Beam test performance of prototype silicon detectors for the Outer Tracker for the Phase-2 Upgrade of CMS

A new CMS tracker detector will be installed for operation at the High Luminosity LHC (HL-LHC). This detector comprises modules with two closely spaced parallel sensor plates and front-end ASICs capable of transmitting tracking information to the CMS Level-1 (L1) trigger at the 40 MHz beam crossing rate. The inclusion of tracking information in the L1 trigger decision will be essential for selecting events of interest efficiently at the HL-LHC. The CMS Binary Chip (CBC) has been designed to read out and correlate hits from pairs of tracker sensors, forming so-called track stubs. For the first time, a prototype irradiated module and a full-sized module, both equipped with the version 2 of the CBC, have been operated in test beam facilities. The efficiency of the stub finding logic of the modules for various angles of incidence has been studied. The ability of the modules to reject tracks with transverse momentum less than 2 GeV has been demonstrated. For modules built with irradiated sensors, no significant drop in the stub finding performance has been observed. Results from the beam tests are described in this paper.


Introduction
The Large Hadron Collider (LHC) at CERN will undergo major upgrades by 2025 to be able to deliver peak instantaneous luminosities of 5 − 7.5 × 10 34 cm −2 s −1 . This High Luminosity upgrade of the LHC (HL-LHC) will allow the CMS (Compact Muon Solenoid) [1] experiment to collect data corresponding to integrated luminosities of the order of 300 fb −1 per year. Eventually, a total of 3000 fb −1 will be collected during ten years of operation. At the nominal instantaneous luminosity of the HL-LHC, a single bunch crossing will produce 140-200 proton-proton collisions. The vast majority of these collisions are "pileup" interactions with low momentum transfer that are of little physics interest.
In order to fully exploit the increased luminosity and to cope with the very high pileup environment, the detector and the trigger system of the CMS experiment need to be upgraded -1 -  4.0 η Figure 1. Sketch of one quarter of the tracker layout in r − z view. The radial region below 200 mm is referred to as Inner Tracker and will be instrumented with pixel modules. In the Outer Tracker, the radial region between 200 and 600 mm is equipped with PS modules (blue lines), while the region beyond 600 mm will be populated with 2S modules (red lines). The CMS coordinate system is defined in ref. [1].

Figure 2.
Illustration of the p T module concept [3]. Correlation of signals in closely spaced sensors enables rejection of low-p T particles. The channels shown in green represent the selection window to define an accepted stub; a low-p T rejected track is shown in red.

The concept of p T discrimination
In the presence of the 3.8 T solenoidal magnetic field inside the CMS detector, the trajectories of charged particles produced in a collision will bend in a plane transverse to the direction of the beam. The radius of the curvature of the trajectory of these particles depends on the particle p T . The concept of p T discrimination is shown in figure 2. As a charged particle passes through the module, it generates signals (hits) in the bottom and top sensors of the module. A hit in the bottom sensor is then matched to the one in the top sensor and if they are within a predefined window, these two hits are combined to form a short track segment or stub. These stubs will be used in the Level-1 (L1) track trigger.
The readout chips will provide the p T discrimination logic described above. The window for hit matching can be set within the readout chip according to the p T threshold to be used. For the 2S module, the readout chip is called the CMS Binary Chip (CBC) [5][6][7][8][9]. Each CBC has 254 readout -3 - , which is bent around a stiffener/spacer sandwich [3], is visible. channels with alternate channels connected to the top and bottom sensors in a module, as shown in figure 3 (right), so that coincidences between channels of the two sensors can be obtained.
The 2S module, shown in figure 3, consists of two sensors (n-type strips in p-type silicon substrate), support structures made from Al-CF (carbon fibre reinforced aluminium), two front-end hybrids [10], each with eight CBCs and one concentrator integrated circuit (CIC) that aggregates data from the CBCs, and a service hybrid for powering and output data serialization followed by opto-electrical conversion.
All prototype modules discussed in this paper use the second prototype of the CMS Binary Chip, the CBC2 [7][8][9]. The block diagram of the analogue front-end (FE) of the CBC2 ASIC is shown in figure 4. Three I 2 C registers are used to control the main settings of the analogue FE : V plus , which controls the global DC baseline of the post-amplifier output, V offset (labelled "Offset" in figure 4) for fine control of the baseline of the post-amplifier output for individual channels on the CBC2, and V CTH , which controls the comparator threshold. The readout for the CBC2 chip is binary, thus it does not measure the amount of charge induced on each strip. If the charge on a strip exceeds the comparator threshold, a hit is registered. Figure 4. Block diagram of the analogue front-end (FE) of the CBC2 ASIC [7][8][9]. Three registers are used to control the analogue FE.

