration register for setting the acquisition mode and the threshold equalisation. The synchronisation logic has three operation modes (counting, ToA and ToT) which can be set by the configuration bits P0 and P1. In order to use the chip in a high-energy physics experiment, the characteristics for different operation modes should be well-known [11], [10]. The ToA and ToT modes which are important for the VELO detector will be discussed next. Figure 4.2: Timepix pixel block diagram [9]. 15

21 (a) Time over threshold (b) Time of arrival Figure 4.3: Timepix modes for a high and a low input charge. 4.1 Time over Threshold Mode The time over threshold (ToT) mode depicted in Figure 4.3 (a) measures the time that the signal in the pixel is above a certain threshold energy. This is an indirect measurement of the amount of charge deposited in the pixel. A high input charge will result in a larger ToT value (T2 in Figure 4.3 (a)) than a low input charge (T1). The discriminator digital to analogue converter determines whether a signal is over threshold or not. The threshold (THL) DAC determines the height of the threshold, and therefore the width of the pulse. A typical threshold is about 50 DAC ( 1250e ) above the noise mean. The ToT range is 14 bits or counts. The resolution of the ToT measurement is determined by the frequency of the counting clock, which can be up to 100 MHz. The shape of the pulse is highly influenced by the settings of the digital to analogue converters [10]. The Ikrum (Krummenacher current) DAC determines the slope of the falling edge of the signal pulse. A high Ikrum current decreases the length of the falling edge, because it enables a faster discharge. A higher Ikrum current decreases the pulse width for a given input signal. Furthermore it decreases the pulse height a little. The preamplifier current influences the rise time of the pulse. A small preamplifier current decreases the rise time, which can vary from 90 to 180 ns. It is important to know how the time over threshold value corresponds to the actual charge deposit in the pixel. As illustrated in Figure 4.4, tests proved linearity from 3-4 ke above threshold up to 40 ke. Values above 40 ke could not be measured directly because of the limited test pulse range, but simulations showed that the ToT is linear from an input charge of 3-4 ke above threshold up to 200 ke, as can be seen in Figure 4.5 [11], [9]. 4.2 Time of Arrival Mode For the time of arrival mode, depicted in Figure 4.3 (b), the clock counter is incremented from the moment the signal goes over threshold until the shutter is closed or until it reaches counts, the limit of the dynamic range of the 14-bit counter. 16

22 Figure 4.4: Measured Timepix ToT versus input charge for different threshold values [11]. The so-called timewalk effect affects the ToA measurements in the beam test data, and it is vital for the VELO upgrade to keep the timewalk as low as possible. Therefore this effect will be discussed in detail in this section. The results of the beam test ToA measurements will be analysed in Section 8.1. As shown in Figure 4.3 (b), a high input charge passes the threshold earlier than a low input charge. Timewalk (TW) can be defined as the difference between the time measured from an input charge that is 1ke ( 0.018V) over threshold and that of an infinite input charge. The timewalk effect is clearly visible in clusters of pixels made by a single passing particle, where pixels receiving only a small signal will have a later time of arrival than the central pixel. In order to have a good timing resolution, this effect should be minimised. In case of the VELO upgrade for example, it is essential to distinguish between bunch crossings which are 25 ns apart. If the timewalk is too large, it can happen that the timestamps of clusters from subsequent bunchcrossings overlap, and reconstruction becomes extremely difficult. If the magnitude of the timewalk is known, a correction can be applied per pixel by using the ToT value. However, the current version of the Timepix chip can only measure either ToA or ToT, which makes it impossible to correct for the timewalk. The specified mean timewalk value for Timepix is 25 ns, with a maximum timewalk of 50 ns if the preamplifier DAC setting is large enough, namely Preamp=1.8µA (255 DAC). A high preamplifier current results in a fast risetime of the pulse, so the difference in time of arrival between large and small charges will be small. The timewalk has been investigated in a set-up using test pulses, in order to study 17

23 Figure 4.5: Simulated Timepix ToT versus threshold for different Ikrum values. the influence of different DAC settings on the timewalk. Figure 4.6 shows the results of a run with test pulses, of which the settings are the ones that have been used for the device under test in the 2009 test beam telescope (shown in Table 5.1). The time of arrival values shown in this plot are the average values over all pixels in the chip. Bad pixels were not masked in the Pixelman data acquisition software, but in the analysis software, by eliminating pixels with zero-values. To measure the timewalk, the ToA of an infinite input charge should be compared to the ToA value of a charge which is 1ke over threshold (THL). To find the THL, the input test charge was lowered until more than one per cent of the pixels in a frame did not detect a charge. This pulse was defined as the lowest measurable charge, since the pulse has fallen below the threshold of those pixels. In Figure 4.6, an infinite input charge gives ToA = ns. The lowest ToA corresponds to a testpulse voltage of V, which can be defined as the lowest measurable point or threshold. Adding 1ke (0.018V) gives a ToA value of ns, from which the timewalk can be determined: ns. Due to uncertainties in the measurement and to variations between pixels, the THL across the entire pixel matrix can actually be lower than the value found (when the pulse falls below the THL in one per cent of the pixels). A lower THL would result in a larger timewalk. That is why this method only gives a lower limit for the timewalk. Similar measurements have been repeated with different DAC settings: The VDDD has not much influence on the timewalk value. A higher preamplifier DAC results in a faster risetime, causing the timewalk to decrease. A high Ikrum decreases the pulse width and therefore determines the time of 18

24 Figure 4.6: ToA mean over entire chip versus testpulse voltage for Ikrum=5, Disc=127, Preamp=255, VDDD=2.2V. threshold crossing more precisely. If the height of the signal is close to the threshold value, high Ikrum causes less distortion of the signal, and the arrival time can be determined more accurately. However, a too large Ikrum current decreases the pulse height, and pulls the entire signal under threshold. This happens for charges smaller than 0.1V ( 5ke ) at Ikrum 40 DAC. For minimum ionising particles (25ke ) however, this causes no problems at least up to Ikrum 30 DAC. From the test pulse measurements, the most favourable DAC settings for the time of arrival mode were determined to be: Ikrum=30, Disc=105, Preamp=255, VDDD=2.2, resulting in a timewalk 52ns. This value does not significantly exclude the specified maximum timewalk, 50 ns. However, similar measurements done with laser pulses gave a much larger timewalk value. Figure 4.7 shows the difference between the timewalk of the laser and of testpulses [4]. The measurements of ToT and ToA have been done separately for varying test pulse height or laser intensity. The plot shows that the ToA of the laser differs much more than the test pulse ToA. An explanation for this discrepancy between test pulses and other measurements has not been found yet. The analysis later on will show that the timewalk in the test beam data is also much larger then expected. 19

25 Figure 4.7: ToA versus ToT for laser measurements and test pulse measurements (plot by A. Borgia) [4]. 4.3 Readout and Data Acquisition Several readout systems exist for the Timepix chip. The readout device used for the 2009 beam test was the USB1 interface [20] (frame rate 4 Hz) developed in Prague CTU. In 2010 the USB2 system [16] was used, which enabled faster readout than the USB1. The frame rates in the beam test were smaller than the specifications, and reached about 2 Hz for the USB, and 5 Hz for USB2. A newly developed readout system is ReLaXd (High REsolution Large Area X- ray Detector) [21]. The data output of the future VELO detector is too large to be handled by the USB readout system. This system is sufficient for a single chip at low frame rate, but not for multiple chips tiled together. The ReLaXd module has been developed for the purpose of reading out a Quad Board of four Timepix chips. It transfers data through an ethernet link, and allows for a large data throughput (1Gbit s 1 ). The ReLaXd board will be able to transfer the data of at least four chips in parallel, with a readout time of 5 ms. The frame rate of ReLaXd in recent measurements was 30 Hz. The Pixelman software [8] is the common user interface to control the Timepix chip, and to store data of the pixel matrix. It provides a preview window, and writes the data to an ASCII file. Furthermore all the DAC settings, like threshold and bias voltage, can be controlled through the Pixelman software. The software also provides the possibility to perform a threshold equalisation of the chip, such that the threshold 20

