Monitoring radiation damage in the LHCb Tracker Turicensis

This paper presents the techniques used to monitor radiation damage in the LHCb Tracker Turicensis from 2011 to 2017. Bulk leakage currents in the silicon sensors are monitored continuously, while the full depletion voltage of the sensors is estimated at regular intervals by performing dedicated scans of the charge collection efficiency as a function of the applied bias voltage. Predictions of the expected leakage currents and full depletion voltages are extracted from the simulated radiation profile, the luminosity delivered by the LHC, and the thermal history of the silicon sensors. Good agreement between measurements and predictions is found.


Introduction
The LHCb experiment [1] at the LHC was designed to study decays of hadrons containing beauty and charm quarks. Its main goal is to perform precision measurements of CP violating observables, and to search for signatures of potential physics beyond the Standard Model in rare decays of such hadrons. The layout of the LHCb detector is illustrated in Fig. 1. The detector is a single-arm forward spectrometer that covers polar angles from about 15 mrad to 250 mrad and consists of a vertex locator, a tracking system comprising a single planar tracking station upstream of the spectrometer dipole magnet and three tracking stations downstream of this magnet, two Ring Imaging Cherenkov detectors, a calorimeter system comprising electromagnetic and hadronic calorimeters, and a muon system. The Silicon Tracker (ST) comprises the tracking station upstream of the dipole magnet, called Tracker Turicensis (TT), and the central part in each of the three tracking stations downstream of the dipole magnet, called Inner Tracker (IT); the outer part of the downstream tracking stations is formed by a straw-tube detector.
The TT employs conventional AC-coupled float-zone p + -on-n silicon micro-strip sensors The four different types of readout sectors employed in each of the detection layers are indicated by different shading: readout sectors close to the beam pipe consist of a single silicon sensor, other readout sectors consist of two, three or four silicon sensors that are connected together in series.
that are 500 µm thick and have 512 strips with a pitch of 183 µm and a length of 96 mm. The total silicon volume per sensor is 4512 mm 3 . The initial full depletion voltages of the sensors were determined from measurements of the bulk capacitance as a function of applied bias voltage and were found to range between 135 and 275 V.
The TT consists of one detector box containing four detection layers arranged in two pairs: the first two layers are centered around z = 232 cm, and the last two around z = 262 cm. An ambient temperature of about 8 • C is maintained inside the box. The box is flushed with dry gas (N 2 ) to avoid condensation on cold surfaces. Silicon sensors within each detection layer are electronically grouped into readout sectors consisting of one, two, three or four sensors, as illustrated in Fig. 2. All sensors within a readout sector are connected in series to a front-end readout hybrid that carries four 128-channel Beetle chips [2].
The Beetle front-end readout chip amplifies and shapes the signals from the readout strips and samples the signal amplitude every 25 ns, corresponding to the LHC bunchcrossing frequency of 40 MHz. The time offset between the LHC bunch clock and the Beetle sampling time is an adjustable parameter. The output data of the Beetle chips are multiplexed, digitised and transmitted optically to the LHCb TELL1 readout boards [3]. In the TELL1 boards, algorithms for common-mode subtraction, cluster finding and zero-suppression are executed during normal data taking. It is, however, also possible to store the raw sampled amplitudes from each input channel of the Beetle chip for offline  analysis. This non-zero-suppressed readout mode is employed for the studies discussed in this paper.
LHCb collected an integrated luminosity of about 3 fb −1 at proton-proton collision energies of √ s =7 and 8 TeV during Run 1 of the LHC (2010-2012), and √ s = 3.7 fb −1 at 13 TeV in 2015-2017. About 2 fb −1 more are expected to be collected in the last year of data taking during Run 2 (2018) at √ s = 13 TeV. The evolution of the integrated luminosity is shown in Fig. 3 (left) for each year of data taking. Expected particle fluences at collision center-of-mass energies of √ s = 7, 8 and 14 TeV have been derived from simulation using Fluka [4], a general purpose tool for calculations of particle transport and interactions with matter, and a detailed description of the geometry of the LHCb experimental area [5,6]. Maps of the particle fluence at √ s = 7 and 8 TeV are scored with a resolution of [1,1] cm, while the map at √ s = 14 TeV is scored with a resolution of [2.5, 2.5] cm and subsequently interpolated to obtain a map with a resolution of [1,1] cm. All maps are produced at a z-coordinate corresponding to the location of the TTaU layer. The statistical uncertainty on the expected fluence is modeled as a power-law function of the radial position from the beam pipe, a 0 × (r/r 0 ) α , where a 0 = 0.7 × 10 −2 cm −2 , r 0 = 1 cm, and α = 0.918. The expected 1-MeV neutron equivalent fluence per proton-proton collision at a center-of-mass energy of √ s = 14 TeV at the location of one of the detection layers of the TT is shown in Figure 3 (right). The highest expected 1-MeV neutron equivalent fluence, in the innermost region of the TT, corresponds to about 10 13 cm −2 per 1 fb −1 of integrated luminosity collected at a proton-proton collision energy of √ s = 14 TeV. Since particles are primarily produced in the forward direction, the expected fluence falls off by almost three orders of magnitude from the innermost to the outermost region of the TT detector.