Prototype detectors
Prototypes of the 2S module have been investigated at different test beam facilities (table 2). For the beam tests described in section 3, two small prototype modules and one full-size module have -4 - been studied. The strip sensors of the modules have 5 cm long n-type strips at 90 µm pitch on about 300 µm thick silicon sensors with p-type bulk. A negative voltage is applied to bias the sensors at the sensor backplane but in the following the absolute values of the bias voltage applied are quoted.
The small prototype modules, called mini-modules, consist of a version of the front-end hybrid housing two CBC2s. The hybrid is made of a rigid material with bond-pads on both sides and the sensors are wire-bonded to the top and bottom sides of it. This contrasts with the flex-kapton design used for full-sized modules that folds over the CF spacer to provide bond-pads for the bottom sensor [3,11]. The sensors have been glued on a small frame made of aluminium. One mini-module was left unirradiated. The sensors of this module have an active thickness of 270 µm and their separation is 2.75 mm. The second mini-module, shown in figure 5 (left), with an active sensor thickness of 240 µm and a sensor separation of 3.05 mm, was irradiated with 23 MeV protons at Irradiation Center Karlsruhe [12] to a fluence of 6×10 14 n eq /cm 2 with an annealing of approximately two weeks at room temperature. The maximum expected fluence for the innermost layer of the 2S modules of the OT is 3 × 10 14 n eq /cm 2 [3]. This value corresponds to 3000 fb −1 of proton-proton (pp) collisions at √ s = 14 TeV assuming a total inelastic cross section, σ pp , of 80 mb. The current-voltage characteristic of the sensors before and after irradiation can be seen in figure 6. The effect of irradiation is reflected by an increase of the leakage current by three orders of magnitude.
The full-size module consists of two sensors of about 10 cm × 10 cm, with two columns of 1016 strips each. The active thickness of each sensor is 240 µm and the sensors are separated by 1.8 mm. Each of the front-end hybrids on both ends of the module houses eight CBC2s. A flex hybrid is used to provide bond-pads for the top and bottom sensors (  Before irradiation Figure 6. The current-voltage characteristic of a sensor of the mini-module before (red) and after (black) irradiation to 6 × 10 14 n eq /cm 2 , showing the increased current after irradiation. The measurements were taken at −20 • C and 20 • C for the irradiated and non-irradiated sensors, respectively. with a rotation angle between the strips of both sensors of below 400 µrad. This module is shown in figure 5 (right).

Beam test infrastructure
The prototype modules have been studied at beam test facilities at CERN, Fermilab and DESY. In all of the facilities, the detector under test (DUT) is placed within a tracking detector, referred to as 'telescope' in the following. The telescope provides a reference to reconstruct the tracks of the incident particles. The beam test facility at CERN is described in detail in the following section, and the key features of the DESY and Fermilab test beam facilities are highlighted. The data acquisition systems (DAQ) of the three facilities are also described.