26 is uniform over the entire pixel matrix. 4.4 Timepix for VELO There are various reasons why the Timepix detector seems a good starting point for the VELO upgrade. The main requirements for the VELO can be summarised as follows: Good spatial resolution (5-10 µm) in order to distinguish between primary and secondary vertices. Ability to distinguish between multiple interactions per LHC bunch crossing Good timing resolution (<25 ns) to distinguish between LHC bunch crossings Process large amount of data (10 GBit/s/cm 2 for the innermost region) Radiation hardness (400 MRad for the electronics, n eq /cm 2 for the sensor in the innermost region) Thin detector planes to reduce multiple scattering in the detector material All of these topics need to be investigated more thoroughly in order to decide whether Timepix is indeed the best solution for the upgrade. The current research focusses on the timing and spatial resolutions, which will be discussed in detail in Section 7 and Section 8. Also the possibilities to reduce the data rate by rebinning the time over threshold information will be investigated. The other requirements will be discussed shortly in the following paragraphs. Firstly, a pixel detector can distinguish between multiple interactions within one event. This is not the case for a strip detector, where ghost hits will deteriorate the position measurement. Therefore a pixel detector is preferred over a strip detector for the upgrade. The data rate which the Timepix chip can process depends on the readout device. At this moment the fastest readout device which can handle the highest data rate is the ReLaXd device. In order to meet the VELO requirements however, more research is needed in this area. The next requirement is radiation hardness. A strip detector needs to be cooled in order to stand a high radiation dose. The hybrid pixel detector is able to stand a higher dose with less cooling. Results from irradiation tests with the Medipix3 chip (similar to the Timepix chip) have shown that the chip can survive an integrated dose of 460 MRad [15]. Finally, the thickness of both the chip and the sensor needs to be minimised. The 2009 beam test has been performed using 300µm thick silicon sensors, but also thinner sensors (150µm) are studied in current beam tests. The current chip board is mm thick, but this could also be reduced. 21

27 One remaining issue is the area of the chip. The active area of a module for the VELO upgrade will be larger than a single Timepix chip which has an area of 1.98 cm 2. Therefore the chips will have to be tiled in a geometry which surrounds the collision point. The detector planes will have to consist of two halves which can be pulled away from the beam axis, similar to the current VELO design. The tiling of four chips has already been performed, so tiling more chips together will be possible, although research on reduction of the dead area between chips is still ongoing. Currently the Medipix collaboration is working on the design of Timepix2, an upgrade of Timepix. Several new specifications will be beneficial for the VELO. For example sparse data readout, simultaneous ToT and ToA measurements, and a low power consumption. The pixel detector which will eventually be used in the VELO upgrade, the Velopix, will be a successor of the Timepix2. 22

28 5 Timepix Beam Test 2009 In order to examine the properties and the performance of the Timepix chip, it has been installed in a beam telescope in the 120 GeV pion SPS beam at CERN in August 2009 for a period of two weeks. The purpose of a beam tracking telescope is to provide high accuracy tracking information. A device under test (DUT) can be placed in the beam telescope in order to determine for example the spatial resolution of this device. 5.1 Telescope Figure 5.1: Sketch of the Timepix-Medipix telescope 2009, showing the detector names and types, and the direction of rotation of the device under test. The beam telescope consisted of four Timepix and two Medipix devices, all installed with angles of 9 degrees with respect to both their row- and column-axes, as shown in Figure 5.1. This geometry resulted in cluster sizes of two to three pixels, which improved the tracking resolution of the telescope, as will be explained in Section 7.2. The distance in the beam direction z between all devices was 80 mm. The device under test was placed in the centre of the telescope, and could be rotated by a stepper motor around its column axis (the vertical y-axis with respect to the beam). The sensors bonded to the chips were 300µm thick silicon. Multiple runs were taken for different DUT angle, threshold and sensor bias. The acquisition mode of the DUT could be configured in either ToT or ToA mode. To achieve the optimal beam telescope resolution the telescope Timepix devices were always in ToT mode. Since the two Medipix devices could not measure ToT, they were always in counting mode. The reference clock frequency was 40 MHz. This set-up allowed for resolution, voltage, threshold and timewalk measurements. The pion beam of the SPS provided one 10-second spill per 45 seconds. The telescope shutters were opened every spill by means of a trigger provided by coincidence 23

29 Figure 5.2: Timepix-Medipix telescope 2009 hits in two scintillators, one at the beginning and one at the end of the telescope. In order to be able to reconstruct the tracks in the telescope, the gate time was set such that about 100 tracks passed the active area of the telescope. Since no further triggering system was present, the shutter was opened for a fixed amount of time, followed by a fixed time delay for readout. The gate time was set by adjusting the acquisition time in the Pixelman software. All assemblies were read out using USB1 devices. The readout frequency achieved with these devices was in the order of two frames per second. Every spill provided about 20 frames, and on average a thousand frames were taken per run. The total amount of data consisted of 200 runs, or approximately 20 million tracks. The setup was controlled through a PC running the Pixelman software. The digital to analogue converter (DAC) settings used for the DUT in the resolution runs are shown in Table 5.1. The data acquisition happened also in the Pixelman software, which stored the raw data on disk. This data consisted of ASCII frames of 256x256 values, and for each frame a description file with information on the DAC settings, the clock frequency and the name and type of the chip. 5.2 Energy Loss Distribution The expected energy loss distribution has a Landau shape as described in Section 3.1. Figure 5.3 shows the time over threshold distribution of clusters in the device under test, which is indeed a typical Landau distribution. The most probable value is 135 ToT counts, which (for a 40 MHz reference clock) corresponds to 3.4µs. As a 24

30 Ikrum Disc Preamp THL Bias voltage TPX clock TPX mode 5 DAC ( 3nA) 127 DAC( 0.8µA) 255 DAC ( 1.8µA) 400 DAC 100V 40 MHz ToT Table 5.1: Setting for the device under test in the resolution runs in the 2009 beam test cross-check, this value can be compared to the energy deposit of a minimum ionising particle traversing 300 µm of silicon. A MIP liberates on average approximately electron-hole pairs in this type of sensor [3]. Figure 4.5 plots the simulated ToT width versus the charge deposit. The Ikrum value used in the beam test is 3nA, which is not shown in this diagram. Extrapolation predicts that line for 3nA has an even higher slope than the line for 5nA. A charge deposit of 24 Ke is estimated to correspond with a ToT width of 3µs, which is in agreement with the energy loss distribution in the test beam of 3.4µs. Figure 5.3: Total ToT count per cluster for DUT at 0 degree angle. 25

31 6 Analysis Software After the telescope data is stored to disk by the Pixelman software, it is zerosuppressed, and the hit information of each frame is stored as an event in a ROOT file by the analysis software environment. The following sections describe the software framework used to analyse the telescope data. Clustering, tracking and alignment are major ingredients for resolution studies, and will be explained in detail. Some improvements that have been made in the software are mentioned here. The linear gain correction, the eta correction and the rebinning procedure will be discussed in separate sections. 6.1 Clustering The first task of the analysis software is to form clusters per detector plane. This can happen either in a binary or an analogue way. The binary reconstruction will be discussed in Section 7.1. The current section will explain the most straightforward way to reconstruct clusters using the time over threshold information, with the centre of gravity method. In order to reconstruct the clusters in the software, each frame is searched for the first hit (non-zero value). Next, adjacent hits in a 3x3 pixel surface around the first hit are added to the cluster. Subsequently, the centre of the cluster is determined, by weighting the position of a hit by its time over threshold value: x centre = N T ot i x i i=1 (6.1) N T ot i Where N is the cluster size, and i are the pixels in the cluster. This centre of gravity method assumes that the position depends linearly on the charge ratio in the pixel, and it results in analogue position reconstruction. Clusters which have a width of more than eight pixels in one direction only and a width of one pixel in the other direction are not considered, since they are probably delta rays which would deteriorate the resolution measurement. Multi-pixel clusters form due to diffusion and the incidence angle of the particle. There are several scenarios possible when a particle traverses the detector. In Figure 6. 1(a), the particle enters close to the centre of the pixel. The small arrows denote the drifting charges, and the green block gives an indication of the charge deposit in the pixel. In this case, all charge is deposited in one pixel, and the position is always reconstructed exactly in the pixel centre. In the second case shown in Figure 6. 1(b), the particle passes close to the edge of the pixel. Because of the diffusion of the charges when drifting towards the readout chip, a small amount of charge will be deposited in the neighbouring pixel. A cluster of hit pixels will be formed, which 26 i=1