Two methods are employed to monitor the radiation damage to the silicon sensors and its impact on the detector performance. The first method, discussed in Section 2, is based on the continuous measurement of detector leakage currents. These measurements are compared to the expected radiation-induced increase of the bulk leakage current as a function of received fluence at an ambient temperature of 8 • C. The second method, discussed in Section 3, is based on the analysis of collision data accumulated during dedicated Charge Collection Efficiency (CCE) scans. These CCE scans are performed at regular intervals and allow an estimation of the full depletion voltage of the sensors. The results of these measurements are compared to predictions derived from the Hamburg model [7], which parametrises the evolution of the effective doping concentration of the silicon bulk as a function of received fluence and temperature. Section 4 presents a summary of the different studies and discusses the expected evolution of the TT performance in terms of radiation damage.

Leakage current measurements
Bias-voltage for the TT is supplied by a commercial high-voltage (HV) system 1 with 152 channels supplying up to 500 V at a maximum current of 10 mA per HV channel. The innermost six silicon sensors in each detection layer, which receive the highest fluence and therefore experience the largest increase in leakage current, are connected to individual HV channels. In the outer regions of the detection layers, groups of two, three, four, nine or twelve silicon sensors are connected to a common HV channel. The current drawn by each HV channel is monitored with a resolution of 1.0 µA, and a maximum interval of 120 minutes allowed between consecutive readings. For the purpose of this analysis, the leakage current, I leak , for a given HV channel is determined for each LHC fill as the maximum current observed in that fill 2 . Measurements from fills with special detector configurations (e.g. higher or lower bias voltage) are discarded in the leakage current measurements. The leakage current has a temperature dependent behaviour given by where T 1,2 are different temperatures, k B is the Boltzmann constant and E g = 1.21 eV is the band-gap energy of silicon. All measured currents are normalised to a nominal temperature of 8 • C, using measurements of the ambient temperature inside the detector box and the well-known temperature dependence of the bulk leakage current in silicon [8].
The normalized leakage currents, scaled to 8 • C and per silicon volume, are shown as a function of integrated delivered luminosity and time in Fig. 4 for the innermost sensors in the second and third detection layers, indicated as U and V layers, respectively. The change ∆I leak in the leakage current is expected to be linear as a function of the fluence, Φ, that the sensor has been exposed to, for a range between 10 11 and 10 15 1-MeV n / cm 2 [7]. So ∆I leak can be described as where α is the current-related damage rate and V the silicon volume. The coefficient α Parameter Value shows a behaviour dependent on temperature, T a , and on time, t, as the irradiation occurs alternating with annealing, i.e. periods without collisions [9]. Short term annealing (on the order of a few days to a month) is described by the sum of a constant and exponential terms, where the first term describes the effects of stable damage. An additional logarithmic term is used to describe annealing effects for time periods longer than a year [10], The temperature dependence of the time constant τ I in Eq. (3) can be described by the Arrhenius relation [11], where k I,0 is the frequency factor and E a,I the activation energy of the process. The values of these parameters are listed in Table 1. Figure 4 also shows the predicted evolution of I leak based on this formalism using the actual running conditions in LHCb (i.e. instantaneous luminosity, duration of the fills, ambient temperature) and the 1-MeV neutron equivalent fluence computed for a given sector by integrating the simulated Fluka radiation map over the sensor area.
