Beam test results of 25 and 35 µ m thick FBK ultra-fast silicon detectors

This paper presents the measurements on ﬁrst very thin Ultra-Fast Silicon Detectors (UFSDs) produced by Fondazione Bruno Kessler; the data have been collected in a beam test setup at the CERN PS, using beam with a momentum of 12 GeV/c. UFSDs with a nominal thickness of 25 and 35 μ m and an area of 1 × 1 mm 2 have been considered, together with an additional HPK 50- μ m thick sensor, taken as reference. Their timing performances have been studied as a function of the applied voltage and gain. A time resolution of about 25 ps and of 22 ps at a voltage of 120 and 240 V has been obtained for the 25 and 35 μ m thick UFSDs, respectively


Introduction
The Ultra-Fast Silicon Detectors (UFSDs) [1] is a silicon detector developed to detect charged particles, based on Low Gain Avalanche Diode (LGAD) technology [2] and improved to achieve excellent time resolution. The core of these detectors is a controlled gain layer in addition to a standard n-on-p silicon detector, right below the n-p junction. Thanks to the moderate internal gain (between 10 and 70), the Signal-to-Noise ratio (S/N) is improved: for a 45-μm thick UFSD pixel and a gain of 20-30 a time resolution of ∼30 ps [3] in a beam test setup has been achieved.
Thanks to the excellent time resolution, this technology is already envisioned for the detector upgrades at the HL-LHC (both in ATLAS [4] and CMS [5]) for 2026. However, new generation of compact experiments will require an even better time resolution on a single layer, thus asking for improvements of the timing capabilities of such detectors. A thinner UFSD design may match the requirements [1]. In this paper, UFSDs with a nominal thickness of 25 and 35 μm have been considered; their time resolutions have been studied in a beam test setup at PS, CERN. Furthermore, a 50 μm thick detector, whose time resolution is known from the literature, has been tested as well as a reference.
The paper is organized as follows: after a description of the detectors, the test beam setup and electronics in Sect. 2, in Sect. 3 the data analysis and the main results will be described.

Detectors
The tested UFSD came from two manufactures, Hamamatsu Photonics K.K. (HPK, Japan) and Fondazione Bruno Kessler (FBK, Italy). The one from HPK, hereinafter denoted HPK50, is a matrix of 4 pads (see Fig. 1b), with a thickness of 50 μm; only one pad has been tested at the beam line. This device has been used as a comparison with previous measurements to validate the analysis and results. Two UFSDs were instead manufactured from FBK, hereinafter denoted FBK25 and FBK35, with a nominal thickness of 25 and 35 μm, respectively; they represent the first thin wafers produced in 2020 by FBK. 1 In Fig. 1a, a picture of FBK25 is shown (similar for FBK35).
All the detectors tested have been previously completely characterized at the INFN Bologna laboratories. The main characteristics of the sensors are reported in Table 1. The breakdown voltage (V bd ) has been extracted from I-V measurements using the methods of LD and ILD (Logarithmic Derivative and Inverse LD, [7]). The internal gain has been extracted considering the charge released from a MIP on the Detector Under Test (DUT) at a certain voltage and comparing it with the charge released in an equivalent detector but without any internal gain.
The actual thickness of the DUTs has been evaluated by performing a Capacitance-Voltage measurement. 2 In Fig. 2 the extracted active thicknesses are reported. As can be noticed, while the HPK50 and FBK35 are independent from the voltage in that range, LGADs tested. The distributions have been fit with a gaussian, see the text for details the FBK25 is instead still depleting and it reaches a plateau of 21 μm only at around 100 V. Notice that the final active thickness is slightly lower than what expected. The different outcome of the FBK25 is due to the low resistivity of this sensor, connected to the very high doping of the bulk, resulting also in a non-uniform electric field of the drift region.

Beam test setup and electronics
The time resolution of the UFSDs has been studied at the T10 beamline at PS-CERN in November 2021. The beam was mainly composed of protons and pions with a momentum of +12 GeV/c. For each data acquisition up to 4 carrier boards were aligned to the beam in a telescope frame and the whole setup was enclosed in a dark environment box at room temperature.
The UFSDs have been mounted on different front-end boards. The board used for the HPK50 was followed by a C2 broadband (2 GHz) and low-noise current amplifier 3 with a gain of 190. For both the FBK sensors instead the board used, V1.4-SCIPP-08/18, contained a wide bandwidth (2 GHz) and low noise inverting amplifier with a measured amplification of factor 6. The board was followed by a second amplification stage, with a gain factor of around 13 and 14, respectively, for the FBK25 and FBK35. 4 Up to 4 amplified signals were sent to a 4 GHz LeCroy WaveRunner 9404M-MS oscilloscope, 5 with 20Gs/s sampling rate, 4 GHz of analog bandwidth and 8-bit vertical resolution. The contribution of the oscilloscope time resolution to the measured one was negligible.
The trigger for the data acquisition was given by the coincidence of the self-trigger from the UFSDs. In particular a threshold has been set for each channel and the coincidence of the 4 has been used.
To evaluate the noise of each DUT, its RMS has been evaluated; in particular for the analysis offline a time window before the signals has been considered in order to have a direct measurement of the noise in the beam test setup. In Fig. 3 the RMS spectra are reported. As can be seen, the FBK35 has a lower noise with respect to the FBK25. For the FBK25 and FBK35 and all the voltages reported, the distributions have a Gaussian shape, with only a moderate non-gaussian right tail that instead is much more pronounced for the HPK50. The distribution mean of the three DUTs is quite stable throughout all the data taking, ranging between 1 mV and 4 mV.

