Test-beam measurements on prototype ladders for the LHCb TT station and Inner Tracker

Transcription

1 LHCb Note Test-beam measurements on prototype ladders for the LHCb TT station and Inner Tracker M. Agari, C. Bauer, J. Blouw, M. Schmelling, B. Schwingenheuer Max-Planck-Institut für Kernphysik, Heidelberg S. Jimenez-Otero, H. Voss Laboratoire de Physique des Hautes Energies, École Polytechnique Fédérale de Lausanne V. Pugatch, D. Volyanskyy Kiev Institute for Nuclear Research National Academy of Science of Ukraine R.P. Bernhard, S. Koestner, F. Lehner, C. Lois, M. Needham, O. Steinkamp, A. Vollhardt Physik-Institut Universität Zürich st September, 23 Abstract The results of a comprehensive measurement program carried out at the CERN X7 test facility in May 23 on prototype ladders for the LHCb Silicon Tracker are described. Introduction The LHCb Silicon Tracker (ST) project consists of two sub-detectors that will be built using silicon micro-strip technology. The Inner Tracker (IT) will cover a cross-shaped area around the beam-pipe in each of the three tracking stations located after the magnet. Research and development for the IT and the resulting technical design are described in []. The Trigger Tracker (TT) will be located upstream of the magnet and will consist of two half-stations, TTa and TTb, each with two layers of silicon. The decision to construct the TT station entirely from silicon micro-strip technology was taken in May 22. At the location of the TT stations, an area of cm 2 has to be covered [, 2]. In order to minimise the amount of dead material in the acceptance, all the front-end chips will be located at the edge of the detector. Kapton cables ranging in length from 33 to 55 cm will be used to connect the inner sensors to their corresponding hybrids [2]. This gives capacitive loads of 5 pf for all the readout sectors. On leave from National Taras Shevchenko Kiev University On leave from Universidad de Santiago de Compostela

2 March 8, 24 Test-beam Results Results of earlier tests on ladders constructed from 32 µm thick sensors are reported in [, 3]. The longest ladder tested so far was 22 cm in length and had a capacitance of around 35 pf. The measured signal to noise (S/N) performance was found to be just acceptable for the IT application. The extrapolated performance for a 5 pf load capacitance do not meet the requirements of the TT station. However, the latest version of the front-end chip the Beetle.2 [4] is expected to provide better S/N performance than the Beetle. that was used in the previous tests. Five prototype ladders have been constructed, with sensors of 32 µm, 4 µm and 5 µm nominal thickness in order to study the performance with the Beetle.2 and to determine the optimal wafer thickness of the sensors for the TT station. First tests of these ladders were carried out in a laser test-stand and are described in [5]. This note presents the results of a comprehensive measurement program undertaken with a 2 GeV π beam at the CERN X7 test-beam facility. 2 Prototype Ladder Properties Three types of sensor were available for ladder construction: the multi-geometry prototype sensors used in earlier tests for the LHCb Inner Tracker [], GLAST2 sensors [6] and CMS-OB2 sensors [7]. All the sensors used have a pitch of around 2 µm. From these sensor types the following ladders were built: LHCb One sensor of LHCb type. LHCb2 Two sensors of LHCb type. LHCb3 Three sensors of LHCb type. GLAST Three sensors of GLAST type. CMS Three sensors of CMS type. For the studies in this note the most important properties of the sensors are the thickness, capacitance and implant width. The thickness of the sensors has been measured with a metrological machine at the Physik-Institut Universität Zürich. The results of these measurements are summarised in Table. The measured numbers are in reasonable agreement with the nominal values. Sensor type Nominal thickness/ µm Measured thickness/ µm LHCb ± 8 GLAST 4 48 ± 5 CMS 5 55 ± 5 Table : Measured sensor thickness. Another important quantity is the total capacitance of each ladder. This has two components the capacitance of the silicon strips themselves and the capacitance of the pitch adapter (C p ). The strip capacitance depends on the ratio of the implant width to the strip pitch 2

3 Test-beam Results March 8, 24 Implant Type Pitch/µm width/µm ρ/pfcm C p /pf LHCb A LHCb B LHCb C LHCb D GLAST CMS Table 2: Prototype sensors properties. The values of ρ are estimated using the numbers given in [8]. (w/p), therefore the different regions on the ladders constructed from LHCb sensors have different capacitances. In addition, each region of a LHCb sensor maps to a specific area on the pitch adaptor. This leads to different values of C p for each region. Values for C p and the strip capacitance per unit length, ρ are given for the all the sensor geometries tested in Table 2. The total capacitance for each region can be calculated using: C strip = C p + ρ l. The resulting numbers are summarised in Table 3. It should be noted that these capacitances are different to those presented in [5] for two reasons. Firstly, the numbers in [5] do not include C ρ. Secondly, the strip lengths for the CMS and GLAST ladders were reversed in the calculation in [5]. Ladder Strip length/cm C Strip /pf LHCbA LHCbB LHCbC LHCbD LHCb2A LHCb2B LHCb2C LHCb2D LHCb3A LHCb3B LHCb3C LHCb3D GLAST CMS Table 3: Calculated capacitances for the different ladders and detector regions. Numbers are not given for region E on the LHCb ladders as it was not tested. 3