32 (a) Single hit (b) Diffusion (c) Angled incidence Figure 6.1: A particle traversing a pixel detector. enables us improve the position determination by weighting the position with the centre of gravity method. The third case in Figure 6. 1(c) shows a particle which enters the detector under an angle, such that multiple pixels are hit directly by the particle. In this case, due to the centre of gravity method, the position is reconstructed at half the sensor thickness. Figure 6.1 shows the cluster size for different angles of the device under test. It is clear that the larger the DUT angle, the larger the average cluster size. Figure 6.2: Percentage of clusters per size per DUT angle. 27

33 6.2 Alignment Since the positioning of the seven detector planes can never be perfect, the relative alignment of the planes is essential for the reconstruction of tracks. The DUT needs to be aligned after every run (after DUT rotation, or any other possible movement of the detector planes), so it is useful to have a software-based alignment which can be rerun for every data run. The alignment of the telescope is based on minimising the chi-squared function of straight tracks through the different telescope planes. Figure 6.3 shows the clusters in all the telescope planes in different colours, with straight tracks fitted through the clusters. The track pointing error is estimated to be 2.3µm in simulations. Figure 6.3: Overview of the different telescope planes with fitted tracks. This shows one acquisition during the beam spill, containing multiple tracks. 6.3 Tracking The next stage in the analysis is track reconstruction. For this step, only straight tracks which pass through all telescope planes are considered. Since there is no magnetic field applied, curved tracks can be ignored. Also multiple scattering in the telescope can be ignored because of the high momentum of the pions in the beam (120 GeV). The clusters per plane are used as input to the track fit. Clusters which lie within a search window of 50 µm in both the x- and y-coordinates and which occur in all telescope detectors are used to create a proto-track with associated clusters. Next, the track coordinates are obtained by fitting a track through the proto-track clusters in all planes except for the device under test. The track fit is described by: f(a, b; z) = az + b. (6.2) When comparing the intersection point of this track in the DUT plane with the position of the closest cluster in the DUT, the unbiased residual is obtained. The width of this residual distribution is the resolution of the device under test. In order 28

34 to get a better understanding of the different detector planes, the unbiased residual of every telescope plane is shown in Table 6.1. This analysis is performed over about tracks. These residuals are obtained by omitting all planes from the track fit one by one. Each row gives the resolutions in each plane, where the number in red is the unbiased plane, and the six others are biased. For example, for the first row, the track fit is performed over detector K05 until E05, whereas C03 is unbiased. The bottom row shows the resolutions for a fit through all detectors. It is clear that the two Medipix planes (I02 and K05) have a significantly worse resolution than the Timepix planes. This is no surprise, since the Medipix planes cannot measure ToT. Furthermore, the two outer Timepix devices (C03 and E05) have a worse unbiased resolution than the three middle detectors. The biased resolution of C03 and E05 on the other hand is better than in the middle Timepix planes. Unbiased: C03 K05 D09 D04 M06 I02 E05 C03 9.1± ± ± ± ± ± ±0.023 K05 3.5± ± ± ± ± ± ±0.028 D09 3.5± ± ± ± ± ± ±0.028 D04 3.7± ± ± ± ± ± ±0.018 M06 3.9± ± ± ± ± ± ±0.024 I02 3.9± ± ± ± ± ± ±0.026 E05 3.3± ± ± ± ± ± ±0.062 none 3.9± ± ± ± ± ± ±0.028 Table 6.1: Unbiased resolution[µm] (in red) per detector plane for the DUT angle 10 degree There are several ways to improve the track fit. Table 6.2 lists some (combinations of) improvements, and the right column shows the result they had on the DUT resolution. The Timepix devices have a significantly better resolution than the Medipix devices, because the unlike the Medipix devices, Timepix measures the charge deposit through the time over threshold value. Therefore a first option is to exclude the Medipixes from the track. The result is that the DUT resolution improves, as can be seen in Table 6.2 when comparing the second (TPX) with the first (TPX+MPX) row. An even better option is to include the two Medipixes, but to weight each device by its resolution (TPX+MPX weighted). Another improvement was made on the z- alignment of the devices. Initially the distances between the planes in the alignment input which is used to determine the alignment parameters did not agree with the real distances. Instead of ( mm) the values used were ( mm). This correction also improved the resolution. The third improvement, an eta correction (which will be explained in Section 7.3) ameliorates the resolution even more, until a final improvement of 0.7µm is achieved with respect to the original DUT resolution. 29

35 z-alignment trackfit eta corr DUT resolution [µm] old TPX+MPX no old TPX no old TPX+MPX weighted no new TPX no new TPX+MPX weighted no new TPX yes new TPX+MPX weighted yes Table 6.2: Summary of various improvements made in the track reconstruction for DUT angle 10 degree 7 Spatial Resolution The spatial resolution is measured by comparing the telescope track with the reconstructed position in the device under test. The width of a Gaussian fit over the residual of those values provides the unbiased resolution of the DUT. An example of such a residual plot is shown in Figure 7.1. Figure 7.1: Residual for 10 degree DUT angle, with Gaussian fit. The fit parameter sigma is the resolution. The position of the centre of a cluster in the device under test can be deduced from the data in several ways. The first is to use a binary cluster reconstruction. In this case the only available information is whether a pixel was hit or not. The cluster centre is always reconstructed in the geometric centre of the cluster. Although this method has limited accuracy, it is important to know the binary accuracy of the chip, as described in Section 7.1. A second option is to use the time over threshold values to weight the position by the charge deposit per pixel. An analogue reconstruction by means of the centre of gravity method will be discussed in Section 7.2. This section 30

36 will also cover the rebinning of time over threshold values in order to reduce the data rate and dead time in the chip. In addition there are correction factors which might improve the spatial resolution. The first is the eta correction (Section 7.3), which improves the reconstruction of the position with respect to the centre of gravity method. The second method, which will be discussed in the Section 7.4, is a linear gain correction which corrects for non-linear behaviour of the time over threshold gain of the chip. 7.1 Binary Spatial Resolution Although a binary reconstruction is less accurate than an analogue one, binary readout might be preferred for the VELO upgrade for several reasons. Firstly it would reduce the data rate, which is already very high with interactions at 40 MHz. It would also shorten the dead time of the pixel, which is beneficial at high occupancies. Furthermore, the signal to noise ratio decreases after irradiation, which would make the centre of gravity method less effective in the long run. The analogue reconstruction using the centre of gravity method is maintained in the telescope planes which are used for tracking. What should be noted here is that there is no lower threshold applied in the software. The hardware THL in the chip is high enough to exclude noise hits. The cluster size (which influences the binary resolution) depends on the threshold. A low threshold results in large cluster sizes since pixels with little charge deposit are also included in the cluster. The dependence of the binary resolution on the threshold has not been studied here. (a) 1 pixel cluster (b) 2 pixel cluster (c) 3 pixel cluster Figure 7.2: Location of centre of cluster in a pixel for different cluster sizes. The binary resolution for single hits depends on the size of the pixel, and is given by the standard deviation of a distribution over the pitch interval [19]: res = 1 12 pitch = = 15.88µm. This formula does not take into account diffusion and the incidence angle of the particle. In order to compare the data with this prediction, it is easiest to split the data 31

