The LHCb Silicon Tracker

The aim of the LHCb experiment is to study rare heavy quark decays and CP violation with the high rate of beauty and charmed hadrons produced in pp collisions at the LHC. The detector is designed as a single-arm forward spectrometer with excellent tracking and particle identification performance. The Silicon Tracker is a key part of the tracking system to measure the particle trajectories to high precision. This paper reports the performance as well as the results of the radiation damage monitoring based on leakage currents and on charge collection efficiency scans during the data taking in the LHC Run I.


Introduction
The LHCb experiment [2] is designed for the study of heavy flavour physics in proton-proton collisions at the LHC. The primary goal of the experiment is to search for New Physics in rare decays of b and c hadrons and in precision measurements of CP violation.
The detector is set-up as a single-arm forward spectrometer covering a pseudorapidity range η = − log(tan θ /2) between 2 and 5, as bb and cc pairs are predominantly produced under small polar angles with respect to the LHC beams. The Silicon Tracker (ST) is part of the tracking system and consists of two sub-detectors: the Tracker Turicensis (TT) placed upstream from the dipole magnet and the Inner Tracker (IT) forming the inner part of the tracking stations downstream from the dipole magnet. Both detectors use single-sided silicon micro-strip sensors. The TT has four planar detector layers (0 • , +5 • , −5 • and 0 • tilted with respect to the field lines of the dipole magnet) made using p + -on-n sensors with a strip pitch of 183 µm and a thickness of 500 µm. The sensors are bonded together into read-out sectors of either 1, 2, 3 or 4 sensors. This leads to read-out strips of up to 37 cm in length. In total there are about 144k read-out strips in the TT. The IT detector uses p + -on-n type sensors with a strip pitch of 198 µm. They are grouped into twelve planar layers. In each layer the sensors in the region on both sides of the beam pipe are paired to form a read-out sector with a total strip length of 22 cm (long ladders). The sensors for this configuration have a thickness of 410 µm, while the read-out sectors below and above the beam pipe consist of single sensors which are 320 µm thick and have a read-out strip length of 11 cm (short ladders). The IT has around 130k read-out strips. Both detectors are operated with a sensor temperature of about 8 • C.

JINST 9 C01009
The electronic read-out of the sensors is the same in both detectors: the Beetle front end chip [3] amplifies, shapes and samples the output signal of the read-out strips which is then transmitted via up to 8 m long copper cables to service boxes close to the detector, but located outside of the acceptance. There the signal is digitized and transmitted via VCSEL 1 diodes and optical fibres to the counting house where the TELL1 boards [4] use FPGAs to perform pedestal and common mode noise subtraction as well as zero suppression.

Performance
At the end of LHC run I the fraction of working read-out channels in TT and IT was very high with 99.4% and 98.4%, respectively. The slightly smaller fraction in IT is due to the more difficult access to the detector during data taking periods. During the shutdown of LHC repair work has been done resulting in a recovery of a large fraction of bad read-out channels.

Time alignment
The time alignment provides the synchronization of the trigger and control signals with the pp collisions of LHC and takes into account differences in cable length and flight time of the particle among the different detector layers.
In ST it is performed by a scan over the delay between the sampling time of the Beetle chip with respect to the LHC clock. The signal amplitude is determined for each delay step of 6.2 ns as the most probable value (MPV) of the signal distribution. The position in time giving the highest signal amplitude is determined from a pulse fit to these data points. The procedure gives a time alignment better than 1 ns.

Signal-to-noise ratio
The signal-to-noise ratio (S/N) is measured in the ST using clusters from tracks with a reconstructed momentum larger than 5 GeV/c. The ratio is between 12 and 15 for TT, while for IT the range is 15 to 18. These values determined from data taken at the beginning of the data taking period in 2011 are close to expectations based on test beam measurements during the R&D phase [5]. Figure 1 shows the average S/N in TT for 1-, 2-, 3-and 4-sensor read-out sectors as a function of the capacitance, and it displays the expected linear decrease of S/N with increasing capacitance. In figure 2 the S/N distribution for the long and short ladders in IT is shown. As the noise is dominated by the read-out electronics and the cabling, there is no significant change in S/N due to detector ageing (cf. section 3) expected.

Spatial alignment
The alignment of the tracking stations in LHCb is based on a global minimisation of track residuals using a Kalman filter fit [6]. Further the alignment takes advantage of the possible mass constraints in J/ψ → µ + µ − and D 0 (D 0 ) → K ± π ∓ samples to constrain degrees of freedom which are weakly constrained by single tracks (e.g. global shearing or scaling of the detector) [7]. Figure 3 shows  the distributions of the minimized track residuals after the alignment procedure for TT and IT. The resulting hit resolutions in TT and IT including alignment effects are 61 µm and 54 µm respectively.
In figure 4, the distributions of the average track residuals for each of the read-out sectors are shown for the 2012 data. From the RMS of these distributions the alignment precision is estimated to be 13.5 µm for TT and 15.0 µm for IT. These values are very good, especially when taking into account the fact that there are long distances between the tracking stations and that the tracking stations in LHCb are outside the magnetic field. Furthermore, LHCb is unable due to its forward geometry to use cosmics, which give a high statistics sample of tracks more uniformly distributed across the detector than tracks from pp collisions.