4 March 8, 24 Test-beam Results 3 Test-beam Setup and Measurement Program The five prototype ladders were tested in a 2 GeV/c π beam at the CERN X7 test facility in May 23. Four double-sided silicon strip detectors provided by the HERA-B vertex detector group [9] served as a beam telescope. This allowed the impact point of the π tracks on the sensors under test to be determined with a resolution of approximately 4 µm. The readout was triggered by a coincidence of four scintillation counters placed upstream and downstream of the beam telescope. A photograph of the setup is shown in Figure. All the components were installed in a light-tight aluminium box. This box could accomodate four prototype ladders at a time, therefore measurements were initially performed with the LHCb, LHCb2, GLAST and CMS ladders installed. Once the measurement program for the LHC ladder was completed, it was removed and replaced by the LHCb3 ladder. Figure : Overview of the test-beam setup in X7. As the acceptance of the beam telescope was smaller than the width of the sensors under test, not all the readout strips on the sensors could be illuminated simultaneously. The ladders constructed from LHCb multi-geometry sensors were installed in such a way that regions A-D were illuminated. No data were accumulated for region E, which had been rejected as an option for the Silicon Tracker based on results from earlier measurements []. Each test ladder was mounted on a separate support rail, which allowed the horizontal position to be adjusted such that the beam spot illuminated different regions along the ladder. To remove the heat generated by the Beetle readout chips, the end of the ladder carrying the readout hybrid was attached to a copper cooling block. Water at a temperature of C was 4

5 Test-beam Results March 8, 24 used as a coolant. An extensive measurement program was carried out in order to study the performance of the prototype ladders. In total, more than 36 million events were saved to disk during the two week test-beam period. Initial bias voltage scans were carried out to determine the working point for all subsequent measurements. The data from these scans were also used to study signal shape parameters as a function of the bias voltage. High-statistics data samples of 25 events each were then accumulated for: Two bias voltage settings, V.5 V dep and V 2 2 V dep, where V dep is the full depletion voltage of the respective sensors. Three different signal shaping times of the Beetle preamplifier. The signal shaping time is controlled by programming the internal register V fs of the Beetle chip, and data were accumulated for V fs = mv (fast shaping), V fs = 4 mv and V fs = mv (slow shaping). Up to five different beam positions along the ladders. The beam spot was centered on each of the sensors on a ladder as well as on the inter-sensor gaps. Prior to each of these main data runs, a low statistic latency scan was performed in order to determine the optimal signal sampling-time for the Beetle chips. To achieve this, the delay between trigger and signal sampling time was varied in three to four steps of 4 ns around the presumed maximum of the signal, and the most probable value of the signal amplitude determined for each ladder and each delay setting. The delay time for the subsequent data taking was then chosen as the one that maximized the most probable signal amplitude averaged over the four ladders 2. The data from the high-statistics runs were used to analyse the signal-to-noise performance and the particle detection efficiency of the ladders as a function of bias voltage, signal shaping and beam position, as well as a function of the π track position with respect to the readout strip centre. In addition, a study of cluster shapes was performed. Finally, high-statistics delay scans covering the full duration of the pulse were performed for the two bias voltage settings (V and V 2 ) and for two different shaping times (V fs = mv and V fs = 4 mv). For these scans, the beam spot was centered on the sensors closest to the readout chips. The data from these runs were used to study signal shapes on the strips closest to the π track and on the neighbouring strips, as a function of bias voltage, shaping time and. 2 The optimum delay is slightly different for each ladder, since the ladders present different load capacitances to the Beetle chips, resulting in a different peaking time of the front-end amplifier. However, the test beam setup did not permit to set individual delay times for each ladder. Based on the results presented in [5], it is estimated that the chosen delay always lay within a window of ± 2.5 ns around the optimum delay time and that the effect on the measured signal amplitude is smaller than ± %. 5

6 March 8, 24 Test-beam Results 4 Analysis Procedure and Data Quality Similar tracking and cluster finding algorithms to those used in previous test-beams were adopted. Therefore, only a brief overview will be given here. More details can be found in [3, ]. Pedestals and strip noise, i.e. the uncorrelated part of the total noise were calculated using a statistical method. After pedestal subtraction, event-to-event common mode fluctuations were estimated using a second order polynomial fit to the data. The three Beetle chips per ladder and in the case of the LHCb ladders the different regions, were treated separately in order to account for gain variations. As a typical example strip noise, pedestals and the the distribution of reconstructed clusters as a function of strip number (the beam profile ) are shown for the case of the GLAST ladder in Figure 2. It can be seen that: The variation in the level of strip noise from channel-to-channel is small. The spikes that can be seen are due to channels that have been bonded to an external PCB to allow for a charge calibration [5]. The beam illuminates the part of the sensor corresponding to the first two chips on each ladder. This beam position was chosen in order to study effects at the sensor edge. For the LHCb ladders this means the behaviour of the three 98 µm pitch regions can be investigated together with the 238 µm pitch region D. charge [ADC counts] channel number charge [ADC counts] channel number entries strip Figure 2: Strip noise, pedestal and beam profile for the example of the GLAST ladder, V fs = 4 mv. Corresponding plots for the other ladders can be found in Appendix A. From these plots a list of noisy and bad channels was extracted. These are summarised in Table 4. The entries in this table can be compared to those listed in the note on the measurement program with the laser setup [5] that preceded the test-beam. There are several differences: Two strips on Beetle E are flagged as noisy. In fact these strips were found to be noisy during the Laser tests but were not recorded as such in the note. Beetle, which was not functional at the time of the laser measurement program has been fixed. Beetle 6 is non operational. Four strips on the GLAST ladder are flagged as noisy. There is one un-bonded strip on the LHCb3 ladder. The majority of the additional faults in the test-beam compared to the laser set-up are probably attributable to handling errors. 6