37 in categories of cluster sizes. Figure 6.1 shows the distribution of cluster sizes for different angles of the device under test. Single-pixel clusters For 1-pixel clusters at 0-degree angle, diffusion is predicted to occur over a distance up to 10µm, as explained in Section 3.2. This means that there are no true hits in the area close to the edge of the pixel, since if there were, the cluster would become 2-pixel sized. Figure 7.2 illustrates this by showing the position of the charge deposit of each cluster within a pixel, at perpendicular incidence. The analysis has been performed over tracks. The figure shows that single pixel clusters are positioned in the centre of the pixel, two pixel clusters at the edge, and three pixel clusters in the corners. This distribution over the pixel is exactly what is expected for a perpendicular particle track. The result of the diffusion is that the effective pitch becomes smaller. For a diffusion width σ diff = 3µm (see Section 3.2), the total spread is about 3σ diff = 9µm. Since diffusion occurs at both ends of the pixel, the effective pitch 35 becomes approximately 37µm, resulting in a binary 1-pixel resolution of 12 = 11µm. This value is confirmed by the measurement of 10.6 µm in Table 7.1. The 10 degree single-pixel resolution is much better than the one at 0 degree. The reason is that the region of charge spread is increased due to the tilt of the device, such that the effective pitch decreases. It should now be clear why the resolution found in the data is better than the 15.8µm calculated at the beginning of this section. Furthermore it can be concluded that for single hits, an analogue and a binary reconstruction have equal resolutions, as expected. cluster size analogue 0 deg[µm] binary 0 deg analogue 10 deg binary 10 deg 1 hit hits hits hits total Table 7.1: Binary and analogue resolutions for 0- and 10-degree angle 2-pixel clusters For perpendicular incidence, the multiple-pixel clusters are caused mainly by diffusion. Because this effect has a range of about than 10µm, the true hit position is close to the edge of the pixel. Binary reconstruction places the hit always at the border between the two pixels, which happens to be close to the true position. The 2-pixel binary = 5.8µm. In the measurement this is 9.4µm. The reason for this discrepancy might be that the tracks do have a small angle with respect to the DUT. In that case diffusion is not the only cause for multiple-pixel clusters, and the resolution will get worse because of effects resolution due to diffusion should amount to approximately 20µm 12 32

38 of angled tracks as explained next. The multiple-pixel clusters at larger incident angles are mainly caused by the trajectory of the particle through several pixels. The true position is not restricted to the edge of the pixel as in the case of diffusion. Therefore the binary reconstruction, which places the position always in the middle of the cluster, will give a worse resolution at large angles than at perpendicular incidence. This explains why in Table 7.1 the 2-pixel 10 degree angle (with 2-pixel clusters mainly due to the incidence angle) has the worst binary resolution. 3-pixel clusters The 3- and 4-pixel clusters at 0 degree angle benefit from similar advantages due to diffusion, since a hit must fall in the corner of a pixel such that the charge can reach the two or three adjacent pixels. The more pixels per cluster, the more accurately the position can be reconstructed, in both the binary and the analogue case. To summarise, the binary resolution of the chip can be accurately predicted. Furthermore diffusion is a very important and beneficial factor for position reconstruction. 7.2 Centre of Gravity The most straightforward cluster reconstruction method which uses the time over threshold information is the centre of gravity method. The resolution found using this method is influenced by the pixel size and the angle of incidence of the beam. The dependence on the pitch is already shown in Section 7.1. The best resolution will be found at an angle which provides most 2-pixel clusters, as explained in Section 3.2. It is expected that the best resolution angle will be at about 9 degrees. Figure 7.3 shows the resolution as a function of the rotation angle of the device under test. Since the rotation is around the column(y) axis, the resolution shown here is that in the x- direction. The resolution indeed strongly depends on the angle under which the device under test is placed in the beam. The angles close to zero contain mainly single-pixel clusters which give a poor resolution. For larger angles, single-pixel clusters would be more beneficial because of the reduced effective pitch, but unfortunately they have less influence in that case since they provide only a small percentage of the clusters. For larger cluster sizes, the analogue resolution improves, since the charge deposit in the pixels allows a more accurate determination of the cluster centre. The best analogue resolution is achieved with a detector angle of about 8 degrees with respect to the beam axis, where the average cluster size is two pixels. At this angle the cluster size resulting in a good resolution is optimally combined with the occurrence of this cluster size. The resolutions given in Figure 7.3 consists partially of the track extrapolation uncertainty, due to the limited resolution of the telescope planes. For this setup, with two Medipix (binary) and four Timepix (analogue) devices used for the track fit, the track resolution amounts to approximately 2.3µm. By quadratically subtracting the 33

39 Figure 7.3: Analogue resolution (centre of gravity method) of the local x coordinate versus DUT angle. track uncertainty from the measured resolution, an intrinsic resolution of 4.4µm is obtained. A final remark concerns the y-resolution. So far only the x-resolution has been discussed, since the device under test is rotated around the x-axis only. The resolutions in the y-direction should remain constant, and the difference between those resolutions lies indeed within 1.5 µm. The average resolution is about 10 µm, which is exactly what is expected for a 0-degree angle. Currently the precision of the time over threshold values only depends on the clock frequency of the Timepix counter in combination with the Ikrum setting which influences the falling edge of the pulse. The period of each reference clock in the test beam experiment is 25 ns. The maximum number of bits that can be used is 14. Artificial reduction of the number of available bits to 1,2,3 and 4 was applied within the software, in order to study the effect on the spatial resolution. The most probable value for the amount of e-h pairs which a minimum ionising particle liberates when traversing the detector is approximately 24000, corresponding to a ToT count of about 125. When rebinning the ToT values, this should be taken into consideration, since the majority of the hits falls within ToT. The following division has been applied for the time over threshold values of the device under test: 1bit: discard all ToT information, all ToT count >0 are placed in one bin. 34

40 2bit: bitvalue = int( value ), all ToT count 94 are placed in the highest bin. 125/4 3bit: bitvalue = int( value ), all ToT count 218 are placed in the highest bin. 250/8 4bit: bitvalue = int( value ), all ToT count 234 are placed in the highest bin. 250/16 Figure 7.4: Resolution versus number of bits for various angles (value 6 = analogue). Figure 7.4 shows that, as expected, the resolution improves as the number of available bits increases. The difference in resolution between the 14-bit and the 4-bit data is never larger than one micron, so a reduction of available bits may be a good option to reduce the data rate and the dead time of the detector. Binary output deteriorates in particular the 10 degree incidence angle. Since this angle provides the optimal resolution, the 2,3 or 4-bit option is preferred in this case. 7.3 Eta Correction The centre of gravity method, which is used to improve the reconstruction of the position by weighting the position with the charge deposit per pixel, assumes that the position is a linear interpolation of the charge distribution between a pixel and its neighbour. However, this method is not optimal if diffusion is the main cause for charge spread, i.e. at small incidence angles. Figure 7.5 illustrates what happens at small incidence angles of the traversing particle. If it enters exactly in between two pixels, an even amount of charge is deposited in both pixels. The position will be reconstructed on the border of the two pixels. If the particle hits the edge of one pixel, some charge will be deposited in the neighbouring pixel. The centre of gravity method improves the resolution with respect to a binary reconstruction. However, when the particle is at a distance from the edge where the diffused charge does not reach the neighbouring pixel anymore, it 35