Beam test setup
A schematic diagram of the setup at CERN is shown in figure 7. Data were collected using a 120 GeV pion beam. The EUDET telescope [13] used in the CERN beam test of the 2S prototype modules is a tabletop tracking detector composed of six planes of MIMOSA-26 [14] silicon pixel sensors for accurate track reconstruction, a fast-timing reference plane (FE-I4) [15] for accurate timing resolution, and a pair of crossed scintillators with photomultiplier tubes (PMTs) located at either end of the telescope for trigger generation. The six MIMOSA-26 sensor planes, each covering an active area of 10.6 × 21.1 mm 2 , consist of 50 µm thick 18.4 µm × 18.4 µm square pixels arranged in 576 rows and 1152 columns. The fast-timing plane covers an active area of 16.8 × 20.0 mm 2 and consists of 200 µm thick pixels arranged in 336 rows and 80 columns read out by the FE-I4 chip, which was designed for the innermost layer of the upgraded pixel detector of the ATLAS -6 -experiment. Each sensor plane is mounted inside a 20 mm thick aluminium jig, and two sets of three jigs are attached via rail systems to the upstream/downstream arms of the telescope. The minimum distance between sensor planes is defined by the thickness of the aluminium jig (and is therefore 20 mm), and the maximum distance between sensor planes is defined by the length of each arm (150 mm for equidistant spacing between the sensor planes). The resolution of the telescope system over the six sensors used is 3.24 µm [16]. The jigs are cooled to a constant temperature of 16 • C to increase the stability of operation. The synchronization of the data streams from the three detector systems (the 2S prototype, the MIMOSA-26 sensor planes, and the FE-I4 plane) is performed by an FPGA-based Trigger Logic Unit (TLU) [17,18]. During the beam tests, dedicated NIM logic is used to generate a trigger signal using the output signals from the two pairs of crossed scintillators at either extremity of the EUDET telescope. This trigger signal is provided as input to the TLU, which distributes this signal to the DUT and to the telescope's sensor planes.
A simple handshake protocol is used by the DAQ system to maintain synchronization among the different detector systems. The detector systems assert busy signals on separate lines, which inhibit triggers from the TLU until all of the lines are cleared. No new triggers are sent by the TLU until all detectors drop their busy-lines. This ensures that detectors with different dead-times can be triggered and read out synchronously. In addition, the TLU can send a timestamp for each trigger via a dedicated clock-data line, or it can receive a back-pressure (veto) signal from the DUTs on the same line.
The additional ATLAS FE-I4 plane is used to improve the timing resolution of the telescope by associating the FE-I4 hits with the individual hits in the 115.2 µs rolling-shutter frame of the telescope during event building. This allows the multiple tracks in a telescope frame to be correlated to individual triggers. Because the FE-I4 readout has no dead-time and runs on an internal 40 MHz clock, the required time resolution of 25 ns for the CBC DAQ is achieved. The data streams from the telescope and the FE-I4 are sent to the EUDAQ [13] online software via the TCP/IP protocol [19]. The two streams are stored together in the same format in a file, which makes the reconstruction easier in the EUDET [20] framework.
The beam test at DESY uses the EUDET based telescope called DURANTA [13], similar to the one used during the CERN beam test. It also uses six MIMOSA-26 pixel sensors with four crossed scintillators for triggering and a TLU, however it was equipped with a CMS Phase-1 pixel [21] -7 -

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module as a timing reference plane instead of the FE-I4. The data were collected with a positron beam of 5 GeV energy.
The Fermilab Test Beam Facility, or FTBF [22], is equipped with two silicon telescopes aligned along the beam line and configured to operate synchronously. It has a pixel telescope assembled from eight planes and a telescope with strip modules made up of 14 detector planes. The strip telescope increases the coverage of the pixel telescope and improves its tracking performance. The trigger is generated by a coincidence signal of three scintillation counters, one placed in front and two placed behind the telescopes. The synchronization of the data streams from the two telescopes and the 2S module is performed by a Fermilab-designed FPGA-based trigger board. The data are taken with a 120 GeV proton beam.

Data acquisition system
The DAQ system for the CBC2 modules at CERN and Fermilab test beams is based on the CERN Gigabit Link Interface Board (GLIB) [23] µTCA Advanced Mezzanine Card (AMC). Different firmware versions are used to read data from the 2 and 16 CBC2s on the tested modules. Control signals and readout data are exchanged between the GLIB and the control PC via the IPBus [24] protocol, whereas trigger, busy and veto signals are interfaced to the TLU/Fermilab equivalent via a dedicated five-channel I/O FPGA Mezzanine Card (FMC). A simple block diagram of the different components of the DAQ system is shown in figure 8.  An external high-precision clock generator was used to provide the clock signals to the GLIB via the same FMC that connects to the TLU. The CBC2 data are processed and formatted by the firmware and then sent to a XDAQ [25] application that formats events in a CMS compatible format and stores the data for later processing within the standard CMS reconstruction software, CMSSW [26]. The binary raw data stream is also stored and can be used for online data quality monitoring.