7 Test-beam Results March 8, 24 Ladder Beetle ID Working Calibration Bad bonds Noisy channels channels channels LHCb B OK 55, 94 LHCb C OK 5, 44, 79, 2 LHCb D Destroyed LHCb2 E OK 94 3, 2 LHCb2 F OK 5, 44, 79, 2 LHCb2 OK 9, 48 CMS 4 OK 23, 24 CMS 5 OK 78 CMS 6 Dead GLAST 7 OK 94 GLAST 8 OK 35, GLAST 9 OK 4, 73 37,7, 8 LHCb3 A OK 55, 94 LHCb3 B OK 5, 44, 79, 2 5 LHCb3 C OK Table 4: Noisy and dead channels at the end of the test-beam period. Channels are numbered per Beetle starting from zero. The same cluster finding strategy as in [3] was adopted. A signal significance for each strip is defined as d 2 /n 2, where d is the pedestal and common mode subtracted ADC value and n is the strip noise. Contiguous regions of strips with positive charge and a signal significance exceeding a given cut parameter (seed-cut) were accepted as clusters, if the sum of the single strip significances was larger than a second cut parameter, the χ 2 -cut. The signal-to-noise ratio (S/N) of all clusters was normalised to that of one-strip clusters. Noise clusters were taken to be those clusters not associated to tracks reconstructed by the telescope. To decrease the rate of fake noise clusters due to real tracks that were not reconstructed by the telescope it was required that there were no additional clusters in the neighbouring ladders. For the determination of the noise rate as well as the efficiency, strips flagged as dead or noisy, calibration channels and the two strips at the edge of the sensor region were masked. In this way a few bad strips will not bias the measurements of the intrinsic sensor properties. The edge channels are discussed in a separate note []. In Figure 3 the efficiency and noise rate as a function of the seed-cut and χ 2 are shown for the CMS and LHCb3 ladders. The results for the LHCb, LHCb2 and GLAST ladders are similar to the CMS case. In studies of the LHCb tracking system performance a noise rate of 6 4 is assumed [2]. For all the ladders apart from the LHCb3, this noise rate can be achieved while maintaining maximum efficiency, by applying seed-cut=3 and χ 2 =. As can be seen in Figure 3 the LHCb3 ladder behaves differently with these cuts yield an efficiency of only 95%. In order to obtain maximum efficiency a seed-cut of 3 and a χ 2 cut of 5 should be used. However, this leads to a noise rate of.55%. Such a noise rate is not acceptable for use in the final experiment. Noise rates for all the ladders and regions tested are summarised in Table 5. 7

8 March 8, 24 Test-beam Results efficiency SeedCut=4 SeedCut=3 SeedCut=2 noise rate% SeedCut=4 SeedCut=3 SeedCut= χ 2 cut χ 2 cut efficiency SeedCut=4 SeedCut=3 SeedCut=2 noise rate% SeedCut=4 SeedCut=3 SeedCut= χ 2 cut χ 2 cut Figure 3: Efficiency (left) and noise rate (right) for the CMS ladder (top) and for region A of the LHCb3 ladder (bottom). Ladder Noise rate (%) LHCbA.48 LHCb2A.48 LHCb3A.48 LHCbB.36 LHCb2B.44 LHCb3B.49 LHCbC.37 LHCb2C.46 LHCb3C.5 LHCbD.39 LHCb2D.64 LHCb3D.56 GLAST.4 CMS.34 Table 5: Noise cluster rates. Known noisy strips and sensor edges have been excluded. 8

9 Test-beam Results March 8, 24 5 Results In the following sections the main results of the measurement program carried out during the test-beam period are presented. 5. Bias Voltage Scans In order to obtain the working points for each ladder bias voltage scans were performed. For each ladder, the bias voltage was varied over a wide range above the expected depletion voltage. Then, for each voltage setting four runs were taken with different sampling delays chosen to encompass the actual maximum of the signal for all the ladders. For each of these runs the most-probable-value (MPV) of the S/N distribution was determined by fitting a Landau convolved with a Gaussian. A Gaussian fit is then made to the MPV as a function of the delay time. From the maximum of this fit the S/N value and the appropriate delay time can be determined for each bias voltage setting. Figure 4 shows the bias voltage scans for the signal/noise 2 8 signal/noise 6 4 signal/noise CMS/on-strip CMS/inter-strip bias voltage [V] GLAST/on-strip GLAST/inter-strip bias voltage [V] 5 lhcb/on-strip lhcb/inter-strip lhcb2/on-strip lhcb2/inter-strip bias voltage [V] Figure 4: The S/N ratio obtained for the CMS, GLAST and LHCb-ladders as a function of the bias voltage. different ladders tested. The two sets of points for each ladder represent the S/N ratio for tracks passing close to a readout strip and the S/N for tracks passing through the inter-strip region 3. The bias voltages at which the S/N reaches a plateau are compared in Table 6 with the measurements of the depletion voltage via the development of the backplane capacitance [8]. In absolute values, much larger over-depletion is needed as the thickness of the sensors increases. However, when comparing the relative over-depletion (V bias /V depletion ), as is done in Figure 5, all the ladders reach a plateau at times the depletion voltage. The test-beam measurements of the start of the plateau are in agreement with those given in [5] except for the CMS ladder. This ladder seems to plateau earlier in the test-beam measurements than with the laser. This may be due to the difference in charge deposition profiles between the Laser and test-beam measurements which is most pronounced for the CMS ladder [5]. 3 The on-strip and inter-strip regions are defined here as ±.66 strip-pitch from the strip centre and the middle between two strips, respectively. These are larger areas than used later in the efficiency determination due to the limited statistics available in the bias voltage scans. 9