41 will always be reconstructed in the centre of the pixel. Therefore the relation between position and charge deposit is not linear, but it is a non-linear s-curve, as shown in Figure 7.6. Figure 7.5: Charge diffusion for particles passing at different positions in the pixel. The size of the blocks represents the amount of charge deposited in a pixel. Figure 7.6: The relation between reconstructed position and charge ratio between a pixel and its neighbour. On the left the centre of gravity method, on the right the η-correction. As an illustration, Figure 7.7 shows a histogram of the predicted x position of the cluster centre minus the x position of the centre of the pixel in millimetres. The entries around 0 and mm represent cluster centres which are reconstructed in the middle of the pixel. Single-pixel clusters are reconstructed closer to the centre of the pixel, and 2-pixel clusters more towards the edge. As expected, the predicted track position is equally distributed over the entire pixel. The fact that the centre of gravity method results in wrongly reconstructed positions becomes clear when comparing the reconstructed cluster position within one pixel with the track position in the pixel. Figure 7.8(a) plots these values for a 0 degree DUT angle. Again, 0 and mm represent a position in the middle of the pixel. For a perfect reconstruction, the points should lie around x=y, but this is not the case. A correction for this inaccuracy should result in an analogue region for 2-pixel hits, and a binary region for 1-pixel hits. The correction from a linear function to a non-linear s-curve is applied with a socalled η-correction [3]. This correction is applied to the reconstructed cluster position. 36

42 Figure 7.7: Predicted cluster centre position distribution within the pixel for different cluster sizes, for 0 degree DUT angle. (a) COG-method (b) After η-correction Figure 7.8: Reconstructed versus predicted x position for 0 degree DUT angle. An example η-correction for 0 degree DUT angle is: x η = x COG (7.1) Though this is still a linear function, it approximates a non-linear s-curve, and leaves little room for improvement. Figure 7.8 shows that after η-correction the reconstructed position in the analogue region is cut off at a certain distance from the edge of the pixel, and the hits falling in this region are instead reconstructed in the centre of the pixel. For larger DUT angles, the charge distribution is indeed more linear, and the η-correction has less effect, as can be seen in Figure 7.9 and Figure The figures show that after correction, the reconstructed position is in better correspondence with the predicted position. The improvement in reconstruction of the cluster position becomes also clear when plotting the resolution with and without η-correction. 37

43 (a) COG-method (b) After η-correction Figure 7.9: Reconstructed versus predicted x position for 5 degree DUT angle. (a) COG-method (b) After η-correction Figure 7.10: Reconstructed versus predicted x position for 10 degree DUT angle. Figure 7.11 shows that the resolution improves particularly at small angles. The reason for this is that at small angles diffusion is the main cause for multiple-pixel clusters, whereas at larger angles the angle of incidence becomes a more dominant factor. 7.4 Linear Gain Correction A final correction concerns the time over threshold gain in the pixels. In the beam test, all runs have been taken with a 120 GeV pion beam. Since the most probable energy deposit of a pion in the device under test is always the same (see Section 3.1), every cluster of hits should have an equal sum of charges. Since the time over threshold width is expected to be linear with the charge deposit in the pixel, as shown in Figure 4.5, the total ToT distribution of a cluster of pixels should always be equal, independent of the number of pixels in the cluster. In the results of the 2009 test beam however, there are differences in the total ToT distribution per cluster size, as illustrated in Figure 7. 12(a). An explanation for the difference in pulse height of 38

44 Figure 7.11: Analogue resolution with and without eta correction of the local x coordinate versus DUT angle. the different cluster sizes could be a characteristic of the Timepix chip. Each pixel has a certain offset which is added to its individual pulse height. Therefore a larger cluster of pixels includes the sum of the individual pixel offsets in the total ADC. The ToT value will be shifted by the amount of pixels in the cluster multiplied by their offset. It is expected that a linear gain correction improves the spatial resolution, since a better charge reconstruction benefits the weighted or the η-corrected position reconstruction. As can be seen in Figure 7. 12(a), a single hit cluster has a peak at ToT count 125 (3125 ns). This ToT width is the total charge deposited in the cluster, so it should be equal for all clusters. However, Figure 7. 12(a) shows that 2-pixel clusters have a ToT peak at 150 (3750 ns). This means that for multiple-pixel clusters, the measured charge per cluster is too large. To correct for this, the peaks of 1- and 2-pixel clusters have been aligned around ToT=125. The formula used for the linear gain correction is [5]: T ot calibrated = [ T ot ot (T )2 ] = T ot ot (T )2 This correction first removes the offset by subtracting 8 counts (200 ns). Subsequently the curvature is approximated by a second order function. The factor is chosen such that T ot calibrated (125) = 125. The coefficients have been tuned to make the 1 39

45 C03-W0015 timepix timepix ADC ADC value, value, C03-W0015 D04-W0015 timepix timepix ADC ADC value, value, D04-W0015 D09-W0015 timepix ADC hit 2 hit hit 2 hit 1 hit 2 hit hit 2 hit 1 hit 2 hit hit 4 hit hit 4 hit 3 hit 4 hit hit 4 hit 3 hit 4 hit ToT count M06-W hit 2 hit 3 hit 4 hit ToT count ToT count ToT count (a) Uncalibrated timepix ADC value, M06-W clear explanation for this can be concluded from this study ToT count ToT count (b) Calibrated Figure 7.12: ADC values per cluster size for a run at 10 degree angle. The most probable values for the energy deposit of the clusters do not align. The height of the peaks is not important for the 300 purpose of the linear gain correction. The 2-pixel peak is higher since there are most 2-pixel clusters at this DUT angle. and cluster sizes overlap. To visualise this correction, the corrected ToT is plotted against the original ToT in Figure 1 hit Figure 7. 12(b) shows the result for the ToT hit values per cluster size, and indeed the peaks now align around hit 100Figure 7.14 plots the resolution 4 hit versus the DUT angle. This shows that the resolution after a linear gain correction is worse than the original resolution. No In order to see if the resolution with a linear gain correction can be improved, the η-correction described in Section 7.3 is applied. This happens after the calibration, because the gain correction influences both the ToT value and cluster position, ToT count whereas the η-correction only changes the position. Figure 7.14 shows the resolution with both corrections. The η-correction has much more influence than the linear gain correction, but the combination of the two does still not improve the η-corrected resolution without linear gain correction In spite of the expectation, the linear gain correction does not improve the resolution. It stays unclear why the linear gain correction does not improve the resolution, even though it aligns the ToT values of the different cluster sizes. Since there may be multiple effects playing a role at the same time, it is hard to correct for the gain in such a way that the resolution improves. Therefore the analyses have been performed without applying this linear gain correction. 40

46 Figure 7.13: Linear gain correction: Calibrated ToT versus original ToT. 8 Timing Resolution Besides the time over threshold, the Timepix chip can also measure the time of arrival of the pulse at the electronics readout chip. This is illustrated in Figure 4.3(b). In the VELO upgrade, a bunch crossing happens every 25 ns, and in order to be able to distinguish one event from another, the hits should get a timestamp. This can be done by using the Timepix time of arrival mode. Different hits or clusters can be associated to the same bunch crossing if they have similar time of arrival values. One limitation for using this method is the timewalk of the chip, as explained in Section 4.2. For the VELO upgrade, the timewalk should be smaller than 25 ns. If this cannot be achieved, it might be a solution to apply a correction of the ToA using the charge deposit in the pixel. However, to do this, accurate information on both the ToA and ToT values is needed, which is currently not available since the chip can only run in one of those modes at a time. In the beam test, several runs were taken with the DUT in ToA mode, and the telescope detector planes in ToT mode. In order to perform analysis with the time of arrival mode of the chip, using the centre of gravity method for reconstruction of the cluster centre is incorrect, since the ToA count is not necessarily proportional to the charge deposited in the pixel. One solution is to only use the spatial information of the hits to determine the cluster centre in ToA mode (binary reconstruction). An alternative would be to use the information of a ToT run to obtain the charge distribution in a certain shape of clusters, and to weight the ToA clusters with the expected charge in equally shaped clusters. The latter method has been tested on 41