2S
The beam test at DESY used a novel DAQ system, based on the FC7 [27] card. The FC7 hosts a Kintex-7 FPGA and comes with a system firmware allowing for communication with other devices -8 -

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on the FC7 card and IPBus communication. A DIO5 FMC is used to send trigger and busy signals via LEMO connectors. These are fed into a custom-built LVDS converter box and sent to the TLU via a standard RJ45 connector.

Pedestal and noise
The pedestal and noise values of an individual channel in a system with binary readout can be inferred from a channel's S-curve. An S-curve is obtained by measuring the noise occupancy as a function of the comparator threshold (V CTH in figure 4). The comparator threshold has been measured in V CTH DAC units. One V CTH DAC unit corresponds to 375 electrons, as measured using an X-ray source. The noise occupancy is given by the fraction of triggers for which a given channel registers a hit. Higher numerical values of V CTH correspond to lower thresholds in the CBC2. Figure 4 also shows the per-channel 8-bit DAC used to control the offset of the output voltage of the second amplification stage to compensate for any channel-to-channel variations.
The pedestal value and the channel noise are extracted directly from the S-curve either by fitting the curve with a sigmoid of the form or by numerically differentiating it. The mean parameter, µ, in eq. (4.1) (or the mean of a Gaussian fitted to the differential histogram) then corresponds to the pedestal and σ (or the RMS of a Gaussian fitted to the differential histogram) corresponds to the noise. An example of an S-curve recorded for a CBC2 on a non-irradiated prototype module and the corresponding differential histogram are shown in figure 9. Both methods return similar (i.e. consistent within 3σ) values for the pedestal and noise. The pedestal value, obtained from fitting the left plot of figure 9 with a sigmoid function, is 120.0 ± 0.1 V CTH DAC units. A pedestal value of 119.3 ± 0.2 V CTH DAC units has been obtained by fitting the distribution shown in figure 9, right, with a Gaussian function. For the noise, 2.12 ± 0.06 V CTH DAC units and 2.14 ± 0.15 V CTH DAC units are obtained, respectively. Figure 10 shows the uniformity of the front-end response after adjustment of the individual channels' offsets. The pedestal and noise values were extracted from the fits to the individual channels' S-curves using eq. (4.1). The channel-to-channel variation in the pedestal, defined as the RMS of the measured distribution, is measured to be 0.30 ± 0.01 and 0.37 ± 0.02 V CTH DAC units for the first and second CBC2, respectively. The mean noise was found to be 1.36 ± 0.06 and 2.38 ± 0.60 V CTH DAC units for the first and second CBC2, respectively. The same figure also clearly shows that 11 of the strips connected to the second CBC2 on the hybrid are significantly noisier than the rest. These 11 strips are included in the noise figure quoted for the second CBC2. The strips exhibiting a value of noise larger than 3 V CTH DAC units (1125 electrons) are not considered for analysis.

Latency scans
After the pedestal and noise scans, two latency scans, one for data and one for stubs, were carried out. The data latency, measured in units of 40 MHz clock cycles and set using an on-chip configuration  Figure 9. S-curve measured for a single input channel on one of the two CBC2s on a non-irradiated prototype module at room temperature with the sensor biased at 250 V. On the left the measured data are shown along with a fit to the measured data performed using eq. (4.1), while on the right the differential histogram is shown with the corresponding Gaussian fit.
register, defines the position in the on-chip RAM from which the data are read upon reception of a trigger. The stub latency, also measured in units of 40 MHz clock cycles and set by a configuration register in the back-end FPGA, defines the delay between hit and stub data arriving at the back-end of the data acquisition system and is required to assemble the data at the back-end.
The resolution of the data latency measurement was improved using a high-resolution time-todigital converter (TDC) in the back-end FPGA. The TDC measures the time of arrival of the trigger signal at the back-end with respect to the 40 MHz clock edge in time slices of 3.125 ns, using a 3 bit counter operating at 320 MHz. The results of the latency scans performed in the CERN beam test are shown in figure 11. These scans were used to identify the stub and data latencies to use during data taking by counting the number of stubs and hits contained in the data stream for a fixed number of triggers and selecting values for the data and stub latency that maximize the fraction of events containing stubs and hits, respectively. Both scans were performed at a threshold of 113 DAC units (3σ away from the pedestal). For further data taking, the data latency and stub latency were fixed at 13 and 4, respectively, as shown by the dashed lines in figure 11.