10 March 8, 24 Test-beam Results ladder depletion voltage signal plateau LHCb 64 V 2 V LHCb2 64 V 2 V GLAST 7 V 5 V CMS 9 V 3 V Table 6: Comparison between depletion voltage measured with a LCR-meter and the observed plateau from the S/N in the test-beam CCE [arbitrary units] lhcb/on-strip lhcb2/on-strip GLAST/on-strip CMS/on-strip V-bias/V-depletion Figure 5: The S/N ratio obtained for different relative over-depletion bias voltages for the CMS, GLAST and LHCb-ladders. Comparing the S/N for large over-depletion between the on-strip and inter-strip regions, indicates that the charge loss in the inter-strip region cannot be explained by insufficient time to collect all the charge that is to say a ballistic deficit, since in that case the difference between the two should become smaller for higher bias voltages. In Figure 6 it can be seen that the charge collection time of the signal decreases with increasing voltage this can be explained by an increase of the velocity of the charge carriers in the silicon bulk. Within the accuracy of the measurement no significant difference is found between the on- and mid-strip data 4. The systematic offset between the LHCb2 and the LHCb ladder can be explained by the higher load capacitance to the Beetle chip of the LHCb2 ladder which affects the rise- and fall-time time of the pulse. Finally, the behaviour of the noise has been studied as a function of the bias voltage. There is expected to be no change in the level of the noise during the scan since the ladders are fully depleted and the leakage currents are small. Figure 7 shows the measured noise as a function of the bias voltage. The noise level varies at a level of less than.5% over the whole scan. There is a small but significant decrease in the noise level for all the ladders at the highest bias voltages. However, it should be noted that these last runs were taken hours after the rest due to loss of beam from the machine. This probably explains the observed difference. 4 It should be noted that in [5] a clear difference in peaking times between on-strip and mid-strip data was observed. No reason has been found for this discrepancy.

11 Test-beam Results March 8, 24 delay [ns] 3 29 delay [ns] delay [ns] CMS/on-strip CMS/inter-strip bias voltage [V] GLAST/on-strip GLAST/inter-strip bias voltage [V] 2 5 lhcb/on-strip lhcb/inter-strip lhcb2/on-strip lhcb2/inter-strip bias voltage [V] Figure 6: Time of the signal maximum as a function of bias voltage. noise [ADC] noise [ADC] noise [ADC] CMS 3.89 GLAST 3.7 LHCB LHCb bias voltage [V] bias voltage [V] bias voltage [V] Figure 7: Strip noise for the CMS, GLAST and LHCb ladders as a function of the bias voltage. 5.2 Pulse-shape studies A series of high statistics latency scans were taken in order to study the pulse-shape as a function of both the applied bias voltage and the Beetle shaping parameter, V fs. For these studies only tracks that passed within ±.2 pitch of the centre of a readout strip were used. As an example in Figure 8 the results of these scans are shown for the bias voltage setting V 2 and for V fs = 4 mv. For the ladders built from the LHCb multi-geometry sensors results are shown for region A only. In each plot the signal on the strip closest to the particle trajectory is shown together with the two strips to its left and to its right. It can be seen that for all the ladders there is a sizeable signal on the neighbouring strips. These signals cannot be due to charge sharing by diffusion between the strips because of the wide pitch of the sensors. In addition the amplitude is too big to be explained by cross-talk within the Beetle chip which has been measured to be 3% [3]. It can also be seen from these plots that the signals induced on the neighbouring strips have a different time dependence to those on the central strip. Firstly, the time of the maximum amplitude for these signals is earlier in time than that of the central strip. Secondly, these signals undershoot earlier in time. Simulation studies of charge collection in silicon and signal generation in the Beetle chips have shown that these signals can be accurately reproduced if capacitive coupling between the readout strips is taken into account [4, 5]. An important parameter for the operation in the LHCb experiment is the signal remainder 25 ns after the signal maximum the fraction of the signal which will be seen in the following LHC bunch crossing. In Figure 9 the measured signal remainder is plotted as a function of detector capacitance for each of the two shaping times. As expected, the size of the

12 March 8, 24 Test-beam Results signal charge [ADC counts] Glast ladder (V=2V Vfs=4mV) central strip left neighbour right neighbour left neighbour - right neighbour + signal charge [ADC counts] CMS ladder (V=45V Vfs=4mV) central strip left neighbour right neighbour left neighbour - right neighbour delay [ns] delay [ns] signal charge [ADC counts] LHCb3 ladder (V=2V Vfs=4mV) central strip left neighbour right neighbour left neighbour - right neighbour + signal charge [ADC counts] LHCb2 ladder (V=2V Vfs=4mV) central strip left neighbour right neighbour left neighbour - right neighbour delay [ns] delay [ns] Figure 8: Pulse-shape scans. remainder decreases with decreasing V fs. As in [5] a roughly linear dependence on the detector capacitance is observed. The results of fitting the data for V fs = 4 mv and V2 with the form: S r = A r + B r C are summarised in Table 7. Also given in this table are the numbers found in the corresponding analysis of tests in the laser set-up [5]. These numbers have been updated to take into account the corrections to the strip capacitances described in Section 2. It can be seen that the values obtained in the two set-ups are in good agreement. In Monte Carlo studies of the LHCb performance signal remainders of less than 5% for the 33 cm long TT ladders and less than for 3% for the 22 cm long IT ladders are assumed [2]. Both these requirements can be met if V fs is set to 4 mv or less. The average efficiencies of finding a cluster from a previous bunch-crossing with this setting and applying the cluster finding cuts described in Section 4 are summarised in Table 8. It should be noted that for in- 2