47 Resolution vs Angle Unbiased Resolution [micron] Uncalibrated no eta corr Calibrated no eta corr Angle [deg] 3 Uncalibrated with eta corr Calibrated with eta corr Angle [deg] DUT Angle Figure 7.14: Linear Uncalibrated gain correction: Binned Calibrated - old and uncalibrated resolution (both with and without eta correction) of the local x coordinate versus DUT angle. Unbiased Resolution [micron] DUT Angle clusters of three hits in two different shapes and on cross-shaped five-pixel clusters. However, there 12 are mainly single-pixel clusters at 0 degree, and only a small amount of clusters has exactly these shapes. Since both methods do not give significantly different results, the chosen option is not to weight the ToA cluster, and rely on the 10 binary reconstruction method. 8.1 Timewalk As explained in Section 4.2, the mean Timepix timewalk has been specified as 25 ns, with a maximum value of 50 ns, and a verification measurement using test pulses confirmed this value. 4 In the beam test, the runs in ToA mode had an acquisition time of 25ms, a reference clock frequency of 40 MHz, bias voltage of 100 V, Ikrum of 5, and the DUT plane perpendicular to the beam. A striking result was that the difference between pixels in the same cluster was quite large. To be more specific, ber of bits [6=analog] number of bins [6=analog] Figure 8.1 shows that the maximum value of the difference within one cluster was 225 ns, which is significantly larger than the expected value. Cluster- and track-based To investigate this problem more thoroughly, the cluster- and tracking-information of the telescope is used. As explained before, clustering in ToA mode is only based on the spatial information of the hit pixels, and not on the charge deposition in the

48 Figure 8.1: Maximum ToA difference within clusters. pixels. Figure 8. 2(a) shows the average difference between the ToA value of the reconstructed cluster centre and the surrounding pixels. If this time difference is positive, the centre pixel has the earliest arrival time. If timewalk is the cause of the ToA difference, this pixel should have the highest charge deposit. If the timing difference would solely be caused by timewalk, all values in Figure 8. 2(a) should be positive. This is clearly not the case, since the mean is close to zero, at 10 ns, and the RMS is large, namely 54 ns. A reason for the unexpectedly low mean value may be that the centre of the cluster is not well reconstructed due to the limited information (only binary reconstruction of the clusters). To improve on this reconstruction, the tracking information of the telescope can be used. Tracks passing through the six detectors are reconstructed, and the intersection point of the track with the DUT gives an unbiased indication of the position of the cluster centre. Figure 8. 2(b) shows the result of this analysis. Indeed the mean is now shifted more to the positive side (mean = 32 ns). An explanation for this is that clusters which have a negative ToA difference cannot be associated with a track, and are not considered in this track difference. The RMS (47 ns) of the track difference is still so large that there is no significant positive value obtained. This indicates that the time of arrival not only dependends on the charge deposited in the pixel. Cluster shapes The methods mentioned before depend highly on the efficiency and precision of the reconstruction of tracks and cluster centres. A wrong reconstruction might appoint the centre of a cluster to a pixel which does not have the highest charge deposit. Another approach, which might be more reliable, is to evaluate a certain cluster shape 43

49 (a) Cluster-based (b) Track-based Figure 8.2: Average ToA difference with cluster centre. in both ToT and ToA mode. However, there is not enough data to draw definite conclusions from this method. For this purpose, a future telescope test should have more ToA runs at larger angles. An evaluation of 3-pixel size clusters in a corner shape (Figure 8.4) showed that 36% of the charge is deposited in the corner pixel, and 32% in both boundary pixels. One would expect that those clusters would have a large timewalk due to a larger charge difference between pixels. More timewalk would result in a large positive difference between the cluster centre and the boundary hits. The corner clusters give an average ToA difference with regard to the centre pixel of 56 ns with RMS 34 ns. As an illustration, Figure 8.3 plots the results of the corner shape pixels. The ToA difference of the boundary pixel in the y direction with respect to the central pixel is plotted versus the ToA difference of the boundary pixel in the x direction. The central pixel usually has an earlier time of arrival value than both boundary pixels (positive ToA difference). This can be explained by the timewalk. Again the timewalk is much larger than expected, namely up to 300 ns. There are still some entries at negative ToA difference which cannot be explained by timewalk. Following expectations, a more precise reconstruction method shows a stronger relation between ToA and ToT. Two-pixel clusters A final approach to determine the relation between ToT and ToA is to look at only two-pixel clusters. If the charge deposit in the two pixels is about equal, the assumption is that the track went through the middle of the cluster, which is at the edge between the two pixels. If the charge in one of the pixels is much higher than in the other, the track will be reconstructed further away from the edge between the pixels, as indicated in Figure 7.5. Therefore the distance from track position to the pixel edge is a measure of the expected charge difference between the two pixels. The next step is to relate the charge difference to the time of arrival difference between the pixels. Assuming the time of arrival differences are caused by timewalk, a small charge difference should result in a small ToA difference. In order to check this, Fig- 44

50 Figure 8.3: Difference in time of arrival between the boundary pixel (both x and y) and the central pixel in corner-shaped clusters. The plot shows the time of arrival difference in y versus the time of arrival difference in x. Figure 8.4: The corner cluster shape. The central pixel is assumed to have the highest charge deposit. ure 8.5 shows the ToA difference of the two pixels versus the distance between the reconstructed track position and the middle edge of the two pixels. The distance is displayed in units of pitch, i.e. 0 represents the edge between two pixels, and 0.5 is the middle of the pixel. The expectation is to see a trend from almost no ToA difference at small distances, up to higher ToA differences at large distance from the edge. However, such a trend cannot be extracted from the data. On the contrary, there are many high ToA difference entries at very small distance from the pixel edge. This shows that the relation between charge deposit and time of arrival is not as expected. The two-pixel analysis shows no correlation between ToT and ToA, whereas this correlation did appear in the method using three-pixel corner shaped clusters. The most probable reason for the discrepancy between the two results is that the two-pixel analysis relies on the tracking, which is apparently not accurate enough to predict the charge deposit in the pixels. Source, laser and test pulses Besides the analysis of the beam test data, an experimental set-up with a Sr 90 source was used to measure ToA in clusters. This has been done with both the MUROS 45

51 Figure 8.5: ToA difference [ns] versus distance from edge between two pixels, in units of pitch. and USB readout devices, for different clock frequencies. A quick investigation with low statistics shows that the maximum difference of the ToA value within clusters is always around 150 ns. This seems to agree with the beam test measurements. However, this value is again much larger than the specified (and measured) timewalk from test pulses. For an Ikrum value of 5 DAC, the maximum difference is 350 ns. A remarkable fact is that neighbouring pixels differ a lot. An Ikrum of 70 DAC can lower this to about 150 ns maximum. In this case ToA depends more clearly on the charge deposit in the cluster. Although a very high Ikrum lowers the gain in ToT mode, it seems that ToA runs benefit from an Ikrum of at least 30 DAC. There are several explanations for the large difference between the specified and the measured timewalk. Those depend on the settings of the chip and on the definition of timewalk. First of all, a higher Ikrum (shorter falling edge of the pulse) results in a smaller ToA difference. The fact that Ikrum influences the ToA values may be caused by the uncertainty on the arrival time. This is increased by a longer falling edge. If a charge is only just above threshold, the region of uncertainty of the time of arrival value is large. Next, the definition of timewalk is the time difference between an infinite input charge and a charge which is 1k over threshold. However, what is measured in the beam test, is the difference between an infinite (very large) 46