Reconstruction
Dedicated software is used to reconstruct the data collected from the telescope system and the DUT. Initially, the reconstruction of tracks of the incident particle is carried out using the hits in the telescope system. The reconstruction of data from the DUT involves the formation of clusters and stubs using the hits from the individual channels. The reconstructed tracks are then extrapolated to the DUT, and the estimated position of the track on the DUT is computed. Using this information, an alignment is performed to correct for the relative offset in position of the DUT with respect to the telescope system. The reconstruction of tracks from the telescope data, clusters and stubs from the DUT data, and alignment procedures are described in the following sections.

DUT reconstruction
The schematic diagram for the processing of the DUT data is shown in figure 12. The raw data received from the 2S modules by the FPGA are converted to the CBC2 event format by the DAQ software and served to the online Data Quality Monitoring (DQM) system. The raw data are also sent to the CMS event builder (EVB) [28] which provides data in the Event Data Model (EDM) format [29,30]. The EDM data are then processed by the CMS offline software, CMSSW [26], to produce clusters and stubs used in the offline analysis. Hits in adjacent strips of the DUT are combined to form a cluster. The number of strips included in a cluster is called the cluster width.
The cluster position is defined by the center of the cluster rounded down to an integer strip number. The CBC2 reconstructs stubs, by calculating the cluster positions in integer strip numbers. However, it outputs only the information that a stub was present, not its position (in contrast to later versions of the chip, which include this functionality). Therefore the stub reconstruction is done offline, by emulating the logic in the CBC2. Clusters with cluster width greater than 3 are excluded from stub formation. The difference in position (in number of strips) of the clusters in the bottom sensor is calculated with respect to clusters in the top sensor. If this difference is less than the predefined window, an offline stub is formed. The position of the stub is defined as the position of the cluster in the bottom sensor seeding the stub. As the DAQ systems for the telescope and for the DUT are different, an -12 -additional processing step is needed to synchronize the events coming from telescope and DUT data streams by matching the individual trigger numbers using the ROOT data analysis framework [31].  Figure 12. A schematic representation of the data processing for the beam tests at CERN. The Telescope event contains information about the incident track parameters. The DUT event contains the information of the hits as read from the DUT and also the clusters and stubs reconstructed using offline software. The CBC event contains the information about CBC errors. Data from all three sources are merged and stored into a single file for offline analysis.

