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Fast-timing Capabilities of Silicon Sensors for the CMS High-Granularity Calorimeter at the High-Luminosity LHC

We report on the signal timing capabilities of thin silicon sensors when traversed by multiple simultaneous minimum ionizing particles (MIP). Three different planar sensors, 133, 211, and 285 μm thick in depletion thickness, have been exposed to high energy muons and electrons at CERN. We describe signal shape and timing resolution measurements as well as the response of these devices as a function of the multiplicity of MIPs. We compare these measurements to simulations where possible. We achieve better than 20 ps timing resolution for signals larger than a few tens of MIPs.


Introduction
Event reconstruction at future hadron colliders will be challenged by the dramatic increase in the number of concurrent interactions (pileup) per beam crossing in the experiments. At the High-Luminosity Large Hadron Collider (HL-LHC) -with up to 200 pileup events per beam crossing-, current detectors will show limitations in the reliance on purely spatial information to resolve interactions and associate particles to vertices. Moreover, the random overlap of energy deposits from neutral particles, which cannot be associated via a track to any vertex, will deteriorate the calorimeter performance in terms of energy measurement and particle identification as particles appear to be less isolated. A compact and highly granular sampling calorimeter based on silicon sensor technology has been chosen to replace the end-cap calorimeter in the CMS experiment at the HL-LHC [1]. Precision time measurement of the energy deposits could provide an additional means to resolve interactions [1,2] by exploiting the spread in the time domain of the collision vertices predicted to be about 150 ps RMS, within the 25 ns bunch crossing structure of the colliding beams at the HL-LHC [3].
The silicon trackers have played crucial roles in many experiments because they afford excellent spatial resolutions at high rates and are robust. There are also a handful of examples of sampling calorimeters based on active silicon sensors. The SICAPO collaboration studied salient features of electromagnetic calorimeters with layers of high-Z absorber and silicon sensors for what were then future colliders [4]. The ALEPH and OPAL collaborations employed luminosity calorimeters consisting of tungsten and silicon sensors [5,6]. The CALICE collaboration has been investigating high-granularity calorimeters with different types of active elements as well as silicon for precision physics at future colliders [7]. In recent times, silicon sensors have also been used for timing applications in high intensity environments. The NA62 Gigatracker is one example [8]. At a rate of 1 GHz, in addition to excellent single track resolution, the achieved timing resolution is better than 120 ps in particle fluxes of over 10 13 particles/cm 2 .
In this paper, we report on the results of our first study with small planar sensors with focus on their precision timing capability, in particular for the case of multiple particles impinging simultaneously on the sensors. We briefly describe the experimental setup in Section 2 and discuss the pulse shape reconstruction and single minimum ionizing particle (MIP) calibration in Section 3. We present sensors' multi-MIP response in Section 4 and evaluate the timing resolution in Section 5 in some detail.

Experimental Setup
The test setup is shown in Figure 1. Two silicon sensors were installed in the beam line at all times. A micro-channel plate (MCP), viewing a Cherenkov radiator, provided a precise timing reference for each event within ∼ 20 ps, with full efficiency for single MIPs at −2750 V [9]. A scintillator counter (2×2 cm 2 ) upstream of the detectors defined the area of triggered events. The impact position of particles on the sensors was estimated by projecting the hit positions, with better than a millimeter resolution, obtained from a set of delay wire chambers ( Figure 1). Lead sheets with different thickness were positioned in front of the sensors to generate electromagnetic showers to be able to investigate the multi-MIP response of these sensors.
The measurements described in this paper were performed at the H2 beam line of the super proton synchrotron (SPS) at CERN in July 2015. 150 GeV muons and 50 GeV electrons were used for the majority of the measurements. The beam particle rates were typically several thousand per spill. Each spill lasted 4.9 s and was repeated twice a minute for most of the data taking period. Although the beam spot size on the sensors varied slightly with the beam tune and settings, the FWHM was about 1 cm in horizontal and vertical directions -larger than the sensors ( Figure 1).
All tested sensors were p-type (n-on-p), 5 × 5 mm 2 in the effective area and physically 320 μm thick. They were biased at 600 V and fully depleted. They were produced by deep-diffused float-zone (dd-FZ) technique by Hamamatsu within the framework of the CMS tracker upgrade project in three different depletion thickness: 133, 211, and 285 μm with capacitances of 22.5, 13.6, and 9.9 pF, respectively [10,11]. The radiation effects on these sensors are currently under study; however, none of the sensors used here was previously irradiated.
The electrical signals from the sensors were amplified by a broadband (2 GHz/40 dB) amplifier 1 , and the waveforms were digitized at 5 GHz by a Domino Ring Sampler (DRS) unit from CAEN (V1742). The signals from MCP and the event trigger were also fed to the same digitizer unit in order to remove trigger jitter off-line. The intrinsic timing resolution of the digitizer was ∼ 5 ps and did not contribute to the systematic uncertainty of our measurements in any significant way [12].