The predictions are in good agreement with the evolution of the leakage currents in data. Significant decreases in the currents are observed, as expected, in the data during periods with no irradiation, i.e. in the long shutdown, LS1, of the LHC in 2013 and 2014, extended stops of the accelerator during the winter season and short technical stops throughout the year (one week about every three months).

Depletion voltage measurements
Non-ionizing energy loss (NIEL) damage in the silicon bulk leads to a change in the effective doping concentration, n eff , of the bulk and therefore to a change in the full where q is the electron charge, εε 0 the effective permittivity of silicon and D the full thickness of the sensor. As mentioned in Section 1, the initial full depletion voltage of all silicon sensors was determined in C − V scans at the foundry and during the construction of the detector. For a subset of the installed detectors, the evolution of V depl during operation has then been measured from scans of the charge-collection efficiency as a function of the applied bias voltage (CCE scans). Such CCE scans require particles from LHC collisions to be recorded using special data taking settings. They are performed about two to four times a year, in particular once at the beginning of LHC operation in spring and once at the end of operation before Christmas. Table 2 summarises the CCE scans performed between 2011 and 2017.
While in the nominal data taking configuration the applied bias voltage V bias is 300 V for all TT readout sectors, during these CCE scans the V bias of one detection layer (TTaU) is scanned in the range from 60 to 400 V. The other detection layers are operated at the nominal bias voltage. The data from these layers and the other detectors of the LHCb tracking system are used to reconstruct the trajectories of charged particles produced in the proton-proton collisions. Tracks reconstructed by the rest of the LHCb tracking system, including the TT layers operating in nominal conditions, are used to interpolate the hit position in the scanned layer. Track quality requirements are applied to remove tracks with poor track fit quality or originating from random combinations of track segments from different parts of the tracking system. The pedestal-subtracted ADC values of the three readout strips closest to this interpolated hit position are then summed to give an estimate of the collected charge. As an example, Fig. 5 shows the signal height distribution in a TT read-out sector for V bias = 100 V and 400 V with δt = 0.00 ns. The incomplete depletion of the silicon bulk at V bias = 100 V induces the clearly visible decrease in signal amplitude.
The most probable value (MPV) of the collected charge is extracted from a fit of this distribution, using a model consisting of the sum of two Gaussians to describe the residual contribution of noise hits due to wrong track extrapolations (blue line), convolved with the sum of two Landau distributions to describe the contribution from signal hits (red line). The second Landau distribution describes a signal component due to photon conversions in the beam pipe and detector material upstream of the TT, creating e + e − pairs that will cross the TT at the same position and deposit twice as much charge as a single track. The MPV and the width of this second Landau distribution are fixed to twice the corresponding values of the first Landau. The MPVs extracted for different sampling times δt at a given bias voltage are then fit with the empirical function describing the semi-Gaussian signal shape output by the pulse shaping circuit employed in the Beetle chip, which is composed of a differentiator (CR) followed by an integrator (RC) [12,13]. The shaping time τ , time offset t 0 and amplitude A are free parameters of the fit. As an example, Figure 6 shows the results of these fits for one of the innermost sensors and for V bias = 100 V and 400 V. The integral of the fitted function between its two zeroes t 0 and t 0 + 3τ is taken as a measure of the collected charge at the given bias voltage. This quantity, referred to as "integrated charge", is shown as a function of V bias in Fig. 7. The three highest V bias data points are fit with a constant to determine the plateau value. The data points are interpolated with a fifth-order spline [14] S and the depletion voltage is determined as the bias voltage at which S(V bias ) reaches the fraction r = 94% of its value in the plateau. The value r = 94% was chosen based on an analysis of the earliest CCE scan, taken on 2011-07-14. First, the ratio analysed readout sectors is shown in Fig. 8(a). The values of r obtained for the different readout sectors were then averaged to determine r.
The systematic uncertainty on V depl due to the choice of r was estimated by applying the full method to the first CCE scan and comparing the values of V depl extracted from the spline fits with r = 94% to the values V 2011-07-04 depl extracted from the initial C − V scans and the Hamburg model. The residual distribution of V depl and V 2011-07-04 depl is shown in Fig. 8(b); the spread of this distribution is taken as systematic uncertainty.
A second source of systematic uncertainty is the choice of a fifth-order spline to interpolate the measurements. To estimate this uncertainty, the entire procedure was repeated using a simple linear interpolation between consecutive measurements instead of the spline fit. The distribution of the differences in V depl obtained using the two types of interpolation are shown in Fig. 8(c) for all analysed readout sectors; the spread of this

Parameter
Value distribution is taken as systematic uncertainty. These two uncertainties are summed in quadrature.