Tracking
Tracks from the EUDET telescope are reconstructed in the EUTelescope [13] framework using MIMOSA-26 planes. A database of noisy pixels (pixels with exceptionally high occupancy), is built and used to exclude such pixels from subsequent steps of the analysis. Clusters are built according to the nearest neighbour search algorithm, which iteratively joins adjacent pixels with hits to form a cluster. A "pre-alignment" is performed in the telescope global frame, correcting only for the misalignment in X and Y directions (as shown in figure 7). The output of this step is used to constrain the alignment step itself, based on solving exact matrix equations with the Millipede II framework [32]. Shifts in X, Y and Z coordinates and 3 Euler rotation angles for each Mimosa plane are corrected for. Tracks are then reconstructed with a Deterministic Annealing Filter (DAF) algorithm [33,34], where all hits within a given radius are used for the track reconstruction. Tracks reconstructed with the DAF are further cleaned to remove any duplicates, defined as two or more tracks with X and Y coordinates at the FE-I4 plane less than 1 µm apart. While Mimosa planes are read out with a rolling shutter having a window of 115 µs, the maximum acquisition rate for the DUT and the FE-I4 plane is 40 MHz. The presence of a hit in the FE-I4 plane that can be matched to the track is used as a timestamp, which largely reduces track combinatorics. Residuals at the FE-I4 plane are used to determine a nominal distance between -13 -the track impact point and the FE-I4 hit. The residuals are fitted with a step rectangular function convolved with a Gaussian smearing. The maximum distance to accept a track is set to half the width of the step function, compatible with the FE-I4 pitch, plus two times the width of the Gaussian, compatible with the track pointing resolution.
Track reconstruction and telescope alignment at the Fermilab test beam facility are performed using a single dedicated software package [22] that provides a graphical interface to execute the various steps. An iterative algorithm implements a least-squares minimization to compute 1storder roto-translational corrections using tracks reconstructed with a preliminary description of the geometry.
The reconstruction of beam test data at DESY follows a similar procedure to that used for beam tests at CERN. The main difference is that the entire reconstruction is performed within the EUTelescope framework and that the General Broken Lines (GBL) [35] algorithm for alignment is used. The GBL algorithm is required to account for the increased multiple scattering of the comparatively low-energy particles available at the DESY beam test facility.

DUT alignment
The DUT alignment procedure consists of minimizing the residuals at the DUT plane to constrain the degrees of freedom of the system: where x DUT is the hit position in X and x TkAtDUT the position of the hit as derived from the track extrapolation to the DUT location, while σ tkres is the telescope pointing resolution. The sum runs over all events in which at least one cluster in the DUT and one track are reconstructed. For each event the closest pair is selected. To remove outliers, the sum is further restricted to events where the residual |x DUT − x TkAtDUT | is less than 3σ tkres away from the mean value of a Gaussian fit of the residual distribution. The track impact point on the FE-I4 plane is propagated to the first sensor plane of the DUT, which corresponds to the plane of the sensor facing the beam direction, including degrees of freedom for the X position of the first plane, Z position of the first plane, θ angle around the Y-axis, and the distance between the two sensor planes of the DUT. This procedure eliminates the sign degeneracy of the θ angle. For efficiency studies reported in section 6, a track is matched to a hit, cluster or stub on the DUT if the residual, |x DUT − x TkAtDUT |, is less than 3σ tkres .

Results
After calibration, the threshold (V CTH ) and the angle of rotation of the DUT with respect to the beam were varied in suitable step sizes and the properties of hits, clusters and stubs were studied. The axis of rotation of the DUT was the Y axis, as shown in figure 7.
A scan of V CTH was performed at vertical beam incidence and measurements of the cluster and stub efficiencies were carried out as a function of a number of functional parameters to fully characterize the mini-modules (section 6.1) and the full-size module (section 6.2).  Figures 13 and 14 show the average number of hits and clusters on the non-irradiated and irradiated mini-modules, respectively. Lower numerical values of V CTH mean a higher signal threshold, as mentioned in section 4.1. For the non-irradiated mini-module, the average number of hits/clusters increases as V CTH is increased and a plateau with a value close to 1 is visible, up to V CTH values of about 110. However, for the irradiated module, the average number of hits/clusters is mostly less than 1 as V CTH is increased. This indicates that, for a given value of V CTH , we see a lower number of hits/clusters in the irradiated mini-module as compared to the non-irradiated one. As the V CTH setting is increased further ( 110 ), the noise increases in both mini-modules, leading to a sharp rise in the average number of hits/clusters. Differential histograms of cluster occupancy as a function of V CTH , derived by numerically differentiating the distributions of the cluster occupancy as shown in figure 14, are shown in figure 15. The differential distributions show an inverted Landau distribution, caused by the actual signal generated from the incident particle, and a noise peak. Comparing the differential distributions, it can again be seen that the total number of clusters is lower in the irradiated mini-module. The loss in the number of clusters for the irradiated minimodule as seen in figure 14 and figure 15 indicates that the charge collection in the irradiated mini-module is worsened due to radiation induced effects. Along with radiation induced effects, the lower sensor active thickness of 240 µm for the irradiated module, compared to 270 µm of the non-irradiated module, also leads to lower charge collection. By choosing appropriate V CTH values of 106 and 110 DAC units for the non-irradiated and irradiated module, respectively, signals from incident particles can be collected preferentially.