Pulse Shape and MIP Calibration
The rise-times from 10% to 90% of the pulse amplitude for the three sensors were measured to be 1.1 ns, as shown in Figure 2. The pulse time was defined as the time when the pulse reaches its 50% amplitude. The offline algorithm searched for a pulse in the data stream, fitted its peak with a Gaussian function requiring at least 5 samples, and calculated the time at which the pulse reached its half amplitude.
We measured the responses of the three different type of sensors to single MIPs. A 50 GeV electron beam was used to perform this measurement. Without the lead plates in front of the sensors, 50 GeV electrons were effectively equivalent to MIPs. The results of the calibration  with electrons have been found to be in agreement with the ones obtained using a 150 GeV muon beam. We selected events with a signal from the MCP and from the second sensor. The presence of a signal in the second sensor ensured that most tracks did pass through the first sensor whose response was being measured. The signal from the first sensor included a correction for a 20% noise correlation between the two sensors. The signal distribution from the first sensor included contributions from zero (e.g. no signal) and single-track (1 MIP) events, as well as from a small number of events with 3 charged tracks (3 MIPs) where a photon emitted by the interacting initial electron produced an electron-positron pair. We modeled this spectrum with a linear sum of a Gaussian and two Landau distributions convolved with a Gaussian distribution, representing contributions from 1 MIP and 3 MIPs. Figure 3 shows the signal distributions. The most probable value (MPV) of the Landau distribution establishes the MIP measurement. The precision of the measurement was limited by the amount of data and by the systematic uncertainties related to the noise correlation between the two sensors. Figure 3. The response of a 211-μm thick sensor to 50 GeV electrons (left): the red solid line depicts the fitted curve, which includes a Gaussian (pedestal centered around zero) and two Landau distributions convoluted with Gaussian distributions accounting for one and three charged particles traversing the sensors. The distribution on the right is the same but for 150 GeV muons. Note the absence of events due to more than one charged track in this case.
The MIP response of the three sensor thicknesses is compared in Figure 4. The signal strength scales nearly linearly with the depletion zone thickness, as expected. We compare the MPVs (solid black squares) for each sensor for a MIP as well as for the signal-to-noise ratios (open red circles).

Multiple MIP Signal
While clearly separated single-MIP response from the background is desirable and maybe used to set the energy scale in calorimetry, measurement of the sensor response to multiple MIPs gives us a sense of response linearity. We consider a signal from 1, . . . , N tracks simultaneously passing through the silicon sensor, where N is small enough so the signals from different track multiplicities are distinguishable. In the absence of independent information providing the number of charged particles passing through the sensor, this study was particularly wellsuited for our setup. Thus, we analyzed the spectrum containing events with different track multiplicities. We modeled the observed spectrum with an analytic function and then evaluated the linearity of the response from the parameters of this function. This procedure was also validated with a GEANT4 [13] simulation.
Two radiation lengths of lead were placed in front of the sensors with a 50 GeV electron beam initiating electromagnetic showers. We also required a signal from the MCP to ensure proper timing/jitter correction in signal reconstruction, as noted earlier.
The signal distribution was fitted with an analytic function ( Figure 5) with multiple components. Each component comprised a Landau distribution to describe ionization loss by a charged particle in a thin silicon layer convolved with a Gaussian distribution to model electronics noise. N + 1 components were added linearly to describe a spectrum with track multiplicities ranging from 1 to N . The pedestal component of the distribution (no charged particle going through the sensor) was modeled by a Gaussian distribution, and its width was used to constrain the Gaussian component in the MIP signals. The only constraint in the fitting procedure was that the widths of the individual distributions were limited to a range. All other parameters were left free in the minimization process.
In order to evaluate the linearity of response, shown in Figure 6, we formed a ratio of the MPVs of the Landau distributions from the measurements and simulations and found that for N < 4, the signal linearity was within 3−4% for the 285-μm-thick sensor.