13 Test-beam Results March 8, 24 Setup A r B r laser.6 ±.5.5 ±.2 Test-beam.9 ±.6.5 ±.2 Table 7: Comparison of remainder parameters with the laser and in the test-beam for V2 and V fs = 4 mv. remainder V, Vfs=4mV V2, Vfs=4mV V, Vfs=mV V2, Vfs=mV detector capacitance [pf] Figure 9: Signal remainder 25 ns after the maximum. For the LHCb ladders results for region A are shown. time events, the efficiency found using these cuts is close to %. For the CMS and GLAST ladders used in the test-beam the relatively high efficiency for finding spillover clusters can be reduced by either re-tuning the χ 2 cut or by making use of the fact that signals on the neighbouring strips are negative in the case of spillover clusters. CMS ladder GLAST ladder LHCb2 ladder LHCb3 ladder eff. after 25 ns 87% 76% 44% 38% Table 8: Efficiency for finding a cluster from the previous bunch-crossing. 5.3 Cluster-shape Analysis The average sizes of the clusters found using the algorithm described in Section 4 are are 3.4, 2.7 and 2.2 strips for the CMS, GLAST and LHCb3 ladders, respectively. The distributions of the cluster sizes are shown in Figure. The different cluster sizes can be explained by the different thicknesses of the sensors and the resulting larger S/N on the individual strips. This makes it more likely for the CMS and GLAST ladders to include neighbouring strips into a cluster than for the LHCb3 ladder. In addition, the size of the signals on the neighbouring strips, the shoulders, that are attributed to capacitive coupling between the strips is largest for the CMS ladder and smallest for the LHCb ladder. This can be seen 3

14 March 8, 24 Test-beam Results relative occurence GLAST ladder relative occurence CMS ladder relative occurence.4.2 LHCb3 ladder cluster width [strips] cluster width [strips] cluster width [strips] Figure : The cluster width distribution. relative signal GLAST ladder relative signal CMS ladder relative signal LHCb3 ladder strip strip strip relative signal (between strips).5 GLAST ladder strip relative signal (between strips).5 CMS ladder strip relative signal (between strips).5 LHCb3 ladder strip Figure : Relative amplitudes on the central strip, neighbours and next neighbours for particles that pass through the centre of a readout strip (top) and through the centre of the gap between two readout strips (bottom). in Figure where the relative signal on the four strips closest to the particle trajectory is plotted. This behaviour is expected since for similar values of the w/p the inter-strip capacitance increases with increasing sensor thickness. The cluster shape for clusters from particles passing through the centre of the gap between two readout strips is shown in the bottom row of Figure. Here the shoulders, i.e. the size of the signal on the neighbouring strips relative to the size of the signals on the two strips closest to the track impact point appear to be larger than for on-strip clusters. This means that the shoulders are not solely determined by the size of the signal on the neighbouring strip. The size of the shoulders also depends on the length of the ladder. This can be seen in Figure 2 where the size of the shoulders is compared for three ladders constructed from 4

15 Test-beam Results March 8, 24 rel. shoulder size LHCb3 LHCb2 LHCb ladder length [cm] rel. shoulder size LHCb LHCb2 LHCb3 (pitch = 98 µm) w/p Figure 2: Relative shoulder size as a function of the ladder length (left) and as a function of w/p (right) for the three different LHCb ladders. The two points per ladder and w/p refer to the left and the right neighbour which have systematically different sizes. LHCb sensors. This observation is consistent with the shoulders being dependent on the inter-strip capacitance. Also shown is the dependence of the shoulder size on the w/p. No clear dependence can be seen within the accuracy of the measurement. The observation that the properties of the shoulders depend on the ladder length and thickness also supports the hypothesis that they are related to signal propagation in the sensor and are not solely due to cross-talk within the Beetle chip. It should also be noted that all these results are in good agreement with those presented in [5]. 5.4 Signal-to-Noise performance One of the main goals of the test-beam was to investigate the S/N performance of the ladders. As in previous studies two alternative definitions of signal were used. The first is to simply sum the ADC counts of the four strips closest to the predicted impact point of the telescope track. The second is to use the results of the clustering procedure described in Section 4. Figure 3 shows the resulting S/N distribution for V fs = 4 mv, using the four strip analysis for the GLAST, CMS and LHCb3 ladders, while Figure 4 shows the S/N distributions obtained with the standard cluster finding algorithm. In both cases, the noise was normalised to the level of the single strip noise. The S/N values obtained with the four strip analysis are larger than those obtained with the clustering algorithm analysis. This demonstrates that in the cluster finding algorithm the neighbouring strips are not always included. The difference in S/N between the two clustering schemes is most pronounced for the LHCb3 ladder (8%) where the average cluster width is 2.2 strips, and least pronounced for the CMS ladder (5%) where the average cluster width is 3.4 strips. Also shown in these plots are the results of a fit to the distribution of a Landau convolved with a Gaussian and the Landau s most probable value (MPV). The plots in Figure 4 produced using the cluster finding algorithm also show the noise cluster distribution. It can be seen that for the GLAST and CMS ladders there is a clear separation between the tail of the noise 5