Results
The data analysis was performed following similar procedures to those reported in [8]. In particular, thanks to the oscilloscope readout, the completed signal waveforms were recorded and analyzed. It was then possible to use the constant fraction discriminator (CFD) method to extract the DUTs time resolutions. Moreover, to filter-out the high-frequency noise, a smoothing of the LGAD signal was applied with four-point moving average.
To extract the time resolution of a single UFSD, a system with three sensors and three differences between the arrival time of each pair of detectors has been considered. In Fig. 4 an example of the time difference between FBK35 and FBK25 is reported. The distribution has been fitted with an asymmetric q-Gaussian function to take into account that the arrival time distribution for a single sensor has a Gaussian shape with a small tail towards late times. The sigma extracted from the fit has then been used to obtain the final time resolution of the three UFSDs at a given voltage and CFD.  In Fig. 5 the measured charge distributions are shown. The ratio between the width of the distributions and the Most Probable Values(MPVs) decreases as a function of the thickness. As expected, the amplitude increases both as a function of the thickness and voltage; moreover, the fluctuations in the number of electrons-holes created in the silicon detector decrease with larger thickness, in accordance with [9] and [10]. Figure 6 reports the measured time resolutions for each sensor as a function of the CFD threshold for all the applied voltages. For the HPK50 the trend and values are totally in agreement with the ones reported in [3,8] for a 50 μm thick UFSD. As expected, the time resolution improves with higher voltages, and the trend as a function of the CFD reflects the higher jitter contribution for very low CFD (smaller slew rates) [1]. At higher CFD instead the time resolution is dominated by the Landau term, which is due to the non-uniform creation of electron-hole pairs along the particle path and which is expected to be smaller for thinner detectors. The trend of the measured values vs CFD flattens for values larger than around 30% and 20%, respectively, for the FBK25 and the FBK35 sensors. To understand the trends reported, different contributions have to be taken into account. In particular the two main ones: the jitter and Landau terms. At low CFD values, the jitter contribution is dominant while for higher CFD values the landau terms start to be the dominant one. In turn they depend on the thickness, S/N and slew rate; these contributions are affected both by electronics and detector, their coupling and their shielding against outer noise [1]. The S/N ratios have then been evaluated for the DUTs; values between 6-24 and 16-63 (depending on the different applied voltage) for the FBK25 and FBK35 sensors have been found, respectively. The jitter has been evaluated for each DUT and the intrinsic time resolution has been extracted: σ 2 intrinsic σ 2 measured − σ 2 jitter .  Fig. 7 the measured time resolutions for a fixed CFD (the one that minimizes the time resolution) are reported as a function of (a) charge and (b) drift electric field 6 for the three DUTs. The time resolution improves with larger charge (as expected due to larger gain) and drift electric field (as expected due to both larger gain and higher velocity of carriers in the drift region).
In Fig. 8 the measured and intrinsic time resolutions for a fixed CFD are reported as a function of gain (a) and voltage (b). In the figure, the three sensors with different investigated thicknesses are compared. As expected, the time resolution improves for higher gain (voltages) for all the detectors.   A time resolution of ∼34 ps has been measured for the HPK50, which confirms previous results [3,8]. As expected, a better time resolution has been reached with the two thinner UFSDs due to a smaller Landau term. However, the measurements of the two samples FBK25 and FBK35, although compatible within the uncertainties, have a trend towards better results for FBK35 w.r.t. FBK25. The behaviour of the FBK25 can be due to several reasons, including a worse S/N ratio (due also to the higher noise RMS, see Fig. 3) and a bulk doping not optimized for timing measurements. Future production of thin sensors with almost intrinsic doping of the substrate are foreseen. On the other side, the time resolution for the FBK35 showed results in agreement with the expectation; the measured time resolution can be compared with the one obtained in [12] of 25.6 ps for the same thickness.
A summary plot of time resolution as a function of both gain and drift electric field is reported in Fig. 9 for the UFSDs tested. As expected [13], it indicates that to obtain a good time resolution a combination of both gain and drift electric field is necessary.
In Table 2 the best time resolutions reached for the three detectors tested are summarized. Finally the results have been also compared with simulation. In Fig. 10 the measured time resolution obtained for all the LGADs is reported as a function of (a) gain and (b) applied voltage and compared with the one obtained from simulation, using WeightField2. The timing capabilities were evaluated applying the CFD method, using the same threshold adopted for the measured data. The time resolution of the different LGAD has been calculated by choosing the parameters of the simulation in order to reproduce the signal

Conclusions
In this paper, several measurements of time resolution for a new generation of UFSDs are reported. The results have been obtained using a 12 GeV/c beam at CERN PS. An HPK UFSD of a standard thickness of 50 μm has been tested and used as reference; it reaches a time resolution of ∼34 ps at a voltage of 245 V, in agreement with previous measurements. For the first time in a beam test, 25 μm (FBK25) and 35 μm (FBK35) thick FBK UFSDs sensors have been tested. The FBK35 sensor reaches a time resolution of 22 ps at a bias voltage of 240 V. FBK25 reaches a time resolution of 25 ps at a bias voltage of 120 V. This result does not show an improvement with respect to FBK35, as the FBK25 sensors have been produced on a highly doped substrate (p-concentration ∼ 10 14 atoms/cm 3 ), not optimized for timing measurements; the low resistivity bulk increases the noise from the sensor and worsen the time resolution. For all sensors, a good agreement between data and simulation has been obtained. The results demonstrate the expectations of improved time resolution with thinner UFSD detectors, going from the standard 50 μm to a thinner design.

Data Availability Statement
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request. This manuscript has associated data in a data repository. [Authors' comment: The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.] Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.