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