16 March 8, 24 Test-beam Results distribution and the signal distribution. This is not the case for the LHCb3. Nota Bene, the S/N ratios quoted here are % worse than those given in [6]. This is due to the correction of an error in the procedure used to determine the noise. clusters GLAST ladder (V= 2V) associated cluster charge MPV= S/N (4 strips) clusters CMS ladder (V= 45V) associated cluster charge MPV= S/N (4 strips) clusters LHCb3 ladder (V= 2V) associated cluster charge MPV= S/N (4 strips) Figure 3: S/N derived from the sum of the four strips closest to the extrapolated track impact point. Region C was used for LHCb3 ladder. V fs was set to 4 mv. clusters 7 6 GLAST ladder (V= 2V) associated cluster charge noise clusters 5 4 MPV= S/N clusters CMS ladder (V= 45V) associated cluster charge noise clusters MPV= S/N clusters LHCb3 ladder (V= 2V) associated cluster charge noise clusters 4 2 MPV= S/N Figure 4: S/N obtained with the cluster finding, averaged over the entire inter-strip region. Region C, was used for the LHCb3 ladder. V fs was set to 4 mv. In Figure 5 similar plots are shown for the LHCb and LHCb2 ladders. Also shown are the plots for the corresponding ladders that were tested in May 22 and read out with the Beetle. chip 5. As expected, for the same setting of V fs the Beetle.2 gives better S/N performance than the Beetle.. It should also be noted that for the same V fs setting the actual shaping time for the Beetle.2 is considerably faster than for the Beetle.. Therefore, in addition to the improvement in the S/N there is a reduction in the signal remainder after 25 ns for the Beetle.2 compared to the Beetle.. The signal remainder achieved with the Beetle. and with V fs set to 4 mv can be now be achieved with the Beetle.2 and with V fs set to mv. It has been observed in previous test-beams that there is a significant charge loss in the region between two readout strips. This can clearly be seen in Figure 6 where the S/N from the four strip analysis is plotted as a function of the inter-strip position of the extrapolated tracks for all ladders. The four strip analysis is used for this plot in order to ensure that the dip 5 The old data have been re-analysed including the fix in the procedure for the determination of the noise mentioned in the text. In contrast to the plot shown in [3], clusters that coincide with a second track in the event or with hits in the other test modules (indicating a real track that was not reconstructed by the telescope) were excluded. 6

17 Test-beam Results March 8, 24 clusters Lhcb2 ladder (V= 2V) associated cluster charge noise clusters MPV= S/N clusters Lhcb ladder (V= 2V) associated cluster charge noise clusters MPV= S/N clusters 45 4 Long ladder (V= 2V) associated cluster charge noise clusters MPV= S/N clusters Short ladder (V= 2V) associated cluster charge noise clusters MPV= S/N Figure 5: S/N obtained with the cluster finding, averaged over the entire inter-strip region. The top plots are from the 23 test-beam with the Beetle.2 and the bottoms plot are from the 22 test-beam with the Beetle.. Region C was used. in S/N is not caused by some artefact of the clustering algorithm. It can also be seen from these plots that the loss in S/N is independent of the shaping time. The same behaviour is seen in the results obtained using the clustering algorithm, shown in Appendix B. This is consistent with the results of the previous test-beam that indicated that the charge loss in the inter-strip region is not caused by a ballistic deficit since this would be reduced for longer shaping times. The effect can be reproduced by simulation if it is assumed that it is caused by charges trapped in the inter-strip region where the electric field lines leave the sensor region before reaching the readout strips [4, 5]. The improvement in performance due to the Beetle.2 as a function of the inter-strip position is shown in Figure 7. Again in these figures data with the same V fs for the Beetle. and Beetle.2 have been compared. It can clearly be seen that although the overall performance is better with the Beetle.2, the improvement for tracks that pass close to the centre of two readout strips is only small. This effect is most pronounced for the case of the LHCb2 ladder. The reason for the relatively small improvement of the S/N from Beetle. to Beetle.2 in the inter-strip region is not understood. However, it is expected that the S/N improvement due to the Beetle.2 is smaller for the LHCb2 ladder than for the LHCb ladder, because for the Beetle.2 the noise rises faster with load capacitance than for the Beetle.. These plots also show that for the LHCb2 ladder with V fs = 4 mv a S/N of only 9.6 is achieved for tracks that pass through the central region between two readout strips. For the LHCb2 and LHCb3 ladders, the charge loss between the two strips translates into a loss in cluster finding efficiency in the region between the readout strips. This can be seen in Figure 8 where the cluster finding efficiency is plotted as a function of the track impact point 7

18 March 8, 24 Test-beam Results S/N (4 strips) 2 S/N (4 strips) 2 V-bias 2V, GLAST ladder Vfs=mV Vfs=4mV Vfs=mV V-bias 45V, CMS ladder Vfs=mV Vfs=4mV Vfs=mV S/N (4 strips) 2 S/N (4 strips) 2 V-bias 2V, LHCb ladder Vfs=mV Vfs=4mV Vfs=mV V-bias 2V, LHCb2 ladder Vfs=mV Vfs=4mV Vfs=mV S/N (4 strips) 2 V-bias 2V, LHCb3 ladder Vfs=mV Vfs=4mV Vfs=mV Figure 6: Comparison of the S/N as a function of the inter-strip position for the different ladders and shaping times (V fs ). For the LHCb ladders, region A is plotted (same w/p as GLAST and CMS ladder). The S/N was determined from the summed charge on four strips. V fs was set to 4 mv. 8

19 Test-beam Results March 8, 24 S/N (4-strips) 2 5 S/N (4-strips) 5 5 bias voltage 2V, Vfs=mV lhcb ladder, Beetle.2 short ladder, Beetle. 5 bias voltage 2V, Vfs=mV lhcb2 ladder, Beetle.2 long ladder, Beetle S/N (4-strips) 2 5 S/N (4-strips) 5 5 bias voltage 2V, Vfs=4mV lhcb ladder, Beetle.2 short ladder, Beetle. 5 bias voltage 2V, Vfs=4mV lhcb2 ladder, Beetle.2 long ladder, Beetle Figure 7: Comparison of the S/N measured for the different inter-strip positions for the LHCb (left) and LHCb2 (right) ladders used in the 23 test-beam with Beetle.2 and the previous test-beam with Beetle.. Region C is compared. for all the ladders. As expected from the poor S/N performance this effect is particularly pronounced for the LHCb3 ladder. For tracks passing close to the middle of two readout strips the efficiency is below 9%. This is not acceptable for use in LHCb. It is also clear from these plots that the S/N performance obtained with the LHCb2 ladder is marginal. In Figure 9 the S/N (averaged over the inter-strip region), the efficiency obtained for tracks close to a readout strip and for track that traverse the detector in between two strips is plotted against the shaping time parameter V fs. As already seen in Figure 6, the S/N ratio increases for longer shaping times (larger V fs ). For the CMS and the GLAST ladders full efficiency is found for all shaping times, due to the high S/N. However, for both the LHCb2 and LHCb3 ladders an increase in the efficiency in the inter-strip strip region is observed as V fs is increased. This effect is most pronounced for the LHCb3 ladder where even for V fs = mv full efficiency in the inter-strip region cannot be achieved. The S/N performance has also been investigated as a function of the beam position along the 9