52 charge and a charge which barely goes over threshold. The very small charge can be depicted by the top of the pulse. The difference between between the 1k over threshold and top of the pulse can be up to 50 ns according to specifications. This means that the timewalk as it is found in the beam test data can be expected to be 110 ns. This would mean that there is a discrepancy between the definitions of the timewalk, and not between the values found. The value which is important for the VELO, namely maximum 25 ns timewalk, should be compared to the beam test data and not to the Timepix specifications. To summarise, the maximum timewalk values in the beam test data are much larger than expected. Furthermore the expected correlation between charge deposit and time of arrival cannot be found when looking at the entire data set. However, more precise charge reconstruction methods, like using the shapes of the clusters, showed that this correlation is present. A possible explanation for the large timewalk is that the detected charges are only just above threshold. For a long falling edge, the error on the time of arrival becomes large. Furthermore, a difference in the definition of timewalk may be the cause for the difference between the specifications and the data. However, the maximum timewalk value of 25 ns which is needed for the VELO upgrade cannot be achieved by the current Timepix chip. One way to reach this goal is to sufficiently shorten the rise time of the pulse through the preamplifier DAC. Future studies of the timewalk effect are needed, and they will be facilitated by the new Timepix2 chip, which will be able to measure ToA and ToT simultaneously. 47

53 9 Timepix Beam Test 2010 In May and July 2010, two more beam tests have been performed. One of the goals of the 2010 beam tests was to get additional statistics for the 2009 data set, for example to investigate the individual pixel pulse-shapes. This was done using the same D04 Timepix chip with a 300µm silicon sensor. Secondly, several other devices were tested. One of those was a silicon strip detector, the PR01 module. The option of using strips for the upgrade is kept open, in case of serious issues with the pixel detector. The goal was to compare the resolution of the strips with the pixel chip. The third device under test was a Timepix device with a thin sensor (150 µm) bump-bonded to the chip. Furthermore some improvements have been made in the telescope with respect to The telescope was installed in the SPS 120 GeV pion beam at CERN. 9.1 Telescope Figure 9.1: Timepix telescope The first difference between the 2010 and 2009 telescopes was the trigger system. An external trigger system has been set up, with two small scintillators at the front and back of the telescope. Within each beam passing (once every 45 seconds), about 40 Timepix frames were taken. The gate time of the frames was determined by the external trigger system, and not by hand as in The shutter of each frame was closed either after 300 particles have passed, or after 300 µs. A delay of 150 ms was introduced after each frame before the next gate start time, in order to provide time for simultaneously reading out the chips. Secondly, the 2010 telescope contained six Timepix chips instead of two Medipix and four Timepix devices. This, together with longer telescope arms, should improve the tracking precision. The distance in z along the beam axis between the devices was 150 mm. The readout of the Timepix chips was done with the USB2 interface, which was about five times faster than the USB1 used in The output files of Pixelman are zero-compressed, which fastened the conversion into ROOT files for analysis. The strip module, PR01, could not be read out by Pixelman, and some adaptations were needed to correctly match the PR01 data with the telescope frames. Eventually, 48

54 Ikrum Disc Preamp THL Bias voltage TPX clock TPX mode 5 DAC ( 3nA) 127 DAC( 0.8µA) 255 DAC ( 1.8µA) 390 DAC 100V 40 MHz ToT Table 9.1: Setting for the device under test in the resolution runs in the 2010 beam test both the PR01 and the Timepix information were written into one ROOT file. The Timepix device under test has number D04, which is the same chip as in The DAC settings used for the DUT in the resolution runs are shown in Table 9.1 The run program of the first beam period in May-June included angle scans for D04 as device under test, and angle scans with the PR01 as device under test and the D04 in ToA mode installed behind the telescope. The D04 runs provided good data, although there was not enough time for sufficient ToA runs to address the timewalk problem. Due to problems in time-alignment of the PR01 data with the telescope, and due to limited beam time, not much PR01 data has been gathered. In the second beam period, in July 2010, the main device under test was the PR01. Several runs showed an acceptable spatial correlation between the PR01 and the telescope. However, the alignment of this device was not well understood, and such a relation could not be found in later runs. In order to gain some time to understand the PR01 alignment, the thin sensor device was inserted as device under test in the meantime. An angle scan and high voltage scan showed that the device was working as expected. Since the measurements of the May period did not provide any useful data to analyse the timewalk problem, no further attention is paid to the results in this report. A thorough analysis of the July data (in particular the thin sensor) is, although very interesting, beyond the time scope of this project. 9.2 First Results Due limited beam time and problems with the timing of the telescope and the PR01 device, the amount of data taken in the May-June period was less then expected. In the runs taken with the D04 as device under test, about 100 straight tracks per frame could be reconstructed. Compared to the 300 incidences recorded within each shutter, this is quite a reasonable number of tracks. The resolution of the D04 can not yet be compared to 2009, since the alignment, eta correction and tracking algorithm still have to be improved. The thin sensor bump-bonded to a Timepix chip gave some nice results. The resolution at perpendicular angle was 12 µm. If the DUT is rotated to the predicted optimal angle of 20 degrees, its resolution is 6.0 µm. Figure 9.2 shows the residual 49

55 localy residuals on C08-W0098 localyresidual_c08-w0098 Entries Mean RMS Prob 0 Constant 1904 ± 7.4 Mean ± Sigma ± localy residuals on H03-W0092 localyresidual_h03-w0092 Entries Mean RMS Prob 0 Constant 3097 ± 12.6 Mean ± Sigma ± localy residuals on H05-W0082 localyresidual_h05-w0082 Entries Mean e-06 RMS Prob 0 Constant 3612 ± 14.8 Mean e-05 ± 1.100e-05 Sigma ± localy residuals on H07-W0082 localyresidual_h07-w0082 Entries Mean -4.17e-05 RMS Prob 0 Constant 3035 ± 12.4 Mean e-05 ± 1.313e-05 Sigma ± localy residuals on H09-W0082 localyresidual_h09-w0082 Entries Mean RMS Prob 0 Constant 3357 ± 13.7 Mean 9.941e-05 ± 1.185e-05 Sigma ± localy residuals on I08-W0092 localyresidual_i08-w0092 Entries Mean e-05 RMS Prob 0 Constant 3234 ± 13.1 Mean e-05 ± 1.236e-05 Sigma ± localy residuals on J09-W0092 localyresidual_j09-w0092 Entries Mean RMS Prob 0 Constant 3448 ± 14.2 Mean ± Sigma ± Figure 9.2: Preliminary results of the beam test Residuals in the y-direction. The telescope planes are at a 9 degree angle in both x an y, and the thin sensor (C08-W0098) DUT is at an angle of 20 degrees in x. 50

56 distributions of all the planes in the telescope and of the device under test (C08- W0098). These are preliminary results, and alignment and tracking still have to be optimised for the 2010 telescope. As for the future test beams, there will probably be a ReLaXd readout system available for the telescope by the end of the summer of 2010, which will enable faster readout and which will provide more frames per beam spill, hence allowing more detailed studies. Furthermore the use of Timepix2 devices, probably available within the next year, will enable analysis of the timewalk using a simultaneous ToA-ToT measurement. 51