Performance of mini-modules
The cluster efficiency, defined as the ratio between the number of events with a cluster matched to a track in a single track event and the total number of events with a single track, is then measured as   -16 -a function of V CTH for different values of the trigger phase (TDC), to check for a potential dependency. The cluster efficiencies for one of the sensors of the non-irradiated and irradiated mini-modules are shown in figure 16. The lower charge collection in the irradiated module results in a smaller effciency plateau (figure 16, bottom) compared to the non-irradiated module ( figure 16, top). As the V CTH increases further (> 110), the efficiency starts to degrade for both the mini-modules due to increase of noise. Due to the higher noise occupancy, the probability of a neighbouring strip to fire increases, resulting in larger cluster width. This shifts the position of the actual cluster away from the track causing the track matching to fail. A small dependency on the trigger phase is present for both sensors and is more evident at lower V CTH . A trigger phase is present in the CERN beam test because the trigger signal is asynchronous with respect to the 40 MHz clock that drives the readout electronics.
Because there is no magnetic field, the dependence of the mini-module performance on the transverse momentum of tracks is emulated by rotating the DUT with respect to the beam direction. As the incident angle (referred to as α) of the particles increases, the charge deposited is shared by multiple strips and hence the cluster width is expected to increase, which is shown in figure 17. This effect is less evident on the irradiated module due to the radiation induced defects both in the sensor bulk and on the surface, that change the electric field inside the sensor. This leads to a modification of the charge sharing and further to a higher average cluster size at normal incidence. The same effect is also evident from the distribution of the fraction of clusters with different strip multiplicities, as shown in figure 18. The non-irradiated module shows a correlation between the cluster fractions and the angle. This dependence is much less significant for the irradiated module.
In figure 19 the cluster efficiencies for different TDC values as a function of the DUT rotation angle for the two modules are shown. The dependency on the trigger phase is negligible and the mean cluster efficiency for the full range of the angular scan is 99.56 ± 0.01% and 98.21 ± 0.02% for the non-irradiated and irradiated module, respectively.
For the CMS field strength of B = 3.8 T, the relationship between the beam incident angle (α) and the emulated transverse momentum p T of the traversing particle for a radial position of the module (R) is given by p T [GeV] ≈ 0.57·R [m] sin (α) . The stub efficiency, defined as the ratio of the number of events with stubs matched to a track in single track events to the number of events with a single track, was measured for each incident angle. Tracks and stubs must match within 4σ of the spatial resolution. The stub efficiency of the two mini-modules as a function of effective p T (beam-incident angle) is shown in figure 20. For larger angles of incidence the relative shift in cluster position in the two sensors of a module is larger, which leads to lower probability of correlating them as stubs. The stub efficiency drops for larger angles for this reason. A stub correlation window of 5 strips is used. A radius of 60 cm was used for the calculation of the effective p T from the beam incident angle. The turn-on curve is different for the two modules due to different sensor spacing.
The turn-on curve was fitted with an error function of the form where A is the efficiency at the plateau, p T µ is the turn-on threshold for which the efficiency is 50%, and σ p T is the width of the Gaussian in the error function. The p T resolution is defined as the ratio of the width of the Gaussian to the p T value at 50% of the plateau height, or σ p T /p  non-irradiated module, the turn-on threshold is 1.88 GeV with a p T resolution of 5%, whereas the expected turn-on threshold is 2 GeV. The plateau efficiency for the non-irradiated module is 99%. The high plateau efficiency with sharp turn-on demonstrates that the module can reject tracks with p T < 2 GeV efficiently. For the irradiated mini-module, the plateau efficiency reaches 97% with a p T resolution of 6%. This shows that the stub finding logic of the 2S modules will work even after being irradiated to a fluence of 6 × 10 14 n eq /cm 2 , which is twice the expected fluence for the first layer of 2S modules. The stub efficiency measured using data collected at the DESY test beam facility with the non-irradiated mini module is found to be 99%.  Figure 17. Mean cluster width of non-irradiated and irradiated 2S mini-modules as a function of the beam incident angle. Due to radiation induced defects, charge sharing is higher in the irradiated module, leading to a larger mean cluster size. A bias voltage of 250 V (600 V) was applied to the non-irradiated (irradiated) mini-module. A V CTH value of 106 (110) DAC units was used for the non-irradiated (irradiated) mini-module.   For the irradiated module three angular scans were performed, each with different stub correlation windows. As shown in figure 21, the turn-on curve of the efficiency depends on the selected correlation window, while the efficiency plateau does not.