20 March 8, 24 Test-beam Results efficiency.99 efficiency V-bias 2V, GLAST ladder Vfs=mV Vfs=4mV Vfs=mV.97 V-bias 2V, CMS ladder Vfs=mV Vfs=4mV Vfs=mV efficiency.99 efficiency V-bias 2V, LHCb ladder Vfs=mV Vfs=4mV Vfs=mV.9 V-bias 2V, LHCb2 ladder Vfs=mV Vfs=4mV Vfs=mV efficiency.95.9 V-bias 2V, LHCb3 ladder Vfs=mV Vfs=4mV Vfs=mV Figure 8: Comparison of the measured efficiency as a function of the inter-strip position for different shaping times (V fs ) for all ladders under test. For the LHCb ladders, Region A is plotted (same w/p as GLAST and CMS ladder). 2

21 Test-beam Results March 8, 24 S/N (4-strips) Efficiency on strips Efficiency between strips LHCb2 Reg.A LHCb Reg.A.9.88 LHCb2 Reg.A LHCb Reg.A.9.88 LHCb2 Reg.A LHCb Reg.A 4 Glast Ladder CMS Ladder LHCb3 Reg.A.86 Glast Ladder CMS Ladder LHCb3 Reg.A.86 Glast Ladder CMS Ladder LHCb3 Reg.A Vfs [mv] Vfs [mv] Vfs [mv] Figure 9: Most probable signal-to-noise ratio averaged over the inter-strip positions obtained with the four strips analysis (left), cluster finding efficiencies for particles traversing the detector at the position of a readout strip (middle) and in the central region between two strips (right) as a function of the shaping time parameter V fs. For the LHCb ladders, Region A is plotted. S/N Glast Ladder CMS Ladder LHCb3 Ladder Near Middle-Near Middle Far-Middle Far sensor position Figure 2: S/N versus beam position on along the ladder. The position marked Near is closest to the readout hybrid. ladder. The results of this study are shown in Figure 2. It can be seen that for all ladders there is no significant dependence in the performance with respect to the position along the ladder. 5.5 Investigation of the charge loss Since several different sensor types have been tested it is possible to investigate the dependence of the charge loss between the strips on the strip geometry. This has been done as 2

22 March 8, 24 Test-beam Results follows. First, tracks that pass within ±. in pitch units around a strip centre are selected. The ADC counts on the three strips closest to the track are then summed and the resulting distribution fitted with a Landau convolved with a Gaussian. The MPV of the Landau from the fit is then taken as the size of the on-strip charge, C on. Next, tracks that pass within ±. of the middle of two readout strips are selected and the four strips closest to the track summed. Again the resulting distribution is fitted with a Landau convolved with a Gaussian. The MPV of the fitted Landau of this distribution is the size of the mid-strip charge, C mid. The relative dip, r d is then defined as: r d = C mid /C on In Figure 2 r d is plotted against x d = (p w)/t where p is the pitch, w the implant width Relative Dip CMS C GLAST B A D (p-w)/t Figure 2: Relative dip as function of x d. and t the detector thickness for the sensor geometries that were tested. It can be seen that r d is approximately linear with x d in the range investigated. Fitting: r d = A d B d x d. gives A d =.6 ±.4 and B d =.66 ±.. This relationship means that the relative size of the dip can be reduced either by increasing w/p or by increasing the sensor thickness. These numbers are consistent with there being no dip when the size of the inter-strip region becomes zero. It might be asked whether the observed dependence of the charge loss on the detector geometry is caused by differences in the amount of capacitive coupling between the readout strips. The effect of the capacitive coupling on the result can be minimized as follows. For the on-strip data the charge deposited on the closest strip to the track impact point is taken to be C on. The mid-strip charge is than taken to be the sum of the charge deposited on the two strip closest to the predicted track impact point. In Figure 22 the results of this analysis are shown. Again an approximately linear dependence is found with A d =.9 ±.4 and B d =.62 ±.. 22

23 Test-beam Results March 8, 24 Relative Dip CMS CMS GLAST GLAST C C B A D D (p-w)/t Figure 22: Relative dip as a function of x d ( single strip analysis). 5.6 Charge calibration An interesting and important question is whether the observed S/N performance is consistent with expectations from the generation of charge in silicon and the performance of the Beetle chip. The best way to investigate this is to perform an electronic charge calibration. For this purpose several channels were bonded to a PCB which allowed a known amount of charge to be injected into the ladder. Analysis of data taken in the test-beam and subsequent lab measurements using this method have shown that a very good grounding scheme is needed in order to obtain reliable results. In particular, sensible results could not be obtained from an analysis of the charge calibration data taken during the test-beam period. An alternative is to proceed as follows. The process of energy loss in silicon is well understood [7, 8, 9]. This allows the calibration of the setup and hence calculate the noise in electrons if two assumptions are made. The first is that if a particle traverses a sensor close to the centre of a readout strip all the charge is collected. That is to say there is no ballistic deficit. The second is that the shoulders observed in the cluster shapes do not come out of the ionisation charge. Then, the equivalent noise charge in electrons, ENC is given by: ENC = p N ADC (noise) MPV(central strip) where p is the most probable value of the Landau calculated from theory in electrons and N ADC (noise) is the observed noise in ADC counts. MPV(central strip) is the most-probable value of the Landau distribution resulting from a fit of a Landau convolved with a Gaussian to the distribution of the number of ADC counts on the hit strip. Values of p for 2 GeV π incident upon the test-beam sensors have been calculated using the equations given in [9] and are summarised in Table 9. In this calculation a value of 3.6 ±. ev was used for the energy required to create an electron-hole pair. The results of these calculations can then be compared to the results of noise measurements made on a Beetle.2 chip in the laboratory [3], where discrete capacitors at the input of the Beetle were used to simulate the detector 23