The change ∆n eff in the effective doping concentration is described in the Hamburg model by three different mechanisms, described in detail in Refs. [7,[15][16][17]: 1. a contribution associated to the effective (incomplete) removal of donor atoms and the addition of stable acceptor atoms due to radiation-induced changes in the band structure of the silicon crystal. This contribution, referred to as "stable damage", is described by ∆n c (Φ 1 MeV-n,eq ) = n c,0 1 − exp(−c Φ 1 MeV-n,eq ) + g c Φ 1 MeV-n,eq ; 2. a temperature-dependent contribution due to the annealing of the induced defects, which can be described by ∆n a (Φ 1 MeV-n,eq , t, T a ) = Φ 1 MeV-n,eq g a exp − t τ a (T a ) ; 3. a contribution due to the combination of individual defects in the silicon lattice, leading to stable defects ("reverse annealing"), described by ∆n r (Φ 1 MeV-n,eq , t, T a ) = Φ 1 MeV-n,eq g r 1 − 1 1 + t/τ r (T a ) .
The sum of the three contributions describes the total change of n eff : ∆n eff = ∆n c + ∆n a + ∆n r .  Figure 9: Measured effective depletion voltage (red points) in the area of two TT sensors: one just above the beam pipe (a) and one further away (b), whose position is indicated in Figure 11(a). The black point and error bars corresponds to the CCE scan used to calibrate the ratio r. The statistical contribution to the total uncertainty is indicated by the solid error bars. The predicted evolution of the depletion voltage, based on the initial depletion voltage measured after sensor production, the running conditions and the Hamburg model, is shown as a solid black line. The grey bands show the uncertainty on the predicted evolution of V depl , while the black dashed lines account for the ±2.5 V uncertainty on the measurement of the initial depletion voltage V 0 depl in CV scans.
The values of the model parameters are listed in Table 3. Their values were measured in dedicated irradiation campaigns and can be found in literature [7]. The parameters τ a and τ r have a temperature dependence described by the Arrhenius relation, cf. Eq. 4, with parameters E aa and k a,0 and E ar and k r,0 , respectively, and the ambient temperature T a is taken from sensors placed inside the detector boxes. Figure 9 shows the measured depletion voltages for a one-sensor and for a two-sensors TT readout sectors, highlighted in Figure 11(a), and their predicted evolution based on the Hamburg model described above. This calculation uses the fluence estimated from the Fluka simulations 3 , the actual running conditions and the temperature measurements in the detector boxes.
For the readout sectors closest to the LHC beam pipe, dedicated measurements only including tracks traversing the sensors within 75 mm from the beam axis are performed. Fig. 10 shows the measured values of V depl of the different TT read-out sectors in the different CCE scans as a function of the 1-MeV-neutron equivalent fluence estimated from the Fluka simulations and the integrated luminosity collected in LHCb. It also shows the expected evolution of V depl based on the stable damage contribution n c . Fig. 11(b) shows the absolute change of V depl in the innermost part of the detector between July 2011 and September 2017.
Good agreement between the measurements and the predicted evolution of V depl is observed. From the measurements it can be concluded that a type inversion in the silicon sensors of the TT is not expected until the end of the current LHCb data taking period (2019).

Conclusion
The evolution of the radiation damage in the LHCb Tracker Turicensis has been monitored using measurements of leakage currents and effective depletion voltages. The latter are performed with data collected in dedicated charge collection efficiency scans. The obtained results show good agreement with predictions based on phenomenological models. At the end of 2017, the innermost sensors, which experience the highest fluence, have not yet reached the point of type inversion, and no modifications to the operation procedure of the detector are expected in its last year of operation. The detector will be replaced as part of the LHCb upgrade [18] during the long shutdown LS2 of the LHC.  Figure 11: Sketch highlighting the TT sectors analysed during the various CCE scans (a). The greyed out sectors were excluded due to poor statistics. The two sectors highlighted with dashes, just above the beam pipe and below the beam pipe on the left hand side, are those which evolution is shown in Figure 9(a) and Figure 9(b), respectively. Absolute change in V depl in the innermost region of TT in September 2017 (b).