Performance of the full-size module
For the full-size 2S module, the primary goal was to check the uniformity of the response across all strips. Figure 22 (top) shows the stub efficiency per strip for the full-size 2S module. The module -20 - Angle (deg) Figure 20. Stub efficiency for the irradiated (blue) and non-irradiated (red) modules as a function of the beam incident angle. As expected, for larger angles of incidence, which corresponds to smaller effective p T , the stub efficiency drops. A radius of 60 cm was used for the calculation of p T from the beam incident angle which is approximately the radius at which the first layer of 2S modules will be installed. The stub correlation window is set to 5 strips.  -21 -

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was operated at a bias voltage of 250 V and V CTH was set to 115 DAC units. The analysis techniques used are the same as reported for the mini-modules. The region between strips 185 and 239 has no data because it was not scanned by the beam. The large statistical uncertainty in efficiency at the edges is due to the limited data collected for the scans performed at the module edges. The mean stub efficiency extracted from a linear fit, where the asymmetric errors on each measurement are taken into account, is 97.4%, and the strip-to-strip variation of the stub efficiency was found to be 1.3%. The efficiency is approximately 2% lower than that measured in the 2S mini-module. The difference is due to a different operational configuration of the modules and a possible remaining contamination of events for which the module was not synchronized with the telescope. The stub efficiency per chip is shown in figure 22 (bottom). The results demonstrate that the response of the full-size 2S module is uniform across strips. The stub efficiency as a function of effective p T for the full-size 2S module measured with data collected at the Fermilab test beam facility is shown in figure 23. The correlation window used for stub formation was set to 5 strips. The figure shows that the behaviour of the fullsize module is similar to that of the mini-modules. From the fit, a turn-on threshold of 1.2 GeV is obtained with a p T resolution of 7.9%. The turn-on threshold is lower compared to the non-irradiated mini-module since the sensor separation is smaller. The efficiency at the plateau is 99%.

Summary
A new silicon strip tracker will be installed in CMS for the HL-LHC period. The new Outer Tracker will comprise novel detector modules with two closely spaced sensors and a new front-end ASIC that is capable of correlating hits between the sensor layers. The performance of 2S prototype modules has been characterized at three test beam facilities. The presence of tracking detectors at these facilities has allowed for spatial matching of the tracks of the incident beam and the hits on the 2S modules. This has provided the first measurements of the absolute efficiency of these prototype detectors.
Cluster efficiencies of approximately 99.5% and 98% have been measured for non-irradiated and irradiated modules, respectively. These results are robust with respect to variations in particle arrival times relative to the trigger. For the non-irradiated module, an increase in the mean cluster width is observed as the beam incident angle increases. For the irradiated module, the average cluster size is higher in general and thus the variation of cluster width with angle is less evident.
The stub efficiency across all the strips of the sensors shows a uniform response. The stub efficiencies of both the non-irradiated mini-module and the full-size module are found to be around 99%. The stub efficiencies obtained from the analysis of data from the three test beam facilities are in agreement with each other. For the irradiated module, the stub efficiency was found to be 97%. All of the modules demonstrate the ability to reject tracks with p T < 2 GeV. The high efficiency of the irradiated module provides evidence that the modules will be able to operate throughout the lifetime of the HL-LHC without much loss of efficiency. Angle (deg) Figure 23. Stub efficiency of the full-size 2S module as a function of particle p T measured at the Fermilab beam test facility during the angular scan. The module was operated at a bias voltage of 250 V and the V CTH value was set to 92. A radius of 60 cm is used to convert the beam incident angle to effective p T .