24 March 8, 24 Test-beam Results Sensor type Measured thickness/µm p /e LHCb 36 ± ± 63 GLAST 48 ± ± 4 CMS 55 ± ± 4 Table 9: Most probable value of the Landau in e, p from theory for the sensors under test. The quoted error on p /e is due to the uncertainty on the sensor thickness only. load capacitance. In these measurements the Beetle noise performance was found to be a linear function of capacitance: ENC = A off + B s C. This procedure has been carried out for all the ladders under test and for the three shaping times. In the case of the LHCb ladders each region was treated separately. For the GLAST and CMS ladders each Beetle was treated separately. As a further cross-check for the GLAST, CMS and LHCb2 ladders, runs taken at the beginning and end of the test-beam period were compared. The resulting ENC numbers are plotted as a function of the strip capacitance in Figure The error bars on the capacitance includes contributions from the measured sensor and pitch adaptor capacitance. The uncertainty on the ENC is dominated by the uncertainties on the measured sensor thickness and the sampling time discussed in Section 4. The line marked best fit is obtained by fitting a straight line to the data for each LHCb region and averaging the results. ENC/e Region A Region B Region C Region D GLAST CMS C/pF Figure 23: Beetle noise performance for V fs = mv. The dashed line is the best fit to the test-beam data, the solid line the expectation from [3]. For all three shaping times the linearity of the data is impressive. That is to say the data show the same dependence on detector capacitance as in the lab measurements. For the GLAST and CMS ladders no significant differences were found from chip-to-chip. In addition the results for the runs taken at different times are consistent within the quoted uncertainty. In Table the values obtained for A off and B s in the test-beam data are compared to those obtained in the lab measurements. It can be seen that the values for B s are consistent within errors. However, the values of A off found are slightly higher in the test-beam than in the lab measurements. This may be partially explained by several small effects that have not been taken account in the calibration procedure described here. First, in the calculation of 24

25 Test-beam Results March 8, Region A Region B Region C Region D GLAST CMS C/pF Figure 24: Beetle noise performance for V fs = 4 mv. The dashed line is the best fit to the test-beam data, the solid line the expectation from [3]. ENC/e- ENC/e Region A Region B Region C Region D GLAST CMS C/pF Figure 25: Beetle noise performance for V fs = mv. The dashed line is the best fit to the test-beam data, the solid line the expectation from [3]. the strip capacitance the effect of the bond wires has not been taken into account. If this was included it would shift the measured points to higher values of capacitance. Second, in the test-beam set-up there are several small sources of noise that have been ignored. For example: Noise due to the strip resistance. Quantization noise from the ADC. Possible imperfections in the common noise subtraction and thr determination of the strip noise. Finally, fluctuations in the number of electron-hole pairs have been ignored. All of the above are individually expected to be small effects but when combined may explain the observed discrepancy. The assumption that shoulders do not come out of the ionisation charge can be tested by repeating the above procedure but using the most probable value of the total charge on the three strips nearest the track instead of MP V (central strip). Doing this for the V fs = mv 25

26 March 8, 24 Test-beam Results V fs /mv Lab measurement Test-beam Measurements Aoff B s A off B s ± 5 ± ± 3.3 ± ± 6 ± ± 3.7 ± ± 6 ± ± 3.5 ± 2 Table : Comparison of Beetle noise parameters found in the test-beam to lab measurements. For the test-beam measurements the first error is due to averaging the results for the four regions on the LHCb ladders; the second is due the uncertainty on the theoretical prediction for the deposited charge and is common to all shaping times. data gives A off = 83 and B s = 36. Such a small value for the slope is in clear disagreement with the front-end measurements and other expectations of the Beetle performance. This is an indication that the hypothesis that the shoulders do not come out of the ionisation charge is correct. 6 Summary The results of test-beam measurements of silicon detectors with strip length of up to 33 cm and with corresponding capacitances of up to 55 pf have been described in detail. These tests have made use of the Beetle.2 front-end chip. The observed S/N performance of the ladders has been found to be consistent with the expectation based on measurements of the Beetle front-end chip. The Beetle.2 chip has also been found to have a significantly faster shaping time than the Beetle. chip used in previous studies. Signal shapes meeting the specifications of less than 5% remainder for the TT-station and less than 3% remainder for the IT stations can be obtained if the shaping time parameter V fs is set to 4 mv. The fact that ladders with different thickness and with regions of different w/p have been tested simultaneously has allowed the effect on sensor properties such as a capacitive coupling and charge collection efficiency to be investigated. This in combination with knowledge of the Beetle noise performance makes it possible to predict the S/N performance both on and mid-strip for possible sensor geometries that have not been tested. Extrapolations made using the numbers given here will be presented in [2]. It is clear from the measurements presented here that 32 µm silicon does not give sufficiently high S/N to give full detection efficiency for ladders with strips of length 33 cm. It therefore seems that ladders with a thickness of at least 4 µm should be used in the TT station. The final choice of sensor thickness for the TT station will also be described in [2]. 26