57 10 Conclusion and Outlook The target of this research is the characterisation of the Timepix chip, in order to see if it is a viable solution for the LHCb VELO upgrade. The main change in the LHCb upgrade is an increase in luminosity. This leads in the VELO to a higher hit occupancy, a larger data rate, and a higher radiation dose. A new detector design is needed to cope with these issues. One of the options that can function as a starting point for the new VELO detector is the Timepix pixel chip. This chip has been characterised in a beam test telescope. The results of this characterisation have consequences for the design of a new VELO chip and for the VELO lay-out Resolution The main topic of this research was the resolution measurement. The current VELO has an optimal resolution of 8 µm at 0 degree particle incidence angle. Since a new design should at least have an equally good resolution, the target resolution of the Timepix is in the order of 5-10 µm. Improvements in the clustering, tracking and alignment software were made to optimise the track reconstruction in the Timepix- Medipix telescope. One of the investigated improvements for clustering is a linear gain correction which corrects for non-linear behaviour of the time over threshold gain of the chip. It was found that this correction does not improve the resolution, and it was therefore abandoned in further analysis. The second method is the eta correction, which improves the reconstruction of the position of a cluster with respect to the centre of gravity method. It was shown that the eta correction improves the resolution, in particular for small particle incidence angles. The tracking of the telescope has been improved by weighting the Medipix planes with a larger error than the Timepix planes. The track extrapolation uncertainty of the telescope was 2.3 µm. This high precision allows for a very precise determination of the resolution of the device under test. The best achieved intrinsic resolution of the Timepix chip was 4.4 µm for an 8 degree particle incidence angle, and a 300µm thick silicon sensor. Besides the analogue resolution, the option of rebinning the time over threshold range has been investigated. This has two advantages for the chip, namely a smaller data rate and a shorter dead time of the pixels. The binary resolutions for different angles and different cluster sizes are comparable to theoretical predictions. The conclusion is that rebinning to 4 bits is the optimal combination of a small data rate and a good resolution. The 4 bit ToT range degrades the spatial resolution with at most one µm compared to the 14 bit range. The 4 bit ToT range will increase the continuous readout frequency at which the chip will operate. The goal is to reach a 40 MHz continuous readout. 52

58 10.2 Timewalk The timing resolution of the chip is very important for the VELO upgrade. The detector should be able to distinguish between bunch crossings which are 25 ns apart. The beam test data shows that the time of arrival difference between pixels in a cluster is up to 300 ns, which is a serious issue for the VELO upgrade. The difference in time of arrival is mainly caused by timewalk. This was shown using several methods to predict the charge distribution in the clusters. The timewalk value in the Timepix specifications is much smaller than the value found in the beam test data. An inconsistency between the definitions may contribute to this difference. The beam test data shows that the maximum timewalk value of 25 ns which is needed for the VELO upgrade cannot be achieved by the current Timepix chip. A new design of the chip should have a shorter rise time of the pulse. Furthermore the timewalk might be reduced by shortening the falling edge of the pulse. This will decrease the uncertainty of the time of arrival of small charges Outlook Much more research will be needed to optimise the Timepix chip for the VELO upgrade. A new design of the Timepix chip, Timepix2, will probably be finished within a year from now. Eventually, this will lead to the design of the Velopix chip, which is a dedicated chip for the VELO upgrade. Several suggestions can be made for future beam tests, using the results of this research. The Timepix2 chip will be able to measure time over threshold and time of arrival simultaneously. This will ease the investigation of the timewalk problem that was seen in the beam test data. Using the timewalk analysis, some improvements can be suggested for the ToA measurements in beam tests. Firstly, a larger particle incidence angle (e.g. 18 degree) will result in larger clusters. This will provide more useable data for the analysis of the time difference within clusters. Secondly, some runs with an Ikrum value of 30 DAC will be needed to see whether the timewalk indeed decreases for a shorter falling edge of the signal pulse, as was suggested in the lab tests. Finally, material thickness is an issue in the VELO detector. In order to reduce resolution deterioration due to multiple scattering, the thickness of the detector planes should be kept to a minimum. In the July 2010 beam test, several tests have been performed with a thin (150µm) sensor. For the pixel detector to be able to compete with the strip detector, more research should be carried out to minimise the pixel detector material. 53

59 References [1] C. Amsler et al. (particle data group). Physics Letters B667, 1, (2008) and 2009 partial update for the 2010 edition. [2] Marina Artuso. The LHCb vertex detector upgrade. arxiv: v1, [3] E. Belau et al. Charge collection in silicon strip detectors. Nuclear Instruments and Methods, 214: , [4] A. Borgia. Timepix Characterization with Laser and Test Pulse at CERN. Presentation, May [5] J. Buytaert. Cluster analysis on August timepix test beam. Presentation, October [6] P. Collins et al. The LHCb VELO Upgrade. Nuclear Instruments and Methods A, [7] S. de Capua. The LHCb Commissioning. arxiv: v2, [8] T. Holy et al. Data acquisition and processing software package for Medipix-2 device. Nuclear Instruments and Methods A, 563: , [9] X. Llopart. Timepix manual, [10] X. Llopart. Design and characterization of 64k pixels chips working in single photon processing mode. PhD thesis, Mid Sweden University, [11] X. Llopart, R. Ballabriga, M. Campbell, L. Tlustot, and W. Wong. Timepix, a 65k programmable pixel readout chip for arrival time, energy and/or photon counting measurements. Nuclear Instruments and Methods in Physics Research A, 581: , [12] X. Llopart, M. Campbell, R. Dinapoli, D. San Segundo, and E. Pemigotti. Medipix2: a 64-k pixel readout chip with 55um square elements working in single photon counting mode. IEEE Transactions on Nuclear Science, 49(5): , [13] F. Muheim. LHCb upgrade plans. arxiv:hep-ex/ v1, [14] A. Papadelis. Characterization and commissioning of the LHCb VELO detector. PhD thesis, Vrije Universiteit Amsterdam, [15] R. Plackett, X. Llopart, et al. Measurement of Radiation Damage to 130nm Hybrid Pixel Detetor Readout Chips. TWEPP-09,

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61 Summary of contribution made to the research Section 4.2: ToA test pulse measurements Section 4.3: Measuring data rates of different readout systems Section 6.3: Implementation of alignment Section 6.4: Definition, implementation in software and verification of improvements in track fit Section 6.4: Verification of pattern recognition Section 7.1: Definition, implementation and interpretation of results of rebinning Section 7.4: Implementation and verification linear gain correction Section 7.5: Definition, implementation, verification and interpretation of eta corrections for different angles Section 8: Improvements in ToA clustering Section 8.1: Definition, implementation and interpretation of different timewalk analysis methods using both beam test data and own measurements Section 9: Preparation of beam test 2010: first implementation of PR01 strip detector in Timepix telescope software Section 9: Two+one weeks at CERN for telescope preparation and shifts 56

62 Samenvatting De Vertex Locator (VELO) detector maakt deel uit van het LHCb experiment, een van de vier grote experimenten van de Large Hadron Collider op CERN. Hoewel de proton-proton versneller pas sinds een jaar data levert, wordt er al nagedacht over de toekomst van het LHCb experiment. Om de statistische fout in metingen te verkleinen zal in 2016 de luminositeit van de protonbundels vergroot worden. Om deze hogere luminositeit aan te kunnen, zal de VELO silicium strip detector vervangen moeten worden. De Timepix pixel detector chip kan een goede basis vormen voor een vervangende detector. De Timepix chip bestaat uit een 256x256 matrix van 50x50 micron pixels, en kan gebruikt worden om de aankomsttijd of het energieverlies van deeltjes in de detector te meten. Om de chip te karakteriseren, is deze geinstalleerd in een bundeltelescoop in een 120 GeV pionenbundel op CERN. Deze scriptie beschrijft de analyse van de resultaten van de bundeltest, met name de resoluties in tijd en ruimte. De telescoop bestond uit Medipix en Timepix detectoren, die het spoor van een deeltje tot op enkele micrometers nauwkeurig konden bepalen. Verbeteringen in de reconstructie van clusters en sporen en in de uitlijning van de telescoop resulteerden in een resolutie van 5 micron onder een hoek van inval van 8 graden. Ook is onderzocht in hoeverre de resolutie verslechtert naar mate het aantal beschikbare bits voor de ladingsmeting in de pixels vermindert. Verder bleek dat door het zogenaamde timewalk effect de meting van de aankomsttijd van de deeltjes nog niet nauwkeurig genoeg is om te voldoen aan de eisen van VELO detector. De resultaten van dit onderzoek kunnen worden gebruikt voor het ontwerpen van een nieuwe VELO pixel chip. 57