Timing Resolution
For three different sensors (133, 211, and 285 μm thick) and three ranges of signal (3 < S 1 and S 2 < 8 MIPs; 8 < S 1 and S 2 < 20 MIPs; and S 1 > 20 and S 2 > 20 MIPs), Figure 7 depicts distributions of time differences between the first (S 1 ) and the second (S 2 ) sensors. The timing resolutions are determined from the standard deviations resulting from the Gaussian fits to these distributions. This difference is divided by √ 2 because the two measurements are assumed to be completely independent. For large signals (S 1 > 20 and S 2 > 20 MIPs), the timing resolution is better than 20 ps for all sensors. In the intermediate range (8 < S 1 and S 2 < 20 MIPs), the timing resolution varies from 30 to 60 ps, and when we require only a few MIPs (3 < S 1 and S 2 < 8 MIPs), the performance degrades significantly from 70 to 150 ps.
We evaluated the timing resolution performance of silicon sensors in three different 6L P Figure 6. The linearity of response to multiple charged tracks as a function of track multiplicity is within 3 to 4 % in this narrow range. The vertical axis is the ratio of MPVs from the experimental data and simulations for the 285-μm thick sensor. The error bars are largely statistical because we measure a differential non-linearity with respect to one MIP where most of the systematic uncertainties cancel.
combinations. The first measurement (I) was carried out using a pair of same-thickness silicon sensors as described above. For the second measurement (II), one silicon sensor was used in conjunction with an MCP. In the third measurement (III), we used the average of signals from two same-thickness silicon sensors and the signal from the same MCP as in the previous case. The results from each measurement are summarized in Table 1. Measurement I: Figure 8 presents the timing resolution as a function of the effective signal strength in units of MIPs and the effective signal-to-noise ratio. We defined the effective signal strength as S eff = S 1 S 2 / S 2 1 + S 2 2 . It can be seen that the timing performance improves with increasing signal strength (Figure 8-left), but that for equal S eff /N the timing performance of the three sensor types is similar (Figure 8-right). The solid lines in Figure 8 represent the fits to a form to quantify the timing resolution of the two-sensor system where A represents the 'noise' and C represents the 'constant' terms. The two terms on the right side of Eq.1 are summed in quadrature as symbolized by ⊕, and the √ 2 factor accounts for the two independent sensors. When the signal strength is large, S eff ≥ 80 MIPs, the constant term dominates, and the timing resolution is about 10 ps. The toy simulation results are also plotted in Figure 8 as dotted lines. This simulation was performed by using the average pulse shapes for each sensor and adding a Gaussian noise corresponding to the measured noise level. No noise correlation was introduced among the samples. The overall 'noise' terms are well reproduced in this way whereas the 'constant' term is underestimated, mainly because only 5 ps timing uncertainty contribution from the V1742 digitizer is accounted for in this simulation. In Measurement III, the average of the timing information from the two indicated silicon sensors is treated as the effective first detector, and the MCP as the second. The mean time is defined as t mean = 1 2 (t S1 + t S2 ). The error on A and C are statistical and derived from fits. MCP, σ(t 1 −t MCP ), the constant term varied from 18 to 24 ps reflecting the limiting performance of the MCP at large signals as shown in Figure 9.
Measurement III: We also studied the average signal from two same-thickness silicon sensors versus the signal from the MCP, σ(t mean −t MCP ). In this case (Figure 10), the timing resolution of the system was dominated by that of the MCP as in measurement II. However, the comparison of the noise terms reveals the potential power and the higher level of performance of the independent timing measurements from multiple silicon sensors. The noise term is a factor of √ 2 better in Measurement I compared to Measurement III for this reason.

Conclusions
In this study, we have shown that it is possible to perform precise timing measurements (O(20) ps) using silicon sensors for large pulse heights, S/N 20. We have also shown that it is possible  Figure 9. The timing resolution between the first silicon sensor and the MCP as a function of the signal (left) and as a function of the signal-to-noise ratio (right). All three different thickness sensors are compared. The constant term, C, is dominated by the MCP resolution, estimated to be 21 ps. to further improve the timing measurement when information from several sensors are combined. For example, the possibility of measuring with high precision the shower time evolution offers novel opportunities, in particular it could allow the separation of nearby showers beyond what is achievable from the spatial segmentation and precise time information associated with each reconstructed shower in calorimetry. These pieces of information have the potential to improve the calorimeter performance in very dense environments, such as the forward region of CMS during HL-LHC operation. In the wake of these measurements, similar timing studies exposing silicon sensors to multiple MIPs have recently also been performed at Fermilab [14].