Hit efficiency
The hit efficiency in the ST is measured from data using isolated tracks with a momentum larger than 10 GeV/c. The track fit is repeated excluding the clusters in the sector under test. The hit efficiency is defined as the fraction of tracks that have a cluster in a search window around the track. The efficiency depends on the size of the search window and saturates at 99.3% in IT and at 99.7% in TT for search window sizes of 1.0 mm and 2.5 mm, respectively.

Radiation damage
The monitoring of radiation damage effects is crucial to predict the long term performance of the detector. Two methods are applied to monitor radiation damage in the ST: the measurement of the leakage current and the estimation of the depletion voltage via dedicated Charge Collection Efficiency (CCE) scans.

Leakage currents
The radiation leads to bulk damage in the silicon sensors which manifests itself by an increase of the leakage current I leak . The leakage current is proportional to the total fluence where Φ 1 MeV-n,eq is the 1 MeV-neutron equivalent fluence, V the volume of the irradiated silicon and α is the damage factor for 1 MeV-neutrons taking into account annealing processes [9]. The effect of the temperature on I leak is given by where E g is the band gap energy of silicon [10]. Figure 5 shows the peak currents per fill for the sensors closest to the beam pipe in two of the TT layers as a function of the delivered integrated luminosity. The currents are normalized to a temperature of 0 • C using eq. (3.2). The spread in I leak is caused by the difference in fluence across the detector. The prediction of the leakage currents based on a FLUKA simulation [8] is also displayed in figure 5 showing a good agreement with the measurement. The annealing taking place during the winter shutdown 2011/2012 is visible as a drop in I leak at about 1250 pb −1 .

Charge collection efficiency scans
Three to four times a year dedicated CCE scans take place. The goal of these scans is to measure the effective full-depletion voltage V depl of the silicon sensors. In these scans the bias voltage V bias is varied for one detection layer in TT and one in IT. Therefore tracks can be still reconstructed using the remaining layers. The extrapolation of the tracks to the scanned layers gives an estimation of the hit position. The summed signal amplitude of the three strips closest to this position is taken as signal amplitude associated to this track. For each V bias setting the optimal sampling time is remeasured, following the procedure in section 2.1, to correct for differences in the signal collection time in the silicon. Figure 6 shows the distribution of the signal amplitudes in a read-out sector for a certain voltage and timing step. The noise distribution around zero is due to track extrapolations missing the track cluster as well as fake tracks created by combining hits from different particles. The MPV  Figure 6. Distribution of the signal heights associated to the extrapolated tracks in the CCE scans for a bias voltage of 400 V. The distribution is described by a double Gaussian for the noise distribution around zero and a convolution of this double Gaussian with a Landau distribution (red dashed curve) for signal. A second Landau distribution convoluted with the double Gaussian (red dotted curve) takes photon conversion into account. of the signal amplitude distribution is extracted from a fit of a double Gaussian for the noise distribution and a convolution of the same double Gaussian with the sum of two Landau distributions. The Landau distribution with the larger yield is the signal contribution while the second Landau distribution smaller in yield (represented by the dotted line in the figure) takes photon conversion in the detector material into account. The maximum MPV of the signal height for a certain voltage step is extracted from a fit of the pulse shape described by a Half-Gaussian from the MPVs of the different sampling times. Figure 7 shows the maximum MPVs as a function of the bias voltage. A sigmoid-like function of the form is used to describe the data points. The effective full-depletion voltage is defined as the bias voltage where the function reaches 85% of its maximum value. This value of 85% has been determined by comparing the results on non-irradiated sensors in the earliest CCE scan with V depl determined from measured 1/C 2 -curves during the detector production. The measured full-depletion voltage values from all TT read-out sectors in all CCE scans are shown in figure 8 as a function of the corresponding 1 MeV-neutron equivalent flux estimated from FLUKA simulations. As expected there is a decrease in V depl in the highest irradiated region of TT. The black line in the figure shows the estimated change in V depl based on the stable damage part of the Hamburg model [11] and is in good agreement with the measurements. The evolution of the effective full-depletion voltage as a function of time using clusters associated with tracks  in a region closer than 45 mm to the beam axis is shown in figure 9. The plot shows also the prediction from the full Hamburg model based on the actual running conditions. There is a very good agreement between prediction and measurement.

Summary
The LHCb Silicon Tracker has shown an excellent performance during LHC Run I between 2010 and 2012. The observed signal-to-noise ratios are for both sub-detectors (TT: 12-15, IT: 15-18) close to the expectation from test beam results during the R&D phase. The spatial alignment, which is in LHCb done based on collision data, has a precision better than 15 µm. The precision of the time alignment is better than 1 ns and the hit efficiency is for both detectors well above 99%.
The monitoring of the radiation damage done by measuring leakage currents and the effective full-depletion voltage shows very good agreement with expectations based on the running conditions. These measurements show that both sub-detectors will be able to cope with the radiation in LHCb up to the planned upgrade of the detector during long shutdown 2 (LS2).
During the long shutdown 1 (LS1) minor maintenance work is performed on the Silicon Tracker such that it will be ready to continue operation with an excellent performance after the restart